COINCIDENT DROP SELECTION, DROP SEPARATION PRINTING METHOD AND SYSTEM

Abstract: Ink is contained under pressure in an ink reservoir. The ink travels to a nozzle, where it is retained in the nozzle by the ink surface tension. An equilibrium is created whereby no ink escapes the nozzle by ensuring that the ink pressure, plus a predetermined external electrostatic or magnetic field, is insufficient to expel the ink from the nozzle. The system can include a heater which is incorporated at the tip of the nozzle. When this heater is energized by a heater control circuit, the ink in contact with the nozzle tip is heated. Convection rapidly transports the heat over the ink meniscus. The ink is formulated so that surface tension reduces with increasing temperature. At an elevated temperature, the surface tension of the ink is reduced sufficiently that the equilibrium is broken, and ink moves out of the nozzle. At a predetermined time, the heater is turned off by the heater control circuit and the falling temperature causes the surface tension to increase. Ink continues to move out of the nozzle by its own momentum. Surface tension and the viscous flow limitation of the nozzle causes the ink drop to "neck" and separate from the body of ink. The ink drop then travels to the recording medium. The thermal drop on demand mechanism operates at low power, making construction of monolithic multiple nozzle print heads using a modified CMOS process practical. The print heads can include extensive fault tolerance to improve yield, device life, and reliability.

Description: COINCroENT DROP SELECTION, DROP SEPARATION PRINTING METHOD AND SYSTEM Field of the Invention The present invention is in the field of computer controlled printing devices. In particular, the field is liquid ink drop on demand (DOD) printing systems. Background of thg Inyentipn Many different types of digitally controlled printing systems have been invented, and many types are currently in production. These printing systems use a variety of actuation mechanisms, a variety of marking materials, and a variety of recording media. Examples of digital printing systems in current use include: laser electrophotographic printers; LED electrophotographic printers; dot matrix impact printers; thermal paper printers; film recorders; thermal wax printers; dye diffusion thermal transfer printers; and inkjet printers. However, at present, such electronic printing systems have not significantly replaced mechanical printing presses, even though this conventional method requires very expensive setup and is seldom commercially viable unless a few thousand copies of a particular page are to be printed. Thus, there is a need for improved digitally controlled printing systems, for example, being able to produce high quality color images at a high-speed and low cost, using standard paper. Inkjet printing has become recognized as a prominent contender in the digitally controlled, electronic printing arena because, e.g., of its non-impact, low-noise characteristics, its use of plain paper and its avoidance of toner transfers and fixing. Many types of ink jet printing mechanisms have been invented. These can be categorized as either continuous ink jet (CIJ) or drop on demand (DOD) inkjet. Continuous inkjet printing dates back to at least 1929: Hansell, US Pat. No. 1,941,001. Sweet et al US Pat. No. 3,373,437, 1967, discloses an array of continuous ink jet nozzles where ink drops to be printed are selectively charged and deflected towards the recording medium. This technique is known as binary deflection CIJ, and is used by several manufacturers, including Elmjet and Scitex. Hertz et al US Pat. No. 3,416,153, 1966, discloses a method of achieving variable optical density of printed spots in CIJ printing using the electrostatic dispersion of a charged drop stream to modulate the number of droplets which pass through a small aperture. This technique is used in inkjet printers manufactured by Iris Graphics. Kyser et al US Pat. No. 3,946,398, 1970, discloses a DOD ink jet printer which applies a high voltage to a piezoelectric crystal, causing the crystal to bend, applying pressure on an ink reservoir and jetting drops on demand. Many types of piezoelectric drop on demand printers have subsequently been invented, which utilize piezoelectric crystals in bend mode, push mode, shear mode, and squeeze mode. Piezoelectric DOD printers have achieved commercial success using hot melt inks (for example, Tektronix and Dataproducts printers), and at image resolutions up to 720 dpi for home and office printers (Seiko Epson). Piezoelectric DOD printers have an advantage in being able to use a wide range of inks. However, piezoelectric printing mechanisms usually require complex high voltage drive circuitry and bulky piezoelectric crystal arrays, which are disadvantageous in regard to manufacturability and performance. Endo et al GB Pat. No. 2,007,162, 1979, discloses an electrothermal DOD ink jet printer which applies a power pulse to an electrothermal transducer (heater) which is in thermal contact with ink in a nozzle. The heater rapidly heats water based ink to a high temperature, whereupon a small quantity of ink rapidly evaporates, forming a bubble. The formation of these bubbles results in a pressure wave which cause drops of ink to be ejected from small apertures along the edge of the heater substrate. This technology is known as Bubblejet™ (trademark of Canon K.K. of Japan), and is used in a wide range of printing systems from Canon, Xerox, and other manufacturers. Vaught et al US Pat. No. 4,490,728, 1982, discloses an electrothermal drop ejection system which also operates by bubble formation. In this system, drops are ejected in a direction normal to the plane of the heater substrate, through nozzles formed in an aperture plate positioned above the heater. This system is known as Thermal Ink Jet, and is manufactured by Hewlett-Packard. In this document, the term Thermal Ink Jet is used to refer to both the Hewlett- Packard system and systems commonly known as Bubblejet™. Thermal Ink Jet printing typically requires approximately 20 μJ over a period of approximately 2 μs to eject each drop. The 10 Watt active power consumption of each heater is disadvantageous in itself and also necessitates special inks, complicates the driver electronics and precipitates deterioration of heater elements. Other ink jet printing systems have also been described in technical literature, but are not currently used on a commercial basis. For example, U.S. Patent No. 4,275,290 discloses a system wherein the coincident address of predetermined print head nozzles with heat pulses and hydrostatic pressure, allows ink to flow freely to spacer-separated paper, passing beneath the print head. U.S. Patent Nos. 4,737,803; 4,737,803 and 4,748,458 disclose ink jet recording systems wherein the coincident address of ink in print head nozzles with heat pulses and an electrostatically attractive field cause ejection of ink drops to a print sheet. Each of the above-described inkjet printing systems has advantages and disadvantages. However, there remains a widely recognized need for an improved inkjet printing approach, providing advantages for example, as to cost, speed, quality, reliability, power usage, simplicity of construction and operation, durability and consumables. Summary of the invention My concurrently filed applications, entitled "Liquid Ink Printing Apparatus and System" and "Coincident Drop-Selection, Drop-Separation Printing Method and System" describe new methods and apparatus that afford significant improvements toward overcoming the prior art problems discussed above. Those inventions offer important advantages, e.g., in regard to drop size and placement accuracy, as to printing speeds attainable, as to power usage, as to durability and operative thermal stresses encountered and as to other printer performance characteristics, as well as in regard to manufacturability and the characteristics of useful inks. One important purpose of the present invention is to further enhance the structures and methods described in those applications and thereby contribute to the advancement of printing technology. Thus, one significant object of the present invention is to provide new methods of drop on demand ink printing that are improved in regard to prior approaches. In important aspects, the methods of this invention offer advantages as to drop size and placement accuracy, as to printing speed, as to power usage, as to durability and operative thermal stresses and to various other printing performance characteristics noted in more detail hereinafter. In other important aspects, the present invention offers significant advantages as to manufacture and as to the nature of its useful inks. In one constitution, the present invention comprises a method of drop on demand printing including the steps of (1) addressing the ink in selected nozzles of a print head with the coincident forces of (a) above ambient manifold pressure and 0b) a selection energy pulse that, in combined effects, are sufficient to cause addressed ink portions to move out of their related nozzle to a predetermined region, beyond the ink in non-selected nozzles, but not so far as to separate from their contiguous ink mass; and (2) during such addressing step, attracting ink from the print head toward a print zone with forces of magnitude and proximity that (a) cause the selected ink moved into said region to separate from its contiguous ink mass and φ) do not cause non-addressed ink to so separate. In certain preferred embodiments, the drop selecting means comprises heating ink to reduce surface tension in coincidence with above ambient air pressure application to the ink. In further preferred embodiments, drop separation means include predetermined ink conductivity characteristics in combination with predetermined uniform electric fields. In another preferred aspect, the present invention comprises a thermally activated liquid ink printing head being characterized by the energy required to eject a drop of ink being less than the energy required to raise the temperature of the bulk ink of a volume equal to the volume of said ink drop above the ambient ink temperature to a temperature which is below the drop ejection temperature. In another preferred aspect, the present invention comprises a thermally activated drop on demand printer wherein ink utilized is solid at room temperature, but liquid at operating temperature and selection means comprise coincidence of varying pressure pulses and selected heating to reduce the viscosity of ink in the vicinity of drops to be selected. In yet another aspect, the invention provides a thermally activated liquid ink printing head being characterized by the energy required to eject a drop of ink being less than the energy required to raise the temperature of the bulk ink of a volume equal to the volume of the ink drop above the ambient ink temperature to a temperature which is below the drop ejection temperature. Brief Description of the Drawings Figure 1(a) shows a simplified block schematic diagram of one exemplary printing apparatus according to the present invention. Figure 1 ) shows a cross section of one variety of nozzle tip in accordance with the invention. Figures 2(a) to 2(f) show fluid dynamic simulations of drop selection. Figure 3(a) shows a finite element fluid dynamic simulation of a nozzle in operation according to an embodiment of the invention. Figure 3(b) shows successive meniscus positions during drop selection and separation. Figure 3(c) shows the temperatures at various points during a drop selection cycle. Figure 3(d) shows measured surface tension versus temperature curves for various ink additives. Figure 3(e) shows the power pulses which are applied to the nozzle heater to generate the temperature curves of figure 3(c) Figure 4 shows a block schematic diagram of print head drive circuitry for practice of the invention. Figure 5 shows projected manufacturing yields for an A4 page width color print head embodying features of the invention, with and without fault tolerance. Figure 6 shows a generalized block diagram of a printing system using one embodiment of the present invention. Figure 7 shows a cross section of an example print head nozzle embodiment of the invention used for computer simulations shown in Figures 8 to 18. Figure 8(a) shows the power sub-pulses applied to the print head for a single heater energizing pulse. Figure 8(b) shows the temperature at various points in the nozzle during the drop selection process. Figure 9 is a graph of meniscus position versus time for the drop selection process. Figure 10 is a plot of meniscus position and shape at 5 μs intervals during the drop selection process. Figure 11 shows the quiescent position of the ink meniscus before the drop selection process. Figures 12 to 17 show the meniscus position and thermal contours at various stages during the drop selection process. Figure 18 shows fluid streamlines 50 μs after the beginning of the drop selection heater pulse. Figure 19 is a graph of the maximum drop energy allowable to maintain self-cooling. Figure 20 shows three cycles of pressure oscillation as a function of time. Figure 21 shows the temperature at various points in the nozzle as a function of time, with an electrothermal pulse applied during the third cycle of Figure 8. Figure 22 shows the position of the meniscus extremum as a function of time during the period of Figure 7. Figure 23(a), 23(c), 23(e), 23(g) and 23(i) show thermal contours and drop evolution at various times during a drop ejection cycle. Figure 23(b), 23(d), 23(f), 23(h) and 23(j) show viscosity contours and drop evolution at various times during a drop ejection cycle. Figure 24 shows the movement of meniscus position during a cycle when the ink drop is not selected. Figure 25 shows the movement of meniscus position during a drop selection cycle. Drop separation is not shown. Figure 26 shows the position of the meniscus extremum as a function of time for a print head operating at half the frequency of the print head in Figures 20 to 25. Figure 27 shows the movement of meniscus position during a cycle when the ink drop is not selected in a print head operating at half the frequency of the print head in Figures 20 to 25. Figure 28 shows the movement of meniscus position during a drop selection cycle in a print head operating at half the frequency of the print head in Figures 20 to 25. Drop separation is not shown. Detailed Description of Preferred Embodiments In one general aspect, the invention constitutes a drop-on-demand printing mechanism wherein the means of selecting drops to be printed produces a difference in position between selected drops and drops which are not selected, but which is insufficient to cause the ink drops to overcome the ink surface tension and separate from the body of ink, and wherein an alternative means is provided to cause separation of the selected drops from the body of ink. The separation of drop selection means from drop separation means significantly reduces the energy required to select which ink drops are to be printed. Only the drop selection means must be driven by individual signals to each nozzle. The drop separation means can be a field or condition applied simultaneously to all nozzles. The drop selection means may be chosen from, but is not limited to, the following list: 1) Electrothermal reduction of surface tension of pressurized ink 2) Electrothermal bubble generation, with insufficient bubble volume to cause drop ejection 3) Piezoelectric, with insufficient volume change to cause drop ejection 4) Electrostatic attraction with one electrode per nozzle The drop separation means may be chosen from, but is not limited to, the following list: 1 ) Proximity (recording medium in close proximity to print head) 2) Proximity with oscillating ink pressure 3) Electrostatic attraction 4) Magnetic attraction The table "DOD printing technology targets" shows some desirable characteristics of drop on demand printing technology. The table also lists some methods by which some embodiments described herein, or in other of my related applications, provide improvements over the prior art. DOD printing technology targets In thermal ink jet (TIJ) and piezoelectric ink jet systems, a drop velocity of approximately 10 meters per second is prefeπed to ensure that the selected ink drops overcome ink surface tension, separate from the body of the ink, and strike the recording medium. These systems have a very low efficiency of conversion of electrical energy into drop kinetic energy. The efficiency of ΗJ systems is approximately O.O2%). This means that the drive circuits for TJJ print heads must switch high currents. The drive circuits for piezoelectric ink jet heads must either switch high voltages, or drive highly capacitive loads. The total power consumption of pagewidth TIJ printheads is also very high. An 800 dpi A4 full color pagewidth ΗJ print head printing a four color black image in one second would consume approximately 6 kW of electrical power, most of which is converted to waste heat. The difficulties of removal of this amount of heat precludes the production of low cost, high speed, high resolution compact pagewidth TIJ systems. One important feature of embodiments of the invention is a means of significantly reducing the energy required to select which ink drops are to be printed. This is achieved by separating the means for selecting ink drops from the means for ensuring that selected drops separate from the body of ink and form dots on the recording medium. Only the drop selection means must be driven by individual signals to each nozzle. The drop separation means can be a field or condition applied simultaneously to all nozzles. The table "Drop selection means" shows some of the possible means for selecting drops in accordance with the invention. The drop selection means is only required to create sufficient change in the position of selected drops that the drop separation means can discriminate between selected and unselected drops. Drop selection means Other drop selection means may also be used. The preferred drop selection means for water based inks is method 1: "Electrothermal reduction of surface tension of pressurized ink". This drop selection means provides many advantages over other systems, including; low power operation (approximately 1% of TU), compatibility with CMOS VLSI chip fabrication, low voltage operation (approx. 10 V), high nozzle density, low temperature operation, and wide range of suitable ink formulations. The ink must exhibit a reduction in surface tension with increasing temperature. The preferred drop selection means for hot melt or oil based inks is method 2: 'Εlectrothermal reduction of ink viscosity, combined with oscillating ink pressure". This drop selection means is particularly suited for use with inks which exhibit a large reduction of viscosity with increasing temperature, but only a small reduction in surface tension. This occurs particularly with non-polar ink carriers with relatively high molecular weight. This is especially applicable to hot melt and oil based inks. The table "Drop separation means" shows some of the possible methods for separating selected drops from the body of ink, and ensuring that the selected drops form dots on the printing medium. The drop separation means discriminates between selected drops and unselected drops to ensure that unselected drops do not form dots on the printing medium. Drop separation means ■ 13- Other drop separation means may also be used. The preferred drop separation means depends upon the intended use. For most applications, method 1: "Electrostatic attraction", or method 2: "AC electric field" are most appropriate. For applications where smooth coated paper or film is used, and very high speed is not essential, method 3: "Proximity" may be appropriate. For high speed, high quality systems, method 4: 'Transfer proximity" can be used. Method 6: "Magnetic attraction" is appropriate for portable printing systems where the print medium is too rough for proximity printing, and the high voltages required for electrostatic drop separation are undesirable. There is no clear 'best' drop separation means which is applicable to all circumstances. Further details of various types of printing systems according to the present invention are described in the foUowing Australian patent specifications filed on 12 April 1995, the disclosure of which are hereby incoφorated by reference: 'A Liquid ink Fault Tolerant (LIFT) printing mechanism' (Filing no. : PN2308); Εlectrothermal drop selection in LIFT printing' (Filing no.: PN2309); 'Drop separation in LIFT printing by print media proximity' (Filing no.: PN2310); 'Drop size adjustment in Proximity LIFT printing by varying head to media distance' (Filing no.: PN2311); 'Augmenting Proximity LIFT printing with acoustic ink waves' (Filing no.: PN2312); 'Electrostatic drop separation in LIFT printing' (Filing no.: PN2313); 'Multiple simultaneous drop sizes in Proximity LIFT printing' (Filing no.: PN2321); 'Self cooling operation in thermally activated print heads' (Filing no.: PN2322); and 'Thermal Viscosity Reduction LIFT printing' (Filing no.: PN2323). A simplified schematic diagram of one prefeπed printing system according to the invention appears in Figure 1(a). An image source 52 may be raster image data from a scanner or computer, or outline image data in the form of a page description language (PDL), or other forms of digital image representation. This image data is converted to a pixel-mapped page image by the image processing system 53. This may be a raster image processor (RIP) in the case of PDL image data, or may be pixel image manipulation in the case of raster image data. Continuous tone data produced by the image processing unit 53 is halftoned. Halftoning is performed by the Digital Halftoning unit 54. Halftoned bitmap image data is stored in the image memory 72. Depending upon the printer and system configuration, the image memory 72 may be a full page memory, or a band memory. Heater control circuits 71 read data from the image memory 72 and apply time-varying electrical pulses to the nozzle heaters (103 in figure 1 (b)) that are part of the print head 50. These pulses are applied at an appropriate time, and to the appropriate nozzle, so that selected drops will form spots on the recording medium 51 in the appropriate position designated by the data in the image memory 72. The recording medium 51 is moved relative to the head 50 by a paper transport system 65, which is electronically controlled by a paper transport control system 66, which in turn is controlled by a microcontroller 315. The paper transport system shown in figure 1(a) is schematic only, and many different mechanical configurations are possible. In the case of pagewidth print heads, it is most convenient to move the recording medium 51 past a stationary head 50. However, in the case of scanning print systems, it is usually most convenient to move the head 50 along one axis (the sub-scanning direction) and the recording medium 51 along the orthogonal axis (the main scanning direction), in a relative raster motion. The microcontroller 315 may also control the ink pressure regulator 63 and the heater control circuits 71. For printing using surface tension reduction, ink is contained in an ink reservoir 64 under pressure. In the quiescent state (with no ink drop ejected), the ink pressure is insufficient to overcome the ink surface tension and ejeci a drop. A constant ink pressure can be achieved by applying pressure to the ink reservoir 64 under the control of an ink pressure regulator 63. Alternatively, for larger printing systems, the ink pressure can be very accurately generated and controlled by situating the top surface of the ink in the reservoir 64 an appropriate distance above the head 50. This ink level can be regulated by a simple float valve (not shown). For printing using viscosity reduction, ink is contained in an ink reservoir 64 under pressure, and the ink pressure is caused to oscillate. The means of producing this oscillation may be a piezoelectric actuator mounted in the ink channels (not shown). When properly arranged with the drop separation means, selected drops proceed to form spots on the recording medium 51, while unselected drops remain part of the body of ink. The ink is distributed to the back surface of the head 50 by an ink channel device 75. The ink preferably flows through slots and/or holes etched through the silicon substrate of the head 50 to the front surface, where the nozzles and actuators are situated. In the case of thermal selection, the nozzle actuators are electrothermal heaters. In some types of printers according to the invention, an external field 74 is required to ensure that the selected drop separates from the body of the ink and moves towards the recording medium 51. A convenient external field 74 is a constant electric field, as the ink is easily made to be electrically conductive. In this case, the paper guide or platen 67 can be made of electrically conductive material and used as one electrode generating the electric field. The other electrode can be the head 50 itself. Another embodiment uses proximity of the print medium as a means of discriminating between selected drops and unselected drops. For small drop sizes gravitational force on the ink drop is very small; approximately 10 " * of the surface tension forces, so gravity can be ignored in most cases. This allows the print head 50 and recording medium 51 to be oriented in any direction in relation to the local gravitational field. This is an important requirement for portable printers. Figure lflb) is a detail enlargement of a cross section of a single microscopic nozzle tip embodiment of the invention, fabricated using a modified CMOS process. The nozzle is etched in a substrate 101, which may be silicon, glass, metal, or any other suitable material. If substrates which are not semiconductor materials are used, a semiconducting material (such as amoφhous silicon) may be deposited on the substrate, and integrated drive transistors and data distribution circuitry may be formed in the surface semiconducting layer. Single crystal silicon (SCS) substrates have several advantages, including: 1 ) High performance drive transistors and other circuitry can be fabricated in SCS; 2) Print heads can be fabricated in existing facilities (fabs) using standard VLSI processing equipment; 3) SCS has high mechanical strength and rigidity; and 4) SCS has a high thermal conductivity. In this example, the nozzle is of cylindrical form, with the heater 103 forming an annulus. The nozzle tip 104 is formed from silicon dioxide layers 102 deposited during the fabrication of the CMOS drive circuitry. The nozzle tip is passivated with silicon nitride. The protruding nozzle tip controls the contact point of the pressurized ink 100 on the print head surface. The print head surface is also hydrophobized to prevent accidental spread of ink across the front of the print head. Many other configurations of nozzles are possible, and nozzle embodiments of the invention may vary in shape, dimensions, and materials used. Monolithic nozzles etched from the substrate upon which the heater and drive electronics are formed have the advantage of not requiring an orifice plate. The elimination of the orifice plate has significant cost savings in manufacture and assembly. Recent methods for eliminating orifice plates include the use of 'vortex' actuators such as those described in Domoto et al US Pat. No. 4,580,158, 1986, assigned to Xerox, and Miller et al US Pat. No. 5,371,527, 1994 assigned to Hewlett-Packard. These, however are complex to actuate, and difficult to fabricate. The preferred method for elimination of orifice plates for print heads of the invention is incoφoration of the orifice into the actuator substrate. This type of nozzle may be used for print heads using various techniques for drop separation. Operation with Electrostatic Drop Separation As a first example, operation using thermal reduction of surface tension and electrostatic drop separation is shown in figure 2. Figure 2 shows the results of energy transport and fluid dynamic simulations performed using FTDAP, a commercial fluid dynamic simulation software package available from Fluid Dynamics Inc., of Illinois, USA. This simulation is of a thermal drop selection nozzle embodiment with a diameter of 8 μm, at an ambient temperature of 30°C. The total energy applied to the heater is 276 nJ, applied as 69 pulses of 4 nJ each. The ink pressure is 10 kPa above ambient air pressure, and the ink viscosity at 30°C is 1.84 cPs. The ink is water based, and includes a sol of 0.1% palmitic acid to achieve an enhanced decrease in surface tension with increasing temperature. A cross section of the nozzle tip from the central axis of the nozzle to a radial distance of 40 μm is shown. Heat flow in the various materials of the nozzle, including silicon, silicon nitride, amoφhous silicon dioxide, crystalline silicon dioxide, and water based ink are simulated using the respective densities, heat capacities, and thermal conductivities of the materials. The time step of the simulation is 0.1 μs. Figure 2(a) shows a quiescent state, just before the heater is actuated. An equilibrium is created whereby no ink escapes the nozzle in the quiescent state by ensuring that the ink pressure plus extemal electrostatic field is insufficient to overcome the surface tension of the ink at the ambient temperature. In the quiescent state, the meniscus of the ink does not protrude significantly from the print head surface, so the electrostatic field is not significantly concentrated at the meniscus. Figure 2(b) shows thermal contours at 5°C intervals 5 μs after the start of the heater energizing pulse. When the heater is energized, the ink in contact with the nozzle tip is rapidly heated. The reduction in surface tension causes the heated portion of the meniscus to rapidly expand relative to the cool ink meniscus. This drives a convective flow which rapidly transports this heat over part of the free surface of the ink at the nozzle tip. It is necessary for the heat to be distributed over the ink surface, and not just where the ink is in contact with the heater. This is because viscous drag against the solid heater prevents the ink directly in contact with the heater from moving. Figure 2(c) shows thermal contours at 5°C intervals 10 μs after the start of the heater energizing pulse. The increase in temperature causes a decrease in surface tension, disturbing the equilibrium of forces. As the entire meniscus has been heated, the ink begins to flow. Figure 2(d) shows thermal contours at 5°C intervals 20 μs after the start of the heater energizing pulse. The ink pressure has caused the ink to flow to a new meniscus position, which protrudes from the print head. The electrostatic field becomes concentrated by the protruding conductive ink drop. Figure 2(e) shows thermal contours at 5°C intervals 30 μs after the start of the heater energizing pulse, which is also 6 μs after the end of the heater pulse, as the heater pulse duration is 24 μs. The nozzle tip has rapidly cooled due to conduction through the oxide layers, and conduction into the flowing ink. The nozzle tip is effectively 'water cooled' by the ink. Electrostatic attraction causes the ink drop to begin to accelerate towards the recording medium. Were the heater pulse significantly shorter (less than 16 μs in this case) the ink would not accelerate towards the print medium, but would instead return to the nozzle. Figure 2(f) shows thermal contours at 5°C intervals 26 μs after the end of the heater pulse. The temperature at the nozzle tip is now less than 5°C above ambient temperature. This causes an increase in surface tension around the nozzle tip. When the rate at which the ink is drawn from the nozzle exceeds the viscously limited rate of ink flow through the nozzle, the ink in the region of the nozzle tip 'necks', and the selected drop separates from the body of ink. The selected drop then travels to the recording medium under the influence of the external electrostatic field. The meniscus of the ink at the nozzle tip then returns to its quiescent position, ready for the next heat pulse to select the next ink drop. One ink drop is selected, separated and forms a spot on the recording medium for each heat pulse. As the heat pulses are electrically controlled, drop on demand inkjet operation can be achieved. Figure 3(a) shows successive meniscus positions during the drop selection cycle at 5 μs intervals, starting at the beginning of the heater energizing pulse. Figure 3(b) is a graph of meniscus position versus time, showing the movement of the point at the centre of the meniscus. The heater pulse starts 10 μs into the simulation. Figure 3(c) shows the resultant curve of temperature with respect to time at various points in the nozzle. The vertical axis of the graph is temperature, in units of 100°C. The horizontal axis of the graph is time, in units of 10 μs. The temperature curve shown in figure 3(b) was calculated by FIDAP, using 0.1 μs time steps. The local ambient temperature is 30 degrees C. Temperature histories at three points are shown: A - Nozzle tip: This shows the temperature history at the circle of contact between the passivation layer, the ink, and air. B - Meniscus midpoint: This is at a circle on the ink meniscus midway between the nozzle tip and the centre of the meniscus. C - Chip surface: This is at a point on the print head surface 20 μm from the centre of the nozzle. The temperature only rises a few degrees. This indicates that active circuitry can be located very close to the nozzles without experiencing performance or lifetime degradation due to elevated temperatures. Figure 3(e) shows the power applied to the heater. Optimum operation requires a shaφ rise in temperature at the start of the heater pulse, a maintenance of the temperature a little below the boiling point of the ink for the duration of the pulse, and a rapid fall in temperature at the end of the pulse. To achieve this, the average energy applied to the heater is varied over the duration of the pulse. In this case, the variation is achieved by pulse frequency modulation of 0.1 μs sub-pulses, each with an energy of 4 nJ. The peak power applied to the heater is 40 mW, and the average power over the duration of the heater pulse is 11.5 mW. The sub-pulse frequency in this case is 5 Mhz. This can readily be varied without significantly affecting the operation of the print head. A higher sub-pulse frequency allows finer control over the power applied to the heater. A sub-pulse frequency of 13.5 Mhz is suitable, as this frequency is also suitable for minimizing the effect of radio frequency interference (RFI). Inks with a negative temperature coefficient of surface tension The requirement for the surface tension of the ink to decrease with increasing temperature is not a major restriction, as most pure liquids and many mixtures have this property. Exact equations relating surface tension to temperature for arbitrary liquids are not available. However, the following empirical equation derived by Ramsay and Shields is satisfactory for many liquids: Where γris the surface tension at temperature T, k is a constant, 7 is the critical temperature of the liquid, M is the molar mass of the liquid, x is the degree of association of the liquid, and p is the density of the hquid. This equation indicates that the surface tension of most liquids falls to zero as the temperature reaches the critical temperature of the liquid. For most liquids, the critical temperature is substantially above the boiling point at atmospheric pressure, so to achieve an ink with a large change in surface tension with a small change in temperature around a practical ejection temperature, the admixture of surfactants is recommended. The choice of surfactant is important. For example, water based ink for thermal ink jet printers often contains isopropyl alcohol (2-propanol) to reduce the surface tension and promote rapid drying. Isopropyl alcohol has a boiling point of 82.4°C, lower than that of water. As the temperature rises, the alcohol evaporates faster than the water, decreasing the alcohol concentration and causing an increase in surface tension. A surfactant such as 1-Hexanol (b.p. 158°C) can be used to reverse this effect, and achieve a surface tension which decreases slightly with temperature. However, a relatively large decrease in surface tension with temperature is desirable to maximize operating latitude. A surface tension decrease of 20 mN/m over a 30°C temperature range is preferred to achieve large operating margins, while as little as lOmN/m can be used to achieve operation of the print head according to the present invention. Inks With Large -Δγ.. Several methods may be used to achieve a large negative change in surface tension with increasing temperature. Two such methods are: 1) The ink may contain a low concentration sol of a surfactant which is solid at ambient temperatures, but melts at a threshold temperature. Particle sizes less than 1,000 A are desirable. Suitable surfactant melting points for a water based ink are between 50°C and 90°C, and preferably between 60°C and 80°C. 2) The ink may contain an oil/water microemulsion with a phase inversion temperature (PIT) which is above the maximum ambient temperature, but below the boiling point of the ink. For stability, the PIT of the microemulsion is preferably 20°C or more above the maximum non- operating temperature encountered by the ink. A PIT of approximately 80°C is suitable. Inks with Surfactant Sols Inks can be prepared as a sol of small particles of a surfactant which melts in the desired operating temperature range. Examples of such surfactants include carboxylic acids with between 14 and 30 carbon atoms, such as: As the melting point of sols with a small particle size is usually slightly less than of the bulk material, it is preferable to choose a carboxylic acid with a melting point slightly above the desired drop selection temperature. A good example is Arachidic acid. These carboxylic acids are available in high purity and at low cost. The amount of surfactant required is very small, so the cost of adding them to the ink is insignificant. A mixture of carboxylic acids with slightly varying chain lengths can be used to spread the melting points over a range of temperatures. Such mixtures will typically cost less than the pure acid. It is not necessary to restrict the choice of surfactant to simple unbranched carboxylic acids. Surfactants with branched chains or phenyl groups, or other hydrophobic moieties can be used. It is also not necessary to use a carboxylic acid. Many highly polar moieties are suitable for the hydrophilic end of the surfactant. It is desirable that the polar end be ionizable in water, so that the surface of the surfactant particles can be charged to aid dispersion and prevent flocculation. In the case of carboxylic acids, this can be achieved by adding an alkali such as sodium hydroxide or potassium hydroxide. Preparation of Inks with Surfactant Sols The surfactant sol can be prepared separately at high concentration, and added to the ink in the required concentration. An example process for creating the surfactant sol is as follows: 1) Add the carboxylic acid to purified water in an oxygen free atmosphere. 2) Heat the mixture to above the melting point of the carboxylic acid. The water can be brought to a boil. 3) Ultrasonicate the mixture, until the typical size of the carboxylic acid droplets is between 100 A and l,OOθA. 4) Allow the mixture to cool. 5) Decant the larger particles from the top of the mixture. 6) Add an alkali such as NaOH to ionize the carboxylic acid molecules on the surface of the particles. A pH of approximately 8 is suitable. This step is not absolutely necessary, but helps stabilize the sol. 7) Centrifuge the sol. As the density of the carboxylic acid is lower than water, smaller particles will accumulate at the outside of the centrifuge, and larger particles in the centre. 8) Filter the sol using a microporous filter to eliminate any particles above 5000 A. 9) Add the surfactant sol to the ink preparation. The sol is required only in very dilute concentration. The ink preparation will also contain either dye(s) or pigment(s), bactericidal agents, agents to enhance the electrical conductivity of the ink if electrostatic drop separation is used, humectants, and other agents as required. Anti-foaming agents will generally not be required, as there is no bubble formation during the drop ejection process. Cationic surfactant sols Inks made with anionic surfactant sols are generally unsuitable for use with cationic dyes or pigments. This is because the cationic dye or pigment may precipitate or flocculate with the anionic surfactant. To allow the use of cationic dyes and pigments, a cationic surfactant sol is required. The family of alkylamines is suitable for this puφose. Various suitable alkylamines are shown in the following table: The method of preparation of cationic surfactant sols is essentially similar to that of anionic surfactant sols, except that an acid instead of an alkali is used to adjust the pH balance and increase the charge on the surfactant particles. A pH of 6 using HCl is suitable. Microemulsion Based Inks An alternative means of achieving a large reduction in surface tension as some temperature threshold is to base the ink on a microemulsion. A microemulsion is chosen with a phase inversion temperature (PIT) around the desired ejection threshold temperature. Below the PIT, the microemulsion is oil in water (O W), and above the PIT the microemulsion is water in oil (W/O). At low temperatures, the surfactant forming the microemulsion prefers a high curvature surface around oil, and at temperatures significantly above the PIT, the surfactant prefers a high curvature surface around water. At temperatures close to the PIT, the microemulsion forms a continuous 'sponge' of topologically connected water and oil. There are two mechanisms whereby this reduces the surface tension. Around the PIT, the surfactant prefers surfaces with very low curvature. As a result, surfactant molecules migrate to the ink/air interface, which has a curvature which is much less than the curvature of the oil emulsion. This lowers the surface tension of the water. Above the phase inversion temperature, the microemulsion changes from O/W to W/O, and therefore the ink/air interface changes from water/air to oil/air. The oil/air interface has a lower surface tension. There is a wide range of possibilities for the preparation of microemulsion based inks. For fast drop ejection, it is preferable to chose a low viscosity oil. In many instances, water is a suitable polar solvent. However, in some cases different polar solvents may be required. In these cases, polar solvents with a high surface tension should be chosen, so that a large decrease in surface tension is achievable. The surfactant can be chosen to result in a phase inversion temperature in the desired range. For example, surfactants of the group poly(oxyethylene)alkylphenyl ether (ethoxylated alkyl phenols, general formula: C n H 2n+ ιC 4 H6(CH 2 CH 2 O) m OH) can be used. The hydrophilicity of the surfactant can be increased by increasing m, and the hydrophobicity can be increased by increasing n. Values of m of approximately 10, and n of approximately 8 are suitable. Low cost commercial preparations are the result of a polymerization of various molar ratios of ethylene oxide and alkyl phenols, and the exact number of oxyethylene groups varies around the chosen mean. These commercial preparations are adequate, and highly pure surfactants with a specific number of oxyethylene groups are not required. The formula for this surfactant is C 8 Hι 7 C 4 H6(CH 2 CH 2 O) n OH (average n=10). Synonyms include Octoxynol-10, PEG- 10 octyl phenyl ether and POE (10) octyl phenyl ether The HLB is 13.6, the melting point is 7°C, and the cloud point is 65°C. Commercial preparations of this surfactant are available under various brand names. Suppliers and brand names are listed in the following table: These are available in large volumes at low cost (less than one dollar per pound in quantity), and so contribute less than 10 cents per liter to prepared microemulsion ink with a 5% surfactant concentration. Other suitable ethoxylated alkyl phenols include those listed in the following table: Microemulsion based inks have advantages other than surface tension control: 1) Microemulsions are thermodynamically stable, and will not separate. Therefore, the storage time can be very long. This is especially significant for office and portable printers, which may be used sporadically. 2) The microemulsion will form spontaneously with a particular drop size, and does not require extensive stirring, centrifuging, or filtering to ensure a particular range of emulsified oil drop sizes. 3) The amount of oil contained in the ink can be quite high, so dyes which are soluble in oil or soluble in water, or both, can be used. It is also possible to use a mixture of dyes, one soluble in water, and the other soluble in oil, to obtain specific colors. 4) Oil miscible pigments are prevented from flocculating, as they are trapped in the oil microdroplets. 5) The use of a microemulsion can reduce the mixing of different dye colors on the surface of the print medium. 6) The viscosity of microemulsions is very low. 7) The requirement for humectants can be reduced or eliminated. Dves and pigments in microemulsion based inks Oil in water mixtures can have high oil contents - as high as 40% and still form O/W microemulsions. This allows a high dye or pigment loading. Mixtures of dyes and pigments can be used. An example of a microemulsion based ink mixture with both dye and pigment is as follows: 1) 70% water 2) 5% water soluble dye 3) 5% surfactant 4) 10% oil 5) 10% oil miscible pigment The following table shows the nine basic combinations of colorants in the oil and water phases of the microemulsion that may be used. The ninth combination, with no colorants, is useful for printing transparent coatings, UV ink, and selective gloss highlights. As many dyes are amphiphilic, large quantities of dyes can also be solubilized in the oil-water boundary layer as this layer has a very large surface area. It is also possible to have multiple dyes or pigments in each phase, and to have a mixture of dyes and pigments in each phase. When using multiple dyes or pigments the absoφtion spectrum of the resultant ink will be the weighted average of the absoφtion spectra of the different colorants used. This presents two problems: 1) The absoφtion spectrum will tend to become broader, as the absoφtion peaks of both colorants are averaged. This has a tendency to 'muddy' the colors. To obtain brilliant color, careful choice of dyes and pigments based on their absoφtion spectra, not just their human-perceptible color, needs to be made. 2) The color of the ink may be different on different substrates. If a dye and a pigment are used in combination, the color of the dye will tend to have a smaller contribution to the printed ink color on more absoφtive papers, as the dye will be absorbed into the paper, while the pigment will tend to 'sit on top' of the paper. This may be used as an advantage in some circumstances. Surfactants with a Krafft point in the drop selection temperature range For ionic surfactants there is a temperature (the Krafft point) below which the solubility is quite low, and the solution contains essentially no micelles. Above the Krafft temperature micelle formation becomes possible and there is a rapid increase in solubility of the surfactant If the critical micelle concentration (CMC) exceeds the solubility of a surfactant at a particular temperature, then the minimum surface tension will be achieved at the point of maximum solubility, rather than at the CMC. Surfactants are usually much less effective below the Krafft point. This factor can be used to achieve an increased reduction in surface tension with increasing temperature. At ambient temperatures, only a portion of the surfactant is in solution. When the nozzle heater is turned on, the temperature rises, and more of the surfactant goes into solution, decreasing the surface tension. A surfactant should be chosen with a Krafft point which is near the top of the range of temperatures to which the ink is raised. This gives a maximum margin between the concentration of surfactant in solution at ambient temperatures, and the concentration of surfactant in solution at the drop selection temperature. The concentration of surfactant should be approximately equal to the CMC at the Krafft point. In this manner, the surface tension is reduced to the maximum amount at elevated temperatures, and is reduced to a minimum amount at ambient temperatures. The following table shows some commercially available surfactants with Krafft points in the desired range. Surfactants with a cloud point in the drop selection temperature range Non-ionic surfactants using polyoxyethylene (POE) chains can be used to create an ink where the surface tension falls with increasing temperature. At low temperatures, the POE chain is hydrophilic, and maintains the surfactant in solution. As the temperature increases, the structured water around the POE section of the molecule is disrupted, and the POE section becomes hydrophobic. The surfactant is increasingly rejected by the water at higher temperatures, resulting in increasing concentration of surfactant at the air/ink interface, thereby lowering surface tension. The temperature at which the POE section of a nonionic surfactant becomes hydrophilic is related to the cloud point of that surfactant POE chains by themselves are not particularly suitable, as the cloud point is generally above 100°C Polyoxypropylene (POP) can be combined with POE in POE/POP block copolymers to lower the cloud point of POE chains without introducing a strong hydrophobicity at low temperatures. Two main configurations of symmetrical POE/POP block copolymers are available. These are: 1) Surfactants with POE segments at the ends of the molecules, and a POP segment in the centre, such as the poloxamer class of surfactants (generically CAS 9003-11-6) 2) Surfactants with POP segments at the ends of the molecules, and a POE segment in the centre, such as the meroxapol class of surfactants (generically also CAS 9003-11-6) Some commercially available varieties of poloxamer and meroxapol with a high surface tension at room temperature, combined with a cloud point above 40°C and below 100°C are shown in the following table: Other varieties of poloxamer and meroxapol can readily be synthesized using well known techniques. Desirable characteristics are a room temperature surface tension which is as high as possible, and a cloud point between 40°C and 100°C, and preferably between 60°C and 80°C. Meroxapol [HO(CHCH 3 CH 2 O) x (CH 2 CH 2 O) y (CHCH 3 CH 2 O) z OH] varieties where the average x and z are approximately 4, and the average y is approximately 15 may be suitable. If salts are used to increase the electrical conductivity of the ink, then the effect of this salt on the cloud point of the surfactant should be considered. The cloud point of POE surfactants is increased by ions that disrupt water structure (such as I ), as this makes more water molecules available to form hydrogen bonds with the POE oxygen lone pairs. The cloud point of POE surfactants is decreased by ions that form water structure (such as Cl " , OH " ), as fewer water molecules are available to form hydrogen bonds. Bromide ions have relatively little effect The ink composition can be 'tuned' for a desired temperature range by altering the lengths of POE and POP chains in a block copolymer surfactant, and by changing the choice of salts (e.g Cl " to Br " to I " ) that are added to increase electrical conductivity. NaCl is likely to be the best choice of salts to increase ink conductivity, due to low cost and non-toxicity. NaCl slightly lowers the cloud point of nonionic surfactants. Hot Melt Inks The ink need not be in a liquid state at room temperature. Solid 'hot melt' inks can be used by heating the printing head and ink reservoir above the melting point of the ink. The hot melt ink must be formulated so that the surface tension of the molten ink decreases with temperature. A decrease of approximately 2 mN/m will be typical of many such preparations using waxes and other substances. However, a reduction in surface tension of approximately 20 mN/m is desirable in order to achieve good operating margins when relying on a reduction in surface tension rather than a reduction in viscosity. The temperature difference between quiescent temperature and drop selection temperature may be greater for a hot melt ink than for a water based ink, as water based inks are constrained by the boiling point of the water. The ink must be liquid at the quiescent temperature. The quiescent temperature should be higher than the highest ambient temperature likely to be encountered by the printed page. T he quiescent temperature should also be as low as practical, to reduce the power needed to heat the print head, and to provide a maximum margin between the quiescent and the drop ejection temperatures. A quiescent temperature between 60°C and 90°C is generally suitable, though other temperatures may be used. A drop ejection temperature of between 160°C and 200°C is generally suitable. There are several methods of achieving an enhanced reduction in surface tension with increasing temperature. 1 ) A dispersion of microfine particles of a surfactant with a melting point substantially above the quiescent temperature, but substantially below the drop ejection temperature, can be added to the hot melt ink while in the liquid phase. 2) A polar/non-polar microemulsion with a PIT which is preferably at least 20°C above the melting points of both the polar and non-polar compounds. To achieve a large reduction in surface tension with temperature, it is desirable that the hot melt ink carrier have a relatively large surface tension (above 30 mN/m) when at the quiescent temperature. This generally excludes alkanes such as waxes. Suitable materials will generally have a strong intermolecular attraction, which may be achieved by multiple hydrogen bonds, for example, polyols, such as Hexanetetrol, which has a melting point of 88°C. Surface tension reduction of various solutions Figure 3(d) shows the measured effect of temperature on the surface tension of various aqueous preparations containing the following additives: 1) 0.1% sol of Stearic Acid 2) 0.1% sol of Palmitic acid 3) 0.1% solution of Pluronic 10R5 (trade mark of BASF) 4) 0.1 % solution of Pluronic L35 (trade mark of BASF) 5) 0.1 % solution of Pluronic L44 (trade mark of BASF) Inks suitable for printing systems of the present invention are described in the following Australian patent specifications, the disclosure of which are hereby incoφorated by reference: 'Ink composition based on a microemulsion' (Filing no.: PN5223, filed on 6 September 1995); 'Ink composition containing surfactant sol' (Filing no.: PN5224, filed on 6 September 1995); 'Ink composition for DOD printers with Krafft point near the drop selection temperature sol' (Filing no.: PN6240, filed on 30 October 1995); and 'Dye and pigment in a microemulsion based ink' (Filing no.: PN6241, filed on 30 October 1995). Operation Using Reduction of Viscosity As a second example, operation of an embodiment using thermal reduction of viscosity and proximity drop separation, in combination with hot melt ink, is as follows. Prior to operation of the printer, solid ink is melted in the reservoir 64. The reservoir, ink passage to the print head, ink channels 75, and print head 50 are maintained at a temperature at which the ink 100 is liquid, but exhibits a relatively high viscosity (for example, approximately 100 cP). The Ink 100 is retained in the nozzle by the surface tension of the ink. The ink 100 is formulated so that the viscosity of the ink reduces with increasing temperature. The ink pressure oscillates at a frequency which is an integral multiple of the drop ejection frequency from the nozzle. The ink pressure oscillation causes oscillations of the ink meniscus at the nozzle tips, but this oscillation is small due to the high ink viscosity. At the normal operating temperature, these oscillations are of insufficient amplitude to result in drop separation. When the heater 103 is energized, the ink forming the selected drop is heated, causing a reduction in viscosity to a value which is preferably less than 5 cP. The reduced viscosity results in the ink meniscus moving further during the high pressure part of the ink pressure cycle. The recording medium 51 is arranged sufficiently close to the print head 50 so that the selected drops contact the recording medium 51, but sufficiently far away that the unselected drops do not contact the recording medium 51. Upon contact with the recording medium 51 , part of the selected drop freezes, and attaches to the recording medium. As the ink pressure falls, ink begins to move back into the nozzle. The body of ink separates from the ink which is frozen onto the recording medium. The meniscus of the ink 100 at the nozzle tip then returns to low amplitude oscillation. The viscosity of the ink increases to its quiescent level as remaining heat is dissipated to the bulk ink and print head. One ink drop is selected, separated and forms a spot on the recording medium 51 for each heat pulse. As the heat pulses are electrically controlled, drop on demand ink jet operation can be achieved. Manufacturing of Print Heads Manufacturing processes for monolithic print heads in accordance with the present invention are described in the following Australian patent specifications filed on 12 April 1995, the disclosure of which are hereby incoφorated by reference: 'A monolithic LIFT printing head' (Filing no.: PN2301); 'A manufacturing process for monolithic LEFT printing heads' (Filing no.: PN2302); 'A self-aligned heater design for LIFT print heads' (Filing no.: PN2303); 'Integrated four color LEFT print heads' (Filing no.: PN2304); 'Power requirement reduction in monolithic LIFT printing heads' (Filing no.: PN2305); 'A manufacturing process for monolithic LIFT print heads using anisotropic wet etching' (Filing no.: PN2306); 'Nozzle placement in monolithic drop-on-demand print heads' (Filing no.: PN2307); 'Heater structure for monolithic LIFT print heads' (Filing no.: PN2346); 'Power supply connection for monolithic LIFT print heads' (Filing no.: PN2347); 'External connections for Proximity LIFT print heads' (Filing no.: PN2348); and 'A self-aligned manufacturing process for monolithic LIFT print heads' (Filing no.: PN2349); and 'CMOS process compatible fabrication of LIFT print heads' (Filing no.: PN5222, 6 September 1995). 'A manufacturing process for LIFT print heads with nozzle rim heaters' (Filing no.: PN6238, 30 October 1995); 'A modular LIFT print head' (Filing no.: PN6237, 30 October 1995); 'Method of increasing packing density of printing nozzles' (Filing no.: PN6236, 30 October 1995); and 'Nozzle dispersion for reduced electrostatic interaction between simultaneously printed droplets' (Filing no.: PN6239, 30 October 1995). Control of Print Heads Means of providing page image data and controlling heater temperature in print heads of the present invention is described in the following Australian patent specifications filed on 12 April 1995, the disclosure of which are hereby incoφorated by reference: 'Integrated drive circuitry in LIFT print heads' (Filing no.: PN2295); 'A nozzle clearing procedure for Liquid Ink Fault Tolerant (LIFT) printing' (Filing no.: PN2294); 'Heater power compensation for temperature in LIFT printing systems' (Filing no.: PN2314); Ηeater power compensation for thermal lag in LIFT printing systems' (Filing no.: PN2315); 'Heater power compensation for print density in LIFT printing systems' (Filing no.: PN2316); 'Accurate control of temperature pulses in printing heads' (Filing no.: PN2317); 'Data distribution in monolithic LIFT print heads' (Filing no.: PN2318); 'Page image and fault tolerance routing device for LIFT printing systems' (Filing no.: PN2319); and 'A removable pressurized liquid ink cartridge for LIFT printers' (Filing no.: PN2320). Image Processing for Print Heads An objective of printing systems according to the invention is to attain a print quality which is equal to that which people are accustomed to in quality color pubhcations printed using offset printing. This can be achieved using a print resolution of approximately 1,600 dpi. However, 1,600 dpi printing is difficult and expensive to achieve. Similar results can be achieved using 800 dpi printing, with 2 bits per pixel for cyan and magenta, and one bit per pixel for yellow and black. This color model is herein called CC'MM' YK. Where high quality monochrome image printing is also required, two bits per pixel can also be used for black. This color model is herein called CC'MM' YKK'. Color models, halftoning, data compression, and real-time expansion systems suitable for use in systems of this invention and other printing systems are described in the following Australian patent specifications filed on 12 April 1995, the disclosure of which are hereby incoφorated by reference: 'Four level ink set for bi-level color printing' (Filing no.: PN2339); 'Compression system for page images' (Filing no.: PN2340); 'Real-time expansion apparatus for compressed page images * (Filing no.: PN2341); and 'High capacity compressed document image storage for digital color printers' (Filing no.: PN2342); 'Improving JPEG compression in the presence of text' (Filing no.: PN2343); 'An expansion and halftoning device for compressed page images' (Filing no.: PN2344); and 'Improvements in image halftoning' Q?iling no.: PN2345). Applications Using Print Heads According to this Invention Printing apparatus and methods of this invention are suitable for a wide range of applications, including (but not limited to) the following: color and monochrome office printing, short run digital printing, high speed digital printing, process color printing, spot color printing, offset press supplemental printing, low cost printers using scanning print heads, high speed printers using pagewidth print heads, portable color and monochrome printers, color and monochrome copiers, color and monochrome facsimile machines, combined printer, facsimile and copying machines, label printing, large format plotters, photographic duplication, printers for digital photographic processing, portable printers incoφorated into digital 'instant' cameras, video printing, printing of PhotoCD images, portable printers for 'Personal Digital Assistants', wallpaper printing, indoor sign printing, billboard printing, and fabric printing. Printing systems based on this invention are described in the following Australian patent specifications filed on 12 April 1995, the disclosure of which are hereby incoφorated by reference: 'A high speed color office printer with a high capacity digital page image store' (Filing no.: PN2329); 'A short run digital color printer with a high capacity digital page image store' (Filing no.: PN2330); 'A digital color printing press using LIFT printing technology' (Filing no.: PN2331); 'A modular digital printing press' (Filing no.: PN2332); 'A high speed digital fabric printer' (Filing no.: PN2333); 'A color photograph copying system' QHling no.: PN2334); 'A high speed color photocopier using a LIFT printing system' (Filing no.: PN2335); 'A portable color photocopier using LIFT printing technology' (Filing no.: PN2336); 'A photograph processing system using LIFT printing technology' (Filing no.: PN2337); 'A plain paper facsimile machine using a LIFT printing system' (Filing no.: PN2338); 'A PhotoCD system with integrated printer' (Filing no.: PN2293); 'A color plotter using LIFT printing technology' (Filing no.: PN2291); 'A notebook computer with integrated LIFT color printing system' (Filing no.: PN2292); 'A portable printer using a LIFT printing system' (Filing no.: PN2300); 'Fax machine with on-line database inteπogation and customized magazine printing' (Filing no.: PN2299); 'Miniature portable color printer' (Filing no.: PN2298); 'A color video printer using a LIFT printing system' (Filing no.: PN2296); and 'An integrated printer, copier, scanner, and facsimile using a LIFT printing system' (Filing no.: PN2297) Compensation of Print Heads for Environmental Conditions It is desirable that drop on demand printing systems have consistent and predictable ink drop size and position. Unwanted variation in ink drop size and position causes variations in the optical density of the resultant print, reducing the perceived print quality. These variations should be kept to a small proportion of the nominal ink drop volume and pixel spacing respectively. Many environmental variables can be compensated to reduce their effect to insignificant levels. Active compensation of some factors can be achieved by varying the power applied to the nozzle heaters. An optimum temperature profile for one print head embodiment involves an instantaneous raising of the active region of the nozzle tip to the ejection temperature, maintenance of this region at the ejection temperature for the duration of the pulse, and instantaneous cooling of the region to the ambient temperature. This optimum is not achievable due to the stored heat capacities and thermal conductivities of the various materials used in the fabrication of the nozzles in accordance with the invention. However, improved performance can be achieved by shaping the power pulse using curves which can be derived by iterative refinement of finite element simulation of the print head. The power applied to the heater can be varied in time by various techniques, including, but not limited to: 1) Varying the voltage applied to the heater 2) Modulating the width of a series of short pulses (PWM) 3) Modulating the frequency of a series of short pulses (PFM) To obtain accurate results, a transient fluid dynamic simulation with free surface modeling is required, as convection in the ink, and ink flow, significantly affect on the temperature achieved with a specific power curve. By the incoφoration of appropriate digital circuitry on the print head substrate, it is practical to individually control the power applied to each nozzle. One way to achieve this is by 'broadcasting' a variety of different digital pulse trains across the print head chip, and selecting the appropriate pulse train for each nozzle using multiplexing circuits. An example of the environmental factors which may be compensated for is listed in the table "Compensation for environmental factors". This table identifies which environmental factors are best compensated globally (for the entire print head), per chip (for each chip in a composite multi-chip print head), and per nozzle. Compensation for environmental factors Most applications will not require compensation for all of these variables. Some variables have a minor effect, and compensation is only necessary where very high image quality is required. Print head drive circuits Figure 4 is a block schematic diagram showing electronic operation of an example head driver circuit in accordance with this invention. This control circuit uses analog modulation of the power supply voltage applied to the print head to achieve heater power modulation, and does not have individual control of the power applied to each nozzle. Figure 4 shows a block diagram for a system using an 800 dpi pagewidth print head which prints process color using the CC'MM'YK color model. The print head 50 has a total of 79,488 nozzles, with 39,744 main nozzles and 39,744 redundant nozzles. The main and redundant nozzles are divided into six colors, and each color is divided into 8 drive phases. Each drive phase has a shift register which converts the serial data from a head control ASIC 400 into parallel data for enabling heater drive circuits. There is a total of 96 shift registers, each providing data for 828 nozzles. Each shift register is composed of 828 shift register stages 217, the outputs of which are logically anded with phase enable signal by a nand gate 215. The output of the nand gate 215 drives an inverting buffer 216, which in tum controls the drive transistor 201. The drive transistor 201 actuates the electrothermal heater 200, which may be a heater 103 as shown in figure 1(b). To maintain the shifted data valid during the enable pulse, the clock to the shift register is stopped the enable pulse is active by a clock stopper 218, which is shown as a single gate for clarity, but is preferably any of a range of well known glitch free clock control circuits. Stopping the clock of the shift register removes the requirement for a parallel data latch in the print head, but adds some complexity to the control circuits in the Head Control ASIC 400. Data is routed to either the main nozzles or the redundant nozzles by the data router 219 depending on the state of the appropriate signal of the fault status bus. The print head shown in figure 4 is simplified, and does not show various means of improving manufacturing yield, such as block fault tolerance. Drive circuits for different configurations of print head can readily be derived from the apparatus disclosed herein. Digital information representing patterns of dots to be printed on the recording medium is stored in the Page or Band memory 1513, which may be the same as the Image memory 72 in figure 1(a). Data in 32 bit words representing dots of one color is read from the Page or Band memory 1513 using addresses selected by the address mux 417 and control signals generated by the Memory Interface 418. These addresses are generated by Address generators 411, which forms part of the 'Per color circuits' 410, for which there is one for each of the six color components. The addresses are generated based on the positions of the nozzles in relation to the print medium. As the relative position of the nozzles may be different for different print heads, the Address generators 411 are preferably made programmable. The Address generators 411 normally generate the address corresponding to the position of the main nozzles. However, when faulty nozzles are present, locations of blocks of nozzles containing faults can be marked in the Fault Map RAM 412. The Fault Map RAM 412 is read as the page is printed. If the memory indicates a fault in the block of nozzles, the address is altered so that the Address generators 411 generate the address corresponding to the position of the redundant nozzles. Data read from the Page or Band memory 1513 is latched by the latch 413 and converted to four sequential bytes by the multiplexer 414. Timing of these bytes is adjusted to match that of data representing other colors by the FIFO 415. This data is then buffered by the buffer 430 to form the 48 bit main data bus to the print head 50. The data is buffered as the print head may be located a relatively long distance from the head control ASIC. Data from the Fault Map RAM 412 also forms the input to the FIFO 416. The timing of this data is matched to the data output of the FIFO 415, and buffered by the buffer 431 to form the fault status bus. The programmable power supply 320 provides power for the head 50. The voltage of the power supply 320 is controlled by the DAC 313, which is part of a RAM and DAC combination (RAMD AC) 316. The RAMD AC 316 contains a dual port RAM 317. The contents of the dual port RAM 317 are programmed by the Microcontroller 315. Temperature is compensated by changing the contents of the dual port RAM 317. These values are calculated by the microcontroller 315 based on temperature sensed by a thermal sensor 300. The thermal sensor 300 signal connects to the Analog to Digital Converter (ADC) 311. The ADC 311 is preferably incoφorated in the Microcontroller 315. The Head Control ASIC 400 contains control circuits for thermal lag compensation and print density. Thermal lag compensation requires that the power supply voltage to the head 50 is a rapidly time- varying voltage which is synchronized with the enable pulse for the heater. This is achieved by programming the programmable power supply 320 to produce this voltage. An analog time varying programming voltage is produced by the DAC 313 based upon data read from the dual port RAM 317. The data is read according to an address produced by the counter 403. The counter 403 produces one complete cycle of addresses during the period of one enable pulse. This synchronization is ensured, as the counter 403 is clocked by the system clock 408, and the top count of the counter 403 is used to clock the enable counter 404. The count from the enable counter 404 is then decoded by the decoder 405 and buffered by the buffer 432 to produce the enable pulses for the head 50. The counter 403 may include a prescaler if the number of states in the count is less than the number of clock periods in one enable pulse. Sixteen voltage states are adequate to accurately compensate for the heater thermal lag. These sixteen states can be specified by using a four bit connection between the counter 403 and the dual port RAM 317. However, these sixteen states may not be linearly spaced in time. To allow non-linear timing of these states the counter 403 may also include a ROM or other device which causes the counter 403 to count in a non-linear fashion. Alternatively, fewer than sixteen states may be used. For print density compensation, the printing density is detected by counting the number of pixels to which a drop is to be printed ('on' pixels) in each enable period. The 'on' pixels are counted by the On pixel counters 402. There is one On pixel counter 402 for each of the eight enable phases. The number of enable phases in a print head in accordance with the invention depend upon the specific design. Four, eight, and sixteen are convenient numbers, though there is no requirement that the number of enable phases is a power of two. The On Pixel Counters 402 can be composed of combinatorial logic pixel counters 420 which determine how many bits in a nibble of data are on. This number is then accumulated by the adder 421 and accumulator 422. A latch 423 holds the accumulated value valid for the duration of the enable pulse. The multiplexer 401 selects the output of the latch 423 which coπesponds to the current enable phase, as determined by the enable counter 404. The output of the multiplexer 401 forms part of the address of the dual port RAM 317. An exact count of the number of 'on' pixels is not necessary, and the most sigmficant four bits of this count are adequate. Combining the four bits of thermal lag compensation address and the four bits of print density compensation address means that the dual port RAM 317 has an 8 bit address. This means that the dual port RAM 317 contains 256 numbers, which are in a two dimensional array. These two dimensions are time (for thermal lag compensation) and print density. A third dimension - temperature - can be included. As the ambient temperature of the head varies only slowly, the microcontroller 315 has sufficient time to calculate a matrix of 256 numbers compensating for thermal lag and print density at the cuπent temperature. Periodically (for example, a few times a second), the microcontroller senses the current head temperature and calculates this matrix. The clock to the print head 50 is generated from the system clock 408 by the Head clock generator 407, and buffered by the buffer 406. To facilitate testing of the Head control ASIC, JTAG test circuits 499 may be included. Comparison with thermal ink iet technology The table "Comparison between Thermal ink jet and Present Invention" compares the aspects of printing in accordance with the present invention with theπnal inkjet printing technology. A direct comparison is made between the present invention and thermal ink jet technology because both are drop on demand systems which operate using thermal actuators and hquid ink. Although they may appear similar, the two technologies operate on different principles. Thermal ink jet printers use the following fundamental operating principle. A thermal impulse caused by electrical resistance heating results in the explosive formation of a bubble in liquid ink. Rapid and consistent bubble formation can be achieved by superheating the ink, so that sufficient heat is transferred to the ink before bubble nucleation is complete. For water based ink, ink temperatures of approximately 280°C to 400°C are required. The bubble formation causes a pressure wave which forces a drop of ink from the aperture with high velocity. The bubble then collapses, drawing ink from the ink reservoir to re-fill the nozzle. Thermal ink jet printing has been highly successful commercially due to the high nozzle packing density and the use of well established integrated circuit manufacturing techniques. However, thermal inkjet printing technology faces significant technical problems including multi-part precision fabrication, device yield, image resolution, 'pepper' noise, printing speed, drive transistor power, waste power dissipation, satellite drop formation, theπnal stress, differential thermal expansion, kogation, cavitation, rectified diffusion, and difficulties in ink formulation. Printing in accordance with the present invention has many of the advantages of thermal ink jet printing, and completely or substantially eliminates many of the inherent problems of thermal ink jet technology. Comparison between Thermal inkjet and Present Invention Yield and Fault Tolerance In most cases, monolithic integrated circuits cannot be repaired if they are not completely functional when manufactured. The percentage of operational devices which are produced from a wafer run is known as the yield. Yield has a direct influence on manufacturing cost. A device with a yield of 5% is effectively ten times more expensive to manufacture than an identical device with a yield of 50%. There are three major yield measurements: 1) Fab yield 2) Wafer sort yield 3) Final test yield For large die, it is typically the wafer sort yield which is the most serious limitation on total yield. Full pagewidth color heads in accordance with this invention are very large in comparison with typical VLSI circuits. Good wafer sort yield is critical to the cost-effective manufacture of such heads. Figure 5 is a graph of wafer sort yield versus defect density for a monolithic full width color A4 head embodiment of the invention. The head is 215 mm long by 5 mm wide. The non fault tolerant yield 198 is calculated according to Muφhy's method, which is a widely used yield prediction method. With a defect density of one defect per square cm, Muφhy's method predicts a yield less than 1 %. This means that more than 99% of heads fabricated would have to be discarded. This low yield is highly undesirable, as the print head manufacturing cost becomes unacceptably high. Muφhy's method approximates the effect of an uneven distribution of defects. Figure 5 also includes a graph of non fault tolerant yield 197 which explicitly models the clustering of defects by introducing a defect clustering factor. The defect clustering factor is not a controllable parameter in manufacturing, but is a characteristic of the manufacturing process. The defect clustering factor for manufacturing processes can be expected to be approximately 2, in which case yield projections closely match Muφhy's method. A solution to the problem of low yield is to incoφorate fault tolerance by including redundant functional units on the chip which are used to replace faulty functional units. In memory chips and most Wafer Scale Integration (WSI) devices, the physical location of redundant sub-units on the chip is not important However, in printing heads the redundant sub-unit may contain one or more printing actuators. These must have a fixed spatial relationship to the page being printed. To be able to print a dot in the same position as a faulty actuator, redundant actuators must not be displaced in the non-scan direction. However, faulty actuators can be replaced with redundant actuators which are displaced in the scan direction. To ensure that the redundant actuator prints the dot in the same position as the faulty actuator, the data timing to the redundant actuator can be altered to compensate for the displacement in the scan direction. To allow replacement of all nozzles, there must be a complete set of spare nozzles, which results in 100% redundancy. The requirement for 100% redundancy would normally more than double the chip area, dramatically reducing the primary yield before substituting redundant units, and thus eliminating most of the advantages of fault tolerance. However, with print head embodiments according to this invention, the minimum physical dimensions of the head chip are determined by the width of the page being printed, the fragility of the head chip, and manufacturing constraints on fabrication of ink channels which supply ink to the back surface of the chip. The minimum practical size for a full width, full color head for printing A4 size paper is approximately 215 mm x 5 mm. This size allows the inclusion of 100% redundancy without significantly increasing chip area, when using 1.5 μm CMOS fabrication technology. Therefore, a high level of fault tolerance can be included without significantly decreasing primary yield. When fault tolerance is included in a device, standard yield equations cannot be used. Instead, the mechanisms and degree of fault tolerance must be specifically analyzed and included in the yield equation. Figure 5 shows the fault tolerant sort yield 199 for a full width color A4 head which includes various forms of fault tolerance, the modeling of which has been included in the yield equation. This graph shows projected yield as a function of both defect density and defect clustering. The yield projection shown in figure 5 indicates that thoroughly implemented fault tolerance can increase wafer sort yield from under 1% to more than 90% under identical manufacturing conditions. This can reduce the manufacturing cost by a factor of 100. Fault tolerance is highly recommended to improve yield and reliability of print heads containing thousands of printing nozzles, and thereby make pagewidth printing heads practical. However, fault tolerance is not to be taken as an essential part of the present invention. Fault tolerance in drop-on-demand printing systems is described in the following Australian patent specifications filed on 12 April 1995, the disclosure of which are hereby incoφorated by reference: 'Integrated fault tolerance in printing mechanisms' (Filing no.: PN2324); 'Block fault tolerance in integrated printing heads' (Filing no.: PN2325); 'Nozzle duplication for fault tolerance in integrated printing heads' (Filing no.: PN2326); 'Detection of faulty nozzles in printing heads' (Filing no.: PN2327); and 'Fault tolerance in high volume printing presses' (Filing no.: PN2328). Printing System Embodiments A schematic diagram of a digital electronic printing system using a print head of this invention is shown in Figure 6. This shows a monolithic printing head 50 printing an image 60 composed of a multitude of ink drops onto a recording medium 51. This medium will typically be paper, but can also be overhead transparency film, cloth, or many other substantially flat surfaces which will accept ink drops. The image to be printed is provided by an image source 52, which may be any image type which can be converted into a two dimensional array of pixels. Typical image sources are image scanners, digitally stored images, images encoded in a page description language 0?DL) such as Adobe Postscript, Adobe Postscript level 2, or Hewlett-Packard PCL 5, page images generated by a procedure-call based rasterizer, such as Apple QuickDraw, Apple Quickdraw GX, or Microsoft GDI, or text in an electronic form such as ASCII. This image data is then converted by an image processing system 53 into a two dimensional aπay of pixels suitable for the particular printing system. This may be color or monochrome, and the data will typically have between 1 and 32 bits per pixel, depending upon the image source and the specifications of the printing system. The image processing system may be a raster image processor (RIP) if the source image is a page description, or may be a two dimensional image processing system if the source image is from a scanner. If continuous tone images are required, then a halftoning system 54 is necessary. Suitable types of halftoning are based on dispersed dot ordered dither or error diffusion. Variations of these, commonly known as stochastic screening or frequency modulation screening are suitable. The halftoning system commonly used for offset printing - clustered dot ordered dither - is not recommended, as effective image resolution is unnecessarily wasted using this technique. The output of the halftoning system is a binary monochrome or color image at the resolution of the printing system according to the present invention. The binary image is processed by a data phasing circuit 55 (which may be incoφorated in a Head Control ASIC 400 as shown in figure 4) which provides the pixel data in the correct sequence to the data shift registers 56. Data sequencing is required to compensate for the nozzle arrangement and the movement of the paper. When the data has been loaded into the shift registers 56, it is presented in parallel to the heater driver circuits 57. At the coπect time, the driver circuits 57 will electronically connect the coπesponding heaters 58 with the voltage pulse generated by the pulse shaper circuit 61 and the voltage regulator 62. The heaters 58 heat the tip of the nozzles 59, affecting the physical characteristics of the ink. Ink drops 60 escape from the nozzles in a pattern which coπesponds to the digital impulses which have been applied to the heater driver circuits. The pressure of the ink in the ink reservoir 64 is regulated by the pressure regulator 63. Selected drops of ink drops 60 are separated from the body of ink by the chosen drop separation means, and contact the recording medium 51. During printing, the recording medium 51 is continually moved relative to the print head 50 by the paper transport system 65. If the print head 50 is the fuD width of the print region of the recording medium 51, it is only necessary to move the recording medium 51 in one direction, and the print head 50 can remain fixed. If a smaller print head 50 is used, it is necessary to implement a raster scan system. This is typically achieved by scanning the print head 50 along the short dimension of the recording medium 51 , while moving the recording medium 51 along its long dimension. The binary image is processed by a data phasing circuit 55 (which may be incoφorated in a Head Control ASIC 400 as shown in figure 4) which provides the pixel data in the correct sequence to the data shift registers 56. Data sequencing is required to compensate for the nozzle arrangement and the movement of the paper. When the data has been loaded into the shift registers 56, it is presented in parallel to the heater driver circuits 57. At the correct time, the driver circuits 57 will electronically connect the corresponding heaters 58 with the voltage pulse generated by the pulse shaper circuit 61 and the voltage regulator 62. The heaters 58 heat the tip of the nozzles 59, affecting the physical characteristics of the ink. Ink drops 60 escape from the nozzles in a pattern which conesponds to the digital impulses which have been applied to the heater driver circuits. The pressure of the ink in the ink reservoir 64 is regulated by the pressure regulator 63. Selected drops of ink drops 60 are separated from the body of ink by the chosen drop separation means, and contact the recording medium 51. During printing, the recording medium 51 is continually moved relative to the print head 50 by the paper transport system 65. If the print head 50 is the full width of the print region of the recording medium 51 , it is only necessary to move the recording medium 51 in one direction, and the print head 50 can remain fixed. If a smaller print head 50 is used, it is necessary to implement a raster scan system. This is typically achieved by scanning the print head 50 along the short dimension of the recording medium 51, while moving the recording medium 51 along its long dimension. Computer simulations of nozzle dynamics Details of the operation of print heads have been extensively simulated by computer. Figures 7 to 9 are some results from an example simulation of nozzle operation using electrothermal drop selection by reduction in surface tension, combined with electrostatic drop separation. Computer simulation is extremely useful in determining the characteristics of phenomena which are difficult to observe directly, nozzle operation is difficult to observe experimentally for several reasons, including: 1) Useful nozzles are microscopic, with important phenomena occurring at dimensions less than lμm. 2) The time scale of a drop ejection is a few microseconds, requiring very high speed observations. 3) Important phenomena occur inside opaque solid materials, making direct observation impossible. 4) Some important parameters, such as heat flow and fluid velocity vector fields are difficult to directly observe on any scale. 5) The cost of fabrication of experimental nozzles is high. Computer simulation overcomes the above problems. A leading software package for fluid dynamics simulation is FIDAP, produced by Fluid Dynamics International Inc. of Illinois, USA (FDI). FIDAP is a registered trademark of FDI. Other simulation programs are commercially available, but FIDAP was chosen for its high accuracy in transient fluid dynamic, energy transport, and surface tension calculations. The version of FIDAP used is FEDAP 7.06. Theoretical basis of calculations The theoretical basis for fluid dynamic and energy transport calculations using the Finite Element Method, and the manner that this theoretical basis is applied to the FIDAP computer program, is described in detail in the FIDAP 7.0 Theory Manual (April 1993) published by FDI, the disclosure of which is hereby incoφorated by reference. Material characteristics The table "Properties of materials used for FIDAP simulation" gives approximate physical properties of materials which may be used in the fabrication of the print head. The properties of 'ink' used in this simulation are actually the properties of pure water. This is to simulate a 'worst case' situation for drop separation, where the surface tension of the ink reduces only very slightly with temperature. Much wider operating margins can be achieved by using inks especially formulated to have a large decrease in surface tension with temperature. To obtain convergence for transient free surface simulations with variable surface tension at micrometer scales with microsecond transients using FIDAP 7.06, it is necessary to nondimensionalize the simulation. The values which have been used in the example simulation using the FIDAP program are shown in the table "Properties of materials used for FTD_ !3 J > simulation". Most values are from CRC Handbook of Chemistry and Physics, 72nd edition, or Lange's handbook of chemistry, 14th edition. Properties of materials used for FIDAP simulation Fluid dynamic simulations Figure 7 is a graph of temperature along the curve from the nozzle rim radially towards the centre of the meniscus of ink in a nozzle operating on the printing principle at various time steps. The vertical axis is in units of 100°C and the horizontal axis is in units of 10 μm. At the time step labeled 5 μs, the radial distance along the meniscus is approximately 10 μm, and the temperature is uniformly 30°C. During the heater active period (curves for 10 μs to 20 μs) the temperature at the nozzle tip end (coordinate 0.0) is almost 100°C. The centre of the meniscus rises to approximately 60°C. As the ink evolves from the nozzle, the curve from the nozzle tip to the centre of the meniscus becomes longer. After the heater is turned off (at time 24μs) the temperature at the nozzle tip falls. The ink also continues to evolve from the nozzle. By 75 μs, the radial line on the meniscus from nozzle tip to meniscus centre is approximately 40 μm long. Plots of an example nozzle at various time steps of a combined thermal and fluid dynamic simulation are shown in figures 8(a) to 8(j). Axi- symmetric simulation is used, as the example nozzle is cylindrical in form. There are four deviations from cylindrical form. These are the connections to the heater, the laminar air flow caused by paper movement, gravity (if the printhead is not vertical), and the presence of adjacent nozzles in the substrate. The effect of these factors on drop ejection is minor. The nozzle radius is 7 μm, and the plots are to scale. Only the region in the tip of the nozzle is shown, as most phenomena relevant to drop selection occur in this region. These plots show a cross section of the nozzle tip, from the axis of symmetry out to a distance of 22.1 μm. Figure 8(a) shows the nozzle in the quiescent state, where the surface tension balances the ink pressure and external electrostatic or magnetic field. In this diagram, 100 is the ink, 101 is silicon, 102 is silicon dioxide, 103 shows the position of the heater, 104 is the tantalum passivation layer, and 108 is the silicon nitride passivation layer. The hydrophobic coating is applied to the exposed silicon nitride layer. The nozzle tip and ink is at the device ambient temperature, which in this case is 30°C. During operation, the device ambient temperature will be slightly higher than the air ambient temperature, as an equilibrium temperature based on printing density is reached over the period of many drop ejections. The heat in the nozzle becomes very evenly distributed between drop ejections, due to the high thermal conductivity of silicon, and due to convection in the ink. Figure 8(b) shows the nozzle 2 μs after the start of the heater active period. This is part of the pre-heat cycle which reduces the peak power required to obtain fast temperature transients. The power applied to the heater at this time is 61 mW. Temperature contours are shown starting at 35°C (marked) and increasing in 5°C intervals. Figure 8(c) shows the nozzle 4 μs after the start of the heater active period. This is the time of peak heater power (97 W) applied to establish a shaφ temperature transient in the ink. Figure 8(d) shows the nozzle 9 μs after the start of the heater active period. Heater power is 43 mW to maintain the temperature at the circle of interface between ink, nozzle and air at just below the boiling point of the ink (approximately 100°C for water based ink). This diagram shows that convection is rapidly carrying the heat towards the centre of the meniscus. Figure 8(e) shows the nozzle 14 μs after the start of the heater active period. Heater power is 40 mW. The entire meniscus has been heated, and the ink has begun to move. Figure 8(f) shows the nozzle 1 μs after the heater is turned off. The heater pulse width for this simulation is 18 μs, and the heater pulse energy is 930 nJ. Figure 8(g) shows the nozzle 16 μs after the heater is turned off. This shows rapid cooling of the substrate, with the highest temperatures (56.6 °C) now in the ink. At this stage, the ink has sufficient momentum to ensure that the pendant drop is not re-absorbed into the nozzle. Figure 8(h) shows the nozzle 36 μs after the heater is turned off. This shows the elevated temperature is very evenly spread around the meniscus of the ink drop, and the temperature at the nozzle tip has fallen to 35 °C. Figure 8(i) shows the nozzle 46 μs after the heater is turned off. Most of the heat energy applied by the heater is carried away by the ink drop. At this stage, the temperature of all of the nozzle has fallen below 35°C. Figure 8(j) shows the nozzle 56 μs after the heater is turned off. The ink has begun to 'neck' at the nozzle tip, and will soon form a separate drop. If eight non-overlapping drop ejection phases of 18μs duration are used, the total drop ejection cycle is 144 μs. This gives sufficient time for remaining heat in the structure to dissipate through the silicon and ink, so there is no significant interference between successive drops. Figure 9 is a graph of meniscus position versus time in a nozzle. The vertical axis is in units of 10 μm, and the horizontal axis is in units of 100 μs. In this simulation, the initial meniscus position is slightly different from the quiescent position, and there is no temperature pulse. This graph shows the resonant frequency (approximately 25 KHz, derived from the distance between successive peaks) and the degree to which the meniscus and ink column are damped. It is clear from this graph that the meniscus quickly returns to the quiescent position, ready for the next drop to be ejected. Fluid dynamic simulations of nozzles Print heads can be designed to operate over a wide range of conditions, and at various print resolutions. Most cuπently available mass-market drop on demand printing systems have a printing resolution of between 300 and 400 dpi. This is not an absolute limit for thermal ink jet designs, but as the print resolution increases the print head design typically becomes progressively more difficult. Print heads can be designed with a wide range of print resolutions, but most of the volume market is likely to between resolutions of 400 dpi and 800 dpi. 400 dpi bi-level printing is generally adequate for text and graphics, but is not adequate for high quality full color photographic reproduction. An exception to this is when printing on cloth, where 400 dpi printing can give results superior to standard cloth. This is because the major limitation on print quality on cloth using mechanical printing techniques is registration, as it is difficult to prevent the cloth from stretching and distorting between each printed color. 800 dpi is likely to be the maximum requirement for mass market printing systems, as 800 dpi 6 color CC'MM'YK printing using stochastic screening can yield results approximately equivalent to the print quality that people are accustomed to from 133 to 150 lpi color offset printing. Simulations of a wide variety of nozzles have been performed. Figures 10(a) to 10(f) show summarized results of simulations of nozzles designed for 400 dpi, 600 dpi, and 800 dpi printing. The fluid dynamic simulations are performed using the FIDAP simulation software. In each case the simulation is over a duration of 100 μs, in 0.1 μs steps. The nozzle tip is cylindrical, with a radius of 20 μm for the 400 dpi simulation, a radius of 14 μm for the 600 dpi simulation, and a radius of 10 μm for the 800 dpi simulation. The ink pressure is 3.85 kPa for the 400 dpi simulation, 5.5 kPa for the 600 dpi simulation, 7.7 kPa for the 800 dpi simulation. The ambient temperature is 30°C in all three simulations. At the beginning of the simulation the ink meniscus is near its quiescent position, and all velocities are zero. A time varying power pulse is applied to the heater, starting at 20 μs. The pulse duration is 30 μs for the 400 dpi simulation, 24 μs for the 600 dpi simulation, and 18 μs for the 800 dpi simulation. The pulse starts at 20 μs to allow time for the ink meniscus to reach the quiescent position before the drop selection pulse. Only the drop selection process is modeled in these simulations. The drop separation process may be proximity, electrostatic, or other means. Separation of the selected drop from unselected drops relies upon a physical difference in meniscus position between the selected drop and the unselected drops. A n axial difference of 15 μm between the position of the centre of the meniscus before and after the drop selection pulse is adequate for drop separation. Figures 10(a), 10(c), and 10(e) are graphs of the position of the centre of the meniscus versus time for a 400 dpi nozzle, a 600 dpi nozzle, and a 800 dpi nozzle respectively. The vertical axis is in units of 10 μm, and the horizontal axis is in units of 100 μs. Visual comparison of these graphs should take into account the variation of vertical scale between the graphs. The important characteristic is the attainment of a meniscus position approximately 15 μm from the quiescent position (the position before the pulse beginning at 20 μs). At this point the drop separation means (not simulated in these simulations) can ensure that selected drops are separated from the body of ink and transfeπed to the recording medium. Oscillations of the meniscus after the drop selection pulse is removed are due to the initial non-spherical nature of the exuded drop: the drop oscillates between an initial prolate form, through a spherical form, to an oblate form, and back again. These variations are unimportant, as the drop separation means becomes the dominant determining factor of ink meniscus position after drop selection. Figures 10(b), 10(d), and 10(f) are plots of the meniscus shape at various instants for a 400 dpi nozzle, a 600 dpi nozzle, and a 800 dpi nozzle respectively. The three plots are shown at the same scale to allow direct comparison. The meniscus positions are shown at 2 us intervals from the start of the drop selection pulse at 20 μs to 4 μs after the end of the pulse. In figures 10(b), 10(d), and 10(f), 100 is ink, 101 is the sihcon substrate, 102 is SiO 2 , 103 marks the position of one side of the annular heater, 108 is a Si 3 N passivation layer and 109 is a hydrophobic surface coating. Although the plots are labeled 'Temperature contour plot', there are no temperature contours shown. The nozzles for which simulation results are shown in figure 10 are of a different design than the nozzles for which simulation results are shown in figures 7, 8, and 9. There are many possible designs for nozzles for print heads. As the fundamental requirements of a nozzle are somewhat simpler than the requirements of a thermal inkjet nozzle, the actual geometry chosen for the nozzle can largely be determined for convenience in the manufacturing process. Self-Cooling Operation in Thermally Activated Printing Heads The current invention provides a system for eliminating or significantly reducing the problem of waste heat removal, allowing print heads with higher speed, smaller size, lower cost, and a greater number of nozzles to be constructed. This system relies upon the ejected ink itself to remove waste heat and provides for the print head to be designed following two constraints: 1 ) The quiescent power consumption (power consumed by the print head when not actually printing) should be low enough so that dissipation of quiescent heat can be achieved by convection or forced air cooling. 2) The maximum active power consumption (power consumed when printing) should be less than the power required to raise the temperature of the ink which is being printed above the a reliable operating temperature. The first constraint can be met by using CMOS driving circuitry. In most circumstances, the use of CMOS driving circuitry results in quiescent power that is so low that it can be dissipated without requiring a heatsink or other special anangements. Bipolar, nMOS or other driving circuitry can also be used, as the thermal resistance from the print head to the ambient environment is low enough to prevent excessive heat accumulation. However, cunent thermal ink-jet (TIJ) printing systems have an active power requirement which is too high to allow the practical use of CMOS or nMOS circuitry. Therefore, bipolar drive circuitry is typically used. Print heads using this invention's printing technology can be designed with sufficiently low active power consumption Oess than 1 % of TIJ) as to make the use of CMOS drive circuitry practical. The second constraint can be met by designing the nozzles of the print head so that the energy required to eject a single drop is less than the energy required to raise an equivalent volume of ink from the ambient ink temperature to the maximum ink temperature where reliable printing operation is maintained. If this BAD ORIGINAL # is achieved, then the full amount of the active power can be dissipated in the printed ink itself. The amount of active power consumption is directly proportional to the number of ink drops printed per unit time. The power that can be dissipated in the printed ink is also directly proportional to the number of ink drops printed per unit time. Therefore, if the energy per drop can be reduced below the required threshold, the constraint that power dissipation places on print speed, number of nozzles, or nozzle density can be completely removed, and "self-cooling operation" is achieved. The value of the self cooling threshold depends upon the ambient temperature, the ink drop radius, the specific heat capacity of the ink, the boiling point of the ink, and the operating margin required. Figure 19 is a graph of the maximum drop ejection energy allowable to maintain self cooling operation. The maximum drop ejection energy is graphed against ink drop radius and ambient temperature, for a water based ink. A 20°C operating margin is assumed. Quiescent power dissipation of the print head is assumed to be negligible. Print heads with drop ejection energies less than the curve in figure 6 can operate in a self-cooling manner. Print-heads which require more energy to eject a drop than is shown in figure 19 cannot be fully cooled by the ejection of ink drops alone. Commercially available thermal ink jet printing technologies currently have a drop ejection energy approximately ten times the threshold for self- cooling operation. It is likely that self-cooling operation is very difficult to achieve for thermal ink jet printers with drop sizes less than 100 pi. However, the nozzles of print heads operating in accordance with the present invention can readily be designed for self-cooling operation. Prefened Embodiment Using Viscosity Reduction Selection In this preferred embodiment, the means of selecting drops to be printed is the thermal reduction of ink viscosity in the presence of oscillating ink pressure. The average pressure of the oscillating ink pressure is insufficient to overcome the surface tension of the ink and eject ink from the nozzle. At ambient temperature, the ink viscosity is such that the amplitude of ink meniscus oscillation resulting from the oscillation in ink pressure is insufficient to result in drop separation. When the thermal actuator of a nozzle is activated, the ink viscosity falls sufficiently that the amplitude of ink meniscus oscillation resulting from the oscillation in ink pressure is sufficient to result in drop separation. In most instances, the velocity of the ink as it emerges from the nozzle will not be sufficient to cause the emerging ink drop to separate from the body of ink. For most drop sizes of interest in computer controlled printing, the force of gravity on the drop is insignificant compared to the surface tension forces, so gravity cannot be used as a means of drop separation. Therefore, a means of separating the selected drop from the body of ink, and ensuring that the selected drop proceeds to form a spot on the recording medium, is required. The ink drop separation means may be chosen from, but is not limited to, the following list: 1 ) Proximity (recording medium in close proximity to print head) 2) Electrostatic attraction 3) Magnetic attraction For effective operation, the ink should exhibit a large reduction in viscosity with temperature. The viscosity of the ink should be high (preferably in excess of 20 cP) for drops which are not selected, and should fall by a factor which is preferably in excess of 10 for selected drops. Appropriate ink properties can be achieved using mixtures various organic waxes, acids, alcohols, oils and other compounds. Viscous printing in accordance with the invention is suitable for hot melt printing, where the ink is solid at room temperature. The ink preferably has a melting point above 60°C, and can also be formulated as a mixture of compounds with different melting points, so that it 'softens' rather than having a distinct melting point. The ink reservoir and printing head are elevated to a temperature above the melting point of the ink (for example, 80°C) prior to printing. This temperature is refeπed to as the quiescent temperature. The temperature of the print head can be regulated to minimize the influence of ambient temperature on the printing characteristics. When a drop is to be printed, an electrothermal actuator in the nozzle is activated, raising the temperature of the ink at the nozzle tip. A suitable ejection temperature may be 100°C above the quiescent temperature, allowing sufficient temperature difference to result in a large reduction in viscosity. For high speed high resolution printing, the viscosity of the ink at the ejection temperature is preferably less than 10 cP, and more preferably in the order of 1 cP. The low viscosity results in the ink moving much more rapidly in response to the oscillating ink pressure, which in turn results in the ink moving further. The reduced viscosity results in selected drops having a peak meniscus position which is further extended from the nozzle than the peak meniscus position of drops which are not selected. This allows the drop separation means to discriminate between selected drops and drops which have not been selected. The oscillating ink pressure can be achieved by applying an acoustic wave to the ink. The waveshape is not critical, but a sinusoidal wave is the simplest to control and predict, and so is assumed herein. The frequency is the same as, or an integral multiple of, the drop ejection frequency from a single nozzle. The phase of the oscillation is preferably accurately timed in relation to the drop ejection cycle. An apparatus to cause the acoustic wave includes a piezoelectric crystal the entire length of the row of nozzles situated in such a way as to cause displacement of the body of ink in the ink channel supplying the row of nozzles. A sinusoidal voltage of the appropriate frequency, amplitude and phase is applied to the piezoelectric crystal. The piezoelectric crystal expands or contracts in response to the applied voltage, causing displacement of the ink. As the displacement is dynamic and continuous, pressure waves form in the ink. Because the addition of acoustic ink waves adds complexity and expense to printing, it is most applicable to those applications which are not highly cost sensitive. Such applications include short run digital color printing, and high quality high speed color office printing. Viscous Operation The exact operation of printing in accordance with this invention using viscosity reduction is dependent upon many factors, many of which can be accurately controlled during the print head manufacturing process, ink manufacturing, or during printer operation. These factors include: 1) Nozzle radius 2) Nozzle length 3) Baπel geometry 4) Ink pressure period 5) Ink pressure wave amplitude 6) Constant offset in ink pressure 7) Phase of heater actuation pulse relative to ink pressure wave 8) Energy of heat pulse 9) Energy distribution of heat pulse with respect to time 10) Heater geometry 11) Heater position relative to nozzle 12) Thermal conductivity of nozzle materials 13) Thermal conductivity of ink 14) Ink viscosity with respect to temperature Computer simulations of nozzle dynamics Details of the operation of print heads have been extensively simulated by computer. Figures 21 to 26 are some results from an example simulation of invention embodiment nozzle operation using electrothermal drop selection by reduction in viscosity. The drop separation means is not modeled in these simulations. As a result, the selected drop is not separated from the body of ink, and returns to the nozzle. To produce an operational drop on demand printer, the drop selection means as modeled herein must be combined with a suitable drop separation means. Computer simulation is extremely useful in determining the characteristics of phenomena which are difficult to observe directly. Nozzle operation is difficult to observe experimentally for several reasons, including: 1 ) Useful nozzles in accordance with the invention are microscopic, with important phenomena occurring at dimensions of order 1 μm. 2) The time scale of a drop ejection is a few microseconds, requiring very high speed observations. 3) Important phenomena occur inside opaque solid materials, making direct optical observation impossible. 4) Some important parameters, such as heat flow, viscosity, and fluid velocity are difficult to directly observe. 5) The cost of fabrication of experimental nozzles is high. Computer simulation overcomes the above problems. A leading software package for fluid dynamics simulation is FTDAP, produced by Fluid Dynamics International Inc. of Illinois, USA (FDI). FIDAP is a registered trademark of FDI. Other simulation programs are commercially available, but FIDAP was chosen for its high accuracy in transient fluid dynamic, energy transport, and surface tension calculations. The version of FIDAP used is FTDAP 7.06. Theoretical basis of calculations The theoretical basis for fluid dynamic and energy transport calculations using the Finite Element Method, and the manner that this theoretical basis is applied to the FIDAP computer program, is described in detail in the FIDAP 7.0 Theory Manual (April 1993) published by FDI, the disclosure of which is hereby incoφorated by reference. Material characteristics The table "Properties of materials used for FTDAP simulation" gives approximate physical properties of materials which may be used in the fabrication of the print head. The properties of 'ink' used in this simulation are estimates for a hot melt black ink containing a solid pigment dispersed in a vehicle comprising a mixture of C J8 -C 2 acids or alcohols and/or appropriate waxes with melting points between 60°C and 80°C. At the ambient temperature of the simulation (80°C), the vehicle is liquid, with a viscosity of approximately 100 cP. The viscosity values for the hot melt ink do not represent any particular formulation, but rather a recommended target viscosity curve. The black colorant is 2% Acheson graphite with a particle size less than 10 μm. The graphite provides an intense black colorant with excellent stability and lightfastness, as well as increasing the thermal conductivity of the ink. Acheson graphite has a thermal conductivity of 150 W m "1 K "1 parallel to the axis of extrusion, and 111 W m '1 K "1 normal to the axis of extrusion at 100°C. Inclusion of graphite as the colorant increases the thermal conductivity of the ink vehicle. This is important, as a relatively high thermal conductivity is desirable for high speed and low power operation. If the colorant chosen does not have a high thermal conductivity, and the ink vehicle has a low thermal conductivity, then additives to increase the thermal conductivity to at least 0.5 W m "1 K "1 are recommended for high speed printers. To obtain convergence for transient free surface simulations with variable surface tension at micrometer scales with microsecond transients using FIDAP 7.06, it is necessary to nondimensionalize the simulation. The values which have been used in the example simulation using the FTDAP program are shown in the table "Properties of materials used for FIDAP simulation". Most values are from CRC Handbook of Chemistry and Physics, 72nd edition, or Lange's handbook of chemistry, 14th edition. Properties of materials used for FIDAP simulation Results of fluid dynamic simulations Figures 20 to 25 are plots of an example nozzle from a combined theπnal and fluid dynamic simulation. Axi-symmetric simulation is used, as the example nozzle is cylindrical in form. There are five deviations from cylindrical form. These are the connections to the heater, the laminar air flow caused by paper movement, gravity (if the printhead is not vertical), the geometry of the nozzle baπel more than 25 μm from the axis of symmetry, and the presence of adjacent nozzles in the substrate. The effect of these factors on drop ejection is minor. Figure 22 is a graph of ink pressure as a function of time. The pressure varies sinusoidally with a period of 72 μs. Three pressure cycles are shown. The horizontal axis is in units of 100 us, from 0 μs to 216 μs. Figure 21 shows the temperature at various points in the nozzle as a function of time, with an electrothermal pulse apphed during the third cycle of figure 20. The pulse starts at 160 μs, and has a duration of 36 μs. The pulse is shaped top maintain the temperature at the nozzle tip (where the ink meniscus meets the nozzle) approximately constant at 180°C for the duration of the pulse. This is shown by the curve B. The curve A shows the temperature at the centre of the heater. The curve C shows the temperature at a point on the surface of the print head 14.5 μm from the heater. The horizontal axis is identical to that of figure 20. The vertical axis is in units of 100°C. The ambient temperature is 80°C. Figure 22 shows the position of the meniscus extremum as a function of time. The horizontal axis is identical to that of figure 20. The first two cycles (0 us to 144 μs) show unselected drops, where the heater is not energized. In this case, the temperature is low and the viscosity is high (100 cP). The high viscosity results in a small motion (approximately 2 μm peak to peak) in response to the pressure variations shown in figure 20. During the third cycle of the pressure wave, the heater is energized, resulting in the temperature increase shown in figure 21. The reduced viscosity results in a meniscus movement of approximately 10 μm. The difference in meniscus position between the unselected drops and the selected drops allows the drop separation means to ensure that selected drops proceed to form spots on the recording medium, and unselected drops do not. The drop separation means is not modeled in this simulation, and therefore the selected drop moves back into the nozzle. This can be seen in figure 22 during the period from 196 μs to 216 μs. Figures 23, 24, 25, 27 and 28 show cross sections of a nozzle during operation. Only the region in the tip of the nozzle is shown, as most phenomena relevant to drop selection occur in this region. These plots show a cross section of the nozzle tip, from the axis of symmetry out to a distance of 22 μm. The nozzle radius is 10 μm, and the plots are to scale. In these figures 100 is ink, 101 is the sihcon substrate, 102 is SiO 2 , 103 marks the position of one side of the annular heater, 108 is a Si 3 N 4 passivation layer and 109 is a lipophobic surface coating. Figures 23(a),23(c), 23(e), 23(i) show thermal contours at 5°C intervals. Figures 23(b), 23(d), 23(f), 23(h), and 23(j) show viscosity contours and drop evolution at various times during a drop ejection cycle. Figure 23(a) shows the temperature contours at the start of the heater energizing pulse, at a time of 160 μs as shown in figures 20 to 22. The power applied to the heater at this time is 180 mW. The ambient temperature is 80°C, and temperature contours are shown at 5°C intervals from 85°C to 120°C. Figure 23(b) shows the viscosity contours at a time of 160 μs. The bulk ink viscosity is 100 cP, and there is little variation in viscosity at this time. The lines in the sohd materials (sihcon 101, SiO 2 102, and Si 3 N 108) show the finite element calculation mesh. Figure 23(c) shows the temperature contours 10 μs after the start of the heater energizing pulse, at a time of 170 μs. The power apphed to the heater at this time is 74 mW. Temperature contours are shown at 5°C intervals from 85°C to 195°C. Figure 23(d) shows the viscosity contours at a time of 170 μs. The ink viscosity varies from 100 cP away from the heater to below 2 cP near the heater. Figure 23(e) shows the temperature contours 20 μs after the start of the heater energizing pulse, at a time of 180 μs. The power apphed to the heater at this time is 60 mW. Figure 23(f) shows the viscosity contours at a time of 180 μs. The reduced ink velocity has allowed the increase in ink pressure to move the ink further than it would have moved had the heater not been energized. The viscosity is lowest at the walls of the nozzle tip, where the temperature is highest. This aids in the movement of the ink, as the retarding effect of ink viscosity on ink movement is greater near the walls of the nozzle than at the axis of the nozzle. Figure 23(g) shows the temperature contours 30 μs after the start of the heater energizing pulse, at a time of 190 μs. The power apphed to the heater at this time is 58 mW. Figure 23(h) shows the viscosity contours at a time of 190 μs. The 'crinkling' of the viscosity contour (especially visible on the 4 cP contour) is a calculation artifact of the finite element simulation, resulting from inteφolation within elements combined with the non-linear relationship between temperature and viscosity. The effect of this inteφolation on the simulation is negligible. Figure 23(i) shows the temperature contours 40 μs after the start of the heater energizing pulse, at a time of 200 μs. This is 4 μs after the heater has been turned off, and the maximum temperature at this stage is 155°C. Figure 23(j) shows the viscosity contours at a time of 200 μs. At this stage, the drop separation means would become the major factor determining meniscus position. Most of the high temperature, low viscosity ink proceeds to form the selected drop and produce a spot on the recording medium. The reduced viscosity and elevated temperature of the selected drop aids in binding the drop to the fibers of a fibrous recording medium before the drop freezes. Figure 24 shows the movement of meniscus position during a cycle when the ink drop is not selected. Ink meniscus positions at 10 μs intervals from 88 μs to 128 μs are shown. These conespond to the same phases of the ink pressure wave as the intervals from 160 μs to 200 μs shown in figure 25. The meniscus moves approximately 2 μm in response to the oscillating pressure. Figure 25 shows the movement of meniscus position during a drop selection cycle. Ink meniscus positions at 10 μs intervals from 160 μs to 200 μs are shown. These coπespond to the same phases of the ink pressure wave as the intervals from 88 μs to 128 μs shown in figure 24. The meniscus moves approximately 10 μm in response to the oscillating pressure, due to the lower viscosity of the heated ink. Figure 26 shows the position of the meniscus extremum as a function of time for a simulation in which the frequency of the ink pressure wave, and frequency of drop selection and separation are halved. The maximum printing rate of this aπangement is one half that of the arrangement for which simulation results are shown in figures 20 to 25. However, the absolute difference in position between unselected drops and selected drops is greater, providing an increased operating margin for the drop separation process. The horizontal axis is similar to that of figure 20, but the time axis is expanded by a factor of two. The vertical scale of this graph is different from that of figure 20. The first two cycles (0 μs to 288 μs) show unselected drops, where the heater is not energized. In this case, the temperature is low and the viscosity is high (100 cP). The high viscosity results in a small motion (approximately 4 μm peak to peak) in response to the pressure variations with a period of 144 μs. During the third cycle of the pressure wave, the heater is energized. The reduced viscosity results in a meniscus movement of approximately 15 μm. The drop separation means is not modeled in this simulation, and therefore the selected drop moves back into the nozzle. This can be seen in figure 26 during the period from 392 μs to 432 μs. Figure 27 shows the movement of meniscus position during a cycle when the ink drop is not selected. Ink meniscus positions at 20 μs intervals from 176 μs to 256 μs are shown. These coπespond to the same phases of the ink pressure wave as the intervals from 320 μs to 400 μs shown in figure 28. The meniscus moves approximately 4 μm in response to the oscillating pressure. Figure 28 shows the movement of meniscus position during a drop selection cycle. Ink meniscus positions at 20 μs intervals from 320 μs to 400 μs are shown. These coπespond to the same phases of the ink pressure wave as the intervals from 176 μs to 256 μs shown in figure 27. The meniscus moves approximately 16 μm in response to the oscillating pressure, due to the lower viscosity of the heated ink. The nozzles for which simulation results are shown in figures 20 to 28 are of a different design than the nozzles shown in figures 1 and 2. There are many possible designs for nozzles for print heads. As the fundamental requirements of a nozzle are somewhat simpler than the requirements of a thermal ink jet nozzle, the actual geometry chosen for the nozzle can largely be determined for convenience in the manufacturing process. Variable drop size Several mechanisms may be used to achieve variable drop size, to allow operation as a contone printer instead of a bi-level printer. The range of drop size variation will depend upon the exact characteristics of the print head, drive circuitry, drop separation means, and ink used. Means of achieving modulation of drop size on a drop-by-drop basis include: 1 ) Modulation of the time of the leading edge of the heater pulse, maintaining the trailing edge constant. 2) Modulation of the time of the trailing edge of the heater pulse, maintaining the leading edge constant. 3) Modulation of the time of the leading edge of the heater pulse, maintaining the pulse width constant. 4) Modulation of the voltage of the heater pulse. The foregoing describes various general and preferred embodiments of the present invention. Characteristics of one detailed prefeπed embodiment are set forth in the tables of Appendix A. Modifications, obvious to those skilled in the art, can be made to the general and specific embodiments without departing from the scope of the invention. Appendix A AppendixA (cont'd.)

Claims: I Claim: 1. A method of drop on demand printing comprising the steps of: (1) addressing the ink in selected nozzles of a print head with the coincident forces of: (a) above ambient manifold pressure and (b) a selection energy pulse that, in combined effects, are sufficient to cause addressed ink portions to move out of their related nozzle to a predetermined region, beyond the ink in non-selected nozzles, but not so far as to separate from their contiguous ink mass; and (2) during such addressing step, attracting ink from the print head toward a print zone with forces of magnitude and proximity that: (a) cause the selected ink moved into said region to separate from its contiguous ink mass and (b) do not cause non-addressed ink to so separate. 2. The method of claim 1 wherein the step of addressing comprises heating ink in selected nozzles. 3. The method of claim 2 wherein the ink composition and heating energy are such that drop selection is effected by surface tension differences between ink in addressed and non-addressed nozzles. 4. The invention defined in claim 2 wherein the ink composition and heating energy are such that drop selection is effected by viscosity differences between ink in addressed and non-addressed nozzles. 5. The invention defined in claim 1 wherein said attracting step employs an electric field and said ink is electrically conductive. 6. The invention defined in claim 1 wherein said attracting step employs a magnetic field and said ink is magnetically attractable. 7. A drop-on-demand printing system comprising an ink that is magnetically or electrically attractable and a printer having nozzles and means for subjecting ink in the nozzles to pressure which is either at least 2% above ambient air pressure, or which varies in a cyclic manner, said printer further including an electrically controlled means for selecting a drop by reducing the surface tension or viscosity of said drop sufficiently so that the meniscus of said selected drop moves, under said pressure, to a different position than the meniscus of unselected drops, and drop separation means for attracting the selected drop from the printer to a recording medium. 8. A system as claimed in claim 7 where said means for reducing surface tension comprises means for applying heat to the tip of selected nozzles. 9. A system as claimed in claim 8 where the means for applying heat to the tip of selected nozzles is an electrothermal actuator. 10. A system as claimed in claim 7 where said means for reducing viscosity comprises means for applying heat to selected nozzles. 11. A system as claimed in claim 10 where said means of applying heat to the tip of selected nozzles is an electrothermal actuator. 12. A system as claimed in claim 7 where the drop separation means is an electric field acting on electrically conductive ink. 13. A system as claimed in claim 7 where the drop separation means is a magnetic field acting on hquid ink which contains magnetically active particles. 14. A system as claimed in claim 7 where the recording medium is paper. 15. A system as claimed in claim 7 where the recording medium is a transparent film. 16 A system as claimed in claim 7 where the recording medium is cloth. 17. The method defined in claim 1 wherein such heating of ink is such that the energy required to select and separate a drop of ink is less than the energy required to raise the temperature of non-separated ink of equal volume to a drop selection level. 18. The system defined in claim 7 wherein said ink and electrically controlled means are constructed so that the energy required to select and separate drops are less than the energy that would raise equivalent non-separated ink volumes to separation level of temperature. 19. A thermally activated liquid ink printing head being characterized by the energy required to eject a drop of ink being less than the energy required to raise the temperature of the bulk ink of a volume equal to the volume of said ink drop above the ambient ink temperature to a temperature which is below the drop ejection temperature. 20. A drop on demand printing system as claimed in claim 7 wherein said drop selection means reduces the viscosity of ink in the vicinity of the drop to be selected. 21. A drop on demand printing system as claimed in claim 20 wherein reduction of ink viscosity is caused by an increase in temperature in the vicinity of the drop to be selected. 22. A drop on demand printing system as claimed in claim 21 wherein the temperature of the ink is raised, in the vicinity of the drop to be selected, by means of an electrothermal actuator. 23. A drop on demand printing system as claimed in claim 22 wherein a difference in meniscus position of said elected drop is produced by said drop selection means and said difference in meniscus position of said selected drop is insufficient to cause selected drops to separate from said body of ink. 24. A drop on demand printing apparatus as claimed in claim 20 wherein said means for subjecting ink to pressure is adapted to apply pressure varying in a cyclic manner. 25. A drop on demand printing system as claimed in claim 20 wherein the ink used is sohd at room temperature, but hquid at the operating temperature of the print head. 26. A drop on demand printing system as claimed in claim 24 wherein said variations in ink pressure are produced by a piezoelectric device to which is applied to a varying voltage. 27. A drop on demand printing system as claimed in claim 26 wherein said ink pressure is caused to fluctuate at the frequency of drop ejection, or a multiple thereof. 28. A drop on demand printing system as claimed in claim 20 wherein the recording medium is a plastic film. 29. A drop on demand printing system as claimed in claim 20 wherein the drop separation means is proximity of the recording medium to the print head.

Inventors: SILVERBROOK KIA, SILVERBROOK, KIA
Applicants: EASTMAN KODAK CO, SILVERBROOK KIA, EASTMAN KODAK COMPANY, SILVERBROOK, KIA
Application year: 1996
Main classification: B41J2
IPC codes: B41J2