Abstract:
A drop on demand microfluidic ink jet printing system includes an ink flow chamber having a nozzle opening in a wall of the flow chamber through which ink droplets are ejected when ink in the flow chamber is at or above a predetermined positive pressure. An inlet channel opens into the flow chamber to supply thermally-responsive ink to the flow chamber at or above the predetermined pressure. A microfluidic outlet channel communicates the flow chamber with a low pressure ink reservoir such that thermally-responsive ink is normally transported from the flow chamber at a flow velocity sufficient to maintain ink in the flow chamber at a pressure less than the predetermined positive pressure. A valve selectively restricts the flow of the thermally-responsive ink through the microfluidic outlet channel sufficiently to cause an increase in ink pressure in the flow chamber to at least the predetermined positive pressure, the valve including a heater in contact with at least a portion of the associated microfluidic outlet channel, whereby the viscosity of the thermally-responsive ink can selectively be increased by heat from the heater to restrict the flow of the thermally-responsive ink from the flow chamber such that an ink droplet is ejected through the nozzle opening.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     Reference is made to commonly assigned co-pending U.S. patent application Ser. No. 09/735,322 filed in the names of Yang et al. on Dec. 12, 2000. 
    
    
     FIELD OF THE INVENTION 
     This invention generally relates to a drop-on-demand ink jet printer having a droplet separator that includes a mechanism for assisting the selective generation of micro droplets of ink. 
     BACKGROUND OF THE INVENTION 
     Drop-on-demand ink jet printers selectively eject droplets of ink toward a printing media to create an image. Such printers typically include a print head having an array of nozzles, each of which is supplied with ink. Each of the nozzles communicates with a chamber that can be pressurized in response to an electrical impulse to induce the generation of an ink droplet from the outlet of the nozzle. Such printers, commercial and theoretically-known, use piezoelectric transducers, thermally-actuated paddles, change in liquid surface tensions, etc. to create the momentary forces necessary to generate an ink droplet. Each of the known technologies has advantages and disadvantages. 
     The present invention proposes a microfluidic system for providing momentary forces necessary to generate an ink droplet, and to provide an attractive alternative to known technologies. Microfluidic systems are very important in several applications. For example, U.S. Pat. No. 5,445,008 discloses these systems in biomedical research such as DNA or peptide sequencing. U.S. Pat. No. 4,237,224 discloses such systems used in clinical diagnostics such as blood or plasma analysis. U.S. Pat. No. 5,252,743 discloses such systems used in combinatorial chemical synthesis for drug discovery. U.S. Pat. No. 6,055,002 also discloses such systems for use in ink jet printing technology. 
     SUMMARY OF THE INVENTION 
     According to a preferred embodiment of the present invention, a drop on demand ink jet printing system includes an ink flow chamber having a nozzle opening in a wall of the flow chamber through which ink droplets are ejected when ink in the flow chamber is at or above a predetermined positive pressure. An inlet channel opens into the flow chamber to supply ink to the flow chamber at or above the predetermined pressure. An outlet channel communicates the flow chamber with a low pressure ink reservoir such that ink is normally transported from the flow chamber at a flow velocity sufficient to maintain ink in the flow chamber at a pressure less than the predetermined positive pressure. A valve selectively restricts the flow of ink through the outlet channel sufficiently to cause an increase in ink pressure in the flow chamber to at least the predetermined positive pressure, whereby an ink droplet is ejected through the nozzle opening. 
     According to another preferred embodiment of the present invention, a microfluidic system includes a fluid flow chamber having a nozzle opening in a wall of the flow chamber through which fluid droplets are ejected when fluid in the flow chamber is at or above a predetermined positive pressure. An inlet channel opens into the flow chamber to supply thermally-responsive fluid to the flow chamber at or above the predetermined pressure. A microfluidic outlet channel communicates the flow chamber with a low pressure fluid reservoir such that thermally-responsive fluid is normally transported from the flow chamber at a flow velocity sufficient to maintain fluid in the flow chamber at a pressure less than the predetermined positive pressure. A valve selectively restricts the flow of the thermally-responsive fluid through the microfluidic outlet channel sufficiently to cause an increase in fluid pressure in the flow chamber to at least the predetermined positive pressure, the valve including a heater in contact with at least a portion of the associated microfluidic outlet channel, whereby the viscosity of the thermally-responsive fluid can selectively be increased by heat from the beater to restrict the flow of the thermally-responsive fluid from the flow chamber such that an fluid droplet is ejected through the nozzle opening. 
     According to still another preferred embodiment of the present invention, a drop on demand microfluidic ink jet printing system includes an ink flow chamber having a nozzle opening in a wall of the flow chamber through which ink droplets are ejected when ink in the flow chamber is at or above a predetermined positive pressure. An inlet channel opens into the flow chamber to supply thermally-responsive ink to the flow chamber at or above the predetermined pressure. A microfluidic outlet channel communicates the flow chamber with a low pressure ink reservoir such that thermally-responsive ink is normally transported from the flow chamber at a flow velocity sufficient to maintain ink in the flow chamber at a pressure less than the predetermined positive pressure. A valve selectively restricts the flow of the thermally-responsive ink through the microfluidic outlet channel sufficiently to cause an increase in ink pressure in the flow chamber to at least the predetermined positive pressure, the valve including a heater in contact with at least a portion of the associated microfluidic outlet channel, whereby the viscosity of the thermally-responsive ink can selectively be increased by heat from the heater to restrict the flow of the thermally-responsive ink from the flow chamber such that an ink droplet is ejected through the nozzle opening. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic cross-sectional side view of a nozzle in a drop-on-demand print head that utilizes a thermally-actuated valve according to an embodiment of the present invention; 
     FIG. 2 is a cross-sectional side view of a print head according to another embodiment of the present invention; 
     FIG. 3 is a cross-sectional top view taken along section line  3 — 3  of FIG. 2; 
     FIGS. 4A-4D illustrate the development and release of a liquid droplet from the print head of FIGS. 2 and 3; and 
     FIG. 5 is a cross-sectional top view similar to FIG. 3 of another embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     With reference to FIG. 1, a print head  10  includes a nozzle plate  12  having an outer surface  14  and an inner surface  16 . A back substrate  18  has an outer surface  20  and an inner surface  22 . Nozzle plate  12  and back substrate  18  may be silicon, glass, quartz, ceramics, or polymeric substrates such as plastics (polyamide, polymethylmethacrylate (PMMA), polycarbonate, polytetrafluoroethylene, Teflon®, polydimethylsiloxane (PDMS), polyvinylchloride (PVC), polysulfone, etc.). Inner surfaces  16  and  22  define an ink flow passage  24  through which is caused to flow from a pressurized source  26  to a low pressure reservoir  28 . Nozzle plate  12  has plurality of circular nozzles  30 , only one of which is shown. Each nozzle has its own dedicated ink flow passage. The liquid ink forms a meniscus  32  around the upper side walls of nozzle  30 . Depending on the pressure of the ink at the nozzle opening, the meniscus may be concave or convex, but it is thought that best operation will be obtained by keeping the ink pressure at the opening just below that necessary to overcome the surface tension of the ink to cause ejection of a droplet from the nozzle. Ink pressure at the nozzle opening is a function of the pressures of source  26  and reservoir  28 , frictional losses through flow passage  24 , and the Bernoulli effect of ink flow past nozzle  30 . A pump  29  maintains a sufficient pressure differential to maintain flow through the system. 
     A pair of heaters  34  and  36  is positioned on inner surfaces  16  and  22 , respectively, such that a microfluidic valve is formed in ink flow passage  24  to ink flow there through. A single heater could extend substantially around ink flow passage  24 . The term, “microfluidic”, “microscale” or “microfabricated” generally refers to structural elements or features of a device, such as ink flow passage  24 , having at least one fabricated dimension in the range from about 0.1 μm to about 500 μm. In devices according to the present invention, microscale ink flow passage  24  preferably have at least one internal cross-section dimension, e.g., depth, width, length, diameter, etc., between about 0.1 μm to about 500 μm, preferably between about 1 μm to about 200 μm. 
     Heaters  34  and  36  are preferably made from appropriately doped polysilicon, is fabricated on surfaces  16  and  22 , respectively. A conducting material, not shown, such as aluminum or copper, is also integrated to serve as wires to connect the heaters to an external power supply. In a preferred embodiment of the invention, the microfluidic devices are fabricated using CMOS compatible fabrication techniques, and the heaters are integrated with a CMOS circuit on the chip, which controls the signals or voltages applied to the heaters to activate the valve. 
     The print heads of the present invention are preferably fabricated with the techniques commonly associated with the semiconductor electronics industry, e.g., photolithography, dry plasma etching, wet chemical etching, etc., on the surface of a suitable substrate material, such as silicon, glass, quartz, ceramics, as well as polymeric substrates, e.g., plastics. In a preferred embodiment of the invention, print heads comprise two or more layers of fabricated components that are appropriately mated or joined together. 
     Various techniques using chip technology for the fabrication of microfluidic devices, and particularly micro-capillary devices, with silicon and glass substrates have been discussed by Manz, et al. ( Trends in Anal. Chem . 1990, 10, 144, and  Adv. In Chromatog . 1993, 33, 1). Other techniques such as laser ablation, air abrasion, injection molding, embossing, etc., are also known to be used to fabricate microfluidic devices, assuming compatibility with the selected substrate materials. 
     The function of a microfluidic valve is to control the flow rate or volume flux of a liquid through a micro-capillary channel. In general, for a fluid with a viscosity of μ that is driven through a micro-capillary channel with a length of L by a pressure of P, the volume flux, Q, of the liquid pass through the channel is:          Q   =       P     μ                 L       ·   f       ,                          
     whereof is the dimension factor of the cross-section for the microfluidic channel. For a circular cross-section capillary channel with a radius r:            f   c     =       π                   r   4       8       ,                          
     while for a rectangular cross-section channel with a width a, height b and aspect ratio η=b/a (η≧1),          f   R     =         a   4          [       η   12     -       16     π   5            tanh        (       π   2        η     )           ]       .                            
     It is generally true that the flow rate or the volume flex is inversely proportional to the internal viscosity of fluid in the channel. Therefore, if one can control the viscosity of the fluid in the channel, one can indeed control the flow rate of the fluid passing though the channel. 
     The microfluidic delivery system of the present invention has a microfluidic valve that utilizes the property of a specially formulated thermally-responsive fluid serving as the carrier fluid for transport of subject materials through a microfluidic channel such as ink flow passage  24 . The viscosity of the formulated thermally-responsive fluid is sensitive to the temperature, and preferably increases with the increase of temperature. 
     The “subject materials” simply refers to the materials, such as chemical or biological compounds, of interest, which may also include a variety of different compounds, including chemical compounds, mixtures of chemical compounds, e.g., a dye, a pigment, a protein, DNA, a peptide, an antibody, an antigen, a cell, an organic compound, a surfactant, an emulsion, a dispersion, a polysaccharide, colloidal particles, organic or inorganic compounds, nucleic acids, or extracts made from biological materials, such as bacteria, plains, fungi, or animal cells or tissues, naturally occurring or synthetic compositions. In the preferred embodiment of the present invention, the subject material is a printing dye or pigment. 
     The thermally-responsive material may comprise at least one kind of block copolymer with at least one block comprising poly(ethylene oxide), commonly referred to as PEO. In another form, the thermally-responsive material comprises a tri-block copolymer of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide), commonly referred to as PEO-PPO-PEO dissolved in an aqueous solution. The preferred concentrations of the solutions are from about 5% to about 80%, preferably from 10% to 40% in weight. 
     The solutions at room temperature, e.g., 22° C., are fluidic with a typical viscosity less than 10 centipoise. The viscosity of the formulated solutions increases dramatically when raising the temperature from about 30° C. to about 80° C., as the solutions rapidly form non-fluidic gels at the elevated temperature. The viscosity change of the formulated solutions in response of temperature change is entirely reversible as the solutions turn to fluidic having the original viscosity when cooled down to its initial temperature. 
     In yet another form, a methyl cellulose polymer may be used as a thermally-responsive material in the carrier fluid. For example, 2.75 wt. % solution of METHOCEL® K100LV (Dow Chemical Co.) having a viscosity of about 1 poise at 50° C. and a viscosity of more than 10 poise at 75° C. can be used. 
     EXAMPLE 1 
     Viscosity vs. Temperature of Thermally-responsive Solutions 
     Thermally-responsive solutions were formulated by dissolving a tri-block copolymer of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide), or PEO-PPO-PEO in an aqueous solution. A series of the PEO-PPO-PEO tri-block copolymers were obtained from BASF under the product trade name of Pluronic®. 
     A Rheometrics ARES Fluids Spectrometer, from Rheometric Scientific, Inc., equipped with a corvette geometry, was used to measure the oscillatory shear properties of the Pluronic® solutions. Dynamic viscosity was measured continuously as the temperature was ramped from 20° C. to 80° C. The typical ramp rate was 1° C. per minute. The fluids were initially characterized at 20° C. in a continuous shear experiment covering a typical range of shear rates from 1 to 100 per second. All were found to have low viscosity and Newtonian response. For the temperature scan experiments, a monitoring frequency of 10 radians per second was used. 
     The results are shown in the following tables: 
     
       
         
               
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
             
             
               
                   
                   
               
               
                   
                 Viscosity (Poise) of Pluronic ® P85 Solutions 
               
             
          
           
               
                 Temperature (° C.) 
                 20% 
                 15% 
                 10% 
               
               
                   
               
             
          
           
               
                 25 
                 0.09 
                 0.037 
                 0.022 
               
               
                 30 
                 0.112 
                 0.033 
                 0.017 
               
               
                 35 
                 0.113 
                 0.031 
                 0.014 
               
               
                 40 
                 0.096 
                 0.026 
                 0.012 
               
               
                 45 
                 0.079 
                 0.022 
                 0.01 
               
               
                 50 
                 0.066 
                 0.019 
                 0.008 
               
               
                 55 
                 0.054 
                 0.016 
                 0.007 
               
               
                 60 
                 0.05 
                 0.014 
                 0.006 
               
               
                 62 
                 0.069 
                 0.016 
                 0.007 
               
               
                 64 
                 0.143 
                 0.029 
                 0.011 
               
               
                 66 
                 0.382 
                 0.065 
                 0.022 
               
               
                 68 
                 1.283 
                 0.185 
                 0.059 
               
               
                 70 
                 5.176 
                 0.792 
                 0.194 
               
               
                 72 
                 15.018 
                 3.684 
                 0.821 
               
               
                 74 
                 31.802 
                 11.303 
                 3.534 
               
               
                 76 
                 46.005 
                 21.505 
                 9.134 
               
               
                 78 
                 52.008 
                 28.574 
                 13.39 
               
               
                 80 
                 51.921 
                 30.369 
                 17.917 
               
               
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Viscosity of 25% Pluronic ® L62 Solution 
               
             
          
           
               
                   
                 Temperature (° C.) 
                 Viscosity (Poise) 
               
               
                   
                   
               
             
          
           
               
                   
                 22 
                 0.072 
               
               
                   
                 25 
                 0.068 
               
               
                   
                 28 
                 0.069 
               
               
                   
                 30 
                 0.073 
               
               
                   
                 32 
                 0.081 
               
               
                   
                 34 
                 0.1 
               
               
                   
                 36 
                 0.136 
               
               
                   
                 38 
                 0.237 
               
               
                   
                 40 
                 0.44 
               
               
                   
                 42 
                 0.834 
               
               
                   
                 44 
                 0.976 
               
               
                   
                 46 
                 1.777 
               
               
                   
                 48 
                 5.864 
               
               
                   
                 49 
                 26.704 
               
               
                   
                 50 
                 37.107 
               
               
                   
                 52 
                 40.677 
               
               
                   
                 54 
                 35.045 
               
               
                   
                 56 
                 31.245 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Viscosity of 22% Pluronic ® F87 Solution 
               
             
          
           
               
                   
                 Temperature (° C.) 
                 Viscosity (Poise) 
               
               
                   
                   
               
             
          
           
               
                   
                 22 
                 0.201 
               
               
                   
                 25 
                 0.242 
               
               
                   
                 30 
                 0.525 
               
               
                   
                 32 
                 0.696 
               
               
                   
                 34 
                 0.968 
               
               
                   
                 36 
                 1.225 
               
               
                   
                 37 
                 1.505 
               
               
                   
                 38 
                 385 
               
               
                   
                 39 
                 13873 
               
               
                   
                 40 
                 17046 
               
               
                   
                 41 
                 15056 
               
               
                   
                 42 
                 14963 
               
               
                   
                 45 
                 14512 
               
               
                   
                 50 
                 15008 
               
               
                   
                 55 
                 15509 
               
               
                   
                   
               
             
          
         
       
     
     The above results show that the Pluronic® P85 solutions with the concentrations from 10% to 20% have viscosity increases of more than 3 orders of magnitude when the temperature increases from 60° C. to 80° C., the 25% Pluronic® L62 solution has a 3 orders of magnitude viscosity increase with temperature from 30° C. to 50° C., and the 22% Pluronic® F87 solution has a more than 5 orders of magnitude viscosity increase with temperature from 30° C. to 40° C. The results demonstrated that these fluids are thermally-responsive and can be used in the device and method of the invention. 
     EXAMPLE 2 
     A Set of Thermally Responsive Inks with Cyan, Magenta, Yellow, and Black (CMYK) Colors 
     The thermally responsive inks were formulated by dissolving 15% wt of Pluronic® P85 in an aqueous solution. For black ink, a 5% wt dye of Food Black2 was added, for cyan ink a 6% wt dye of Avecia ProJet® Cyan Fast2 was added, for magenta ink a 5% wt dye of Tricon acid Red52 was added, and for yellow ink a 5% wt dye of acid Yellow was added. 
     The viscosity vs. temperature measurements of thermally responsive inks were carried as descript above in Example 1 and the results are shown in Table 4 
     
       
         
               
             
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Viscosity vs. temperature of the thermally responsive inks 
               
             
          
           
               
                   
                 Viscosity (CentiPoise) of Thermally Responsive 
               
               
                   
                 Inks 
               
             
          
           
               
                 Temperature (° C.) 
                 Black 
                 Cyan 
                 Magenta 
                 Yellow 
               
               
                   
               
             
          
           
               
                 25 
                 6.9 
                 5.1 
                 5.1 
                 6.1 
               
               
                 60 
                 3.2 
                 2.0 
                 2.1 
                 2.8 
               
               
                 85 
                 3200 
                 3100 
                 41 
                 30 
               
               
                   
               
             
          
         
       
     
     The above results show that all the formulated thermally responsive inks have viscosities less than 7 centipoise from room temperature to about 60° C. and have viscosities more than 30 centipoise at 85° C. The black and cyan inks even have viscosities more than 3000 centipoise at 85° C. The results demonstrated that these inks are thermally responsive and can be used in the method of the invention. 
     In operation, dye or pigment in a specially formulated thermally-responsive carrier fluid is transported through ink flow passage  24  past nozzle  30  and microfluidic valve heaters  34  and  36 . The liquid forms meniscus  32  around the upper side walls of nozzle  30 . Depending on the pressure of the liquid at the nozzle opening, the meniscus may be concave or convex, but it is thought that best operation will be obtained by keeping the ink pressure at the opening just, below that necessary to overcome the surface tension of the ink to cause ejection of a droplet from the nozzle. Ink pressure at the nozzle opening is a function of the pressures of source  26  and reservoir  28 , frictional losses through flow passage  24 , and the Bernoulli effect of ink flow past nozzle  30 . 
     Droplets are emitted from nozzle  30  by applying electrical pulses to heaters  34  and  36  causing heat generated by the heaters to be transmitted to the solution. The viscosity of the formulated solution increases dramatically when raising the temperature from about 30° C. to about 80° C., as the solutions rapidly form non-fluidic gels at the elevated temperature. The increased viscosity quickly forms a gel, blocking the right side of ink flow passage  24  and increasing the pressure at nozzle  30 . The increased pressure overcomes the surface tension on the meniscus, causing a droplet to be generated. Details of droplet generation will be illustrated in detail herein below with respect to another embodiment of the invention. The end result is that an ink droplet is expelled at a high velocity from the nozzle outlet, which in turn causes it to strike its intended position on a printing medium with greater accuracy. 
     The viscosity change of the formulated solutions in response of temperature change is entirely reversible as the solutions turn to fluidic having the original viscosity when cooled down to its initial temperature. Flow resumes through the right side of passage  24  and the pressure returns to a level incapable of droplet formation. 
     FIG. 2 is a side sectional view of a print head according to another embodiment of the present invention. FIG. 3 is a cross-sectional top view taken along section line  3 — 3  of FIG. 2. A print head  40  includes a nozzle plate  44  having an outer surface  42  and an inner surface  46 . A back substrate  48  has an inner surface  52 . Inner surfaces  46  and  52  define an ink flow passage  54  through which is caused to flow from a pressurized source, not shown, to a low pressure reservoir  58 . Nozzle plate  44  has plurality of circular nozzles  60 , only one of which is shown. Each nozzle  60  has its own dedicated ink flow passage in fluid isolation one from another. The plural nozzles are spaced from each other at least sufficiently that the flow passages of adjacent nozzles do not interfere with its neighbor. 
     As illustrated in FIG. 4A, the liquid ink forms a meniscus  62  around the upper side walls of nozzle  60 . Depending on the pressure of the ink at the nozzle opening, the meniscus may be concave or convex. It is thought that best operation will be obtained by keeping the ink pressure at the opening just below that necessary to overcome the surface tension of the ink to cause ejection of a droplet from the nozzle. Ink pressure at the nozzle opening is a function of the pressures of the ink source and reservoir  58 , frictional losses through flow passage  54 , the Bernoulli effect of ink flow past nozzle  60  and, referring again to FIGS. 2 and 3, the amount of flow restriction imposed by a micro-capillary grill made up of a plurality of heater rings shown schematically as rings  64  and  66 . 
     The heater rings are positioned in back substrate  48  such that the micro-capillary grill forms a microfluidic valve in the ink flow path between passage  54  and reservoir  58 . The flow passages of the grill has radial opening dimensions in the range from about 0.1 μm to about 500 μm, preferably between about 1 μm to about 200 μm. Conducting material, not shown, such as aluminum or copper, is integrated to serve as wires to connect the heater rings to an external power supply. The microfluidic valve controls the flow rate or volume flux of liquid through the micro-capillary grill; the flow rate or the volume flex being inversely proportional to the internal viscosity of fluid in the channel. The viscosity of the formulated thermally-responsive fluid is sensitive to the temperature, and preferably increases with the increase of temperature. 
     In operation, dye or pigment in a specially formulated thermally-responsive carrier fluid is transported radially inwardly through ink flow passage  54 , past nozzle  60  through the micro-capillary grill formed by rings  64  and  66 , into reservoir  58 . Droplets are emitted from nozzle  60  by applying electrical pulses to heater rings  64  and  66 , and to a heater on the inner wall  70  of the circular opening through back substrate  48 ; causing heat generated by the heaters to be transmitted to the solution. Referring sequentially to FIGS. 4B-4D, the viscosity of the formulated solution increases dramatically when raising the temperature from about 30° C. to about 80° C., as the solutions rapidly form non-fluidic gels at the elevated temperature. The increased viscosity quickly forms a gel, blocking the flow through the micro-capillary grill and increasing the pressure at nozzle  60 . The increased pressure overcomes the surface tension on the meniscus, causing a droplet to be generated. An ink droplet is expelled at a high velocity from the nozzle outlet, which in turn causes it to strike its intended position on a printing medium with greater accuracy. 
     The viscosity change of the formulated solutions in response of temperature change is entirely reversible as the solutions turn to fluidic having the original viscosity when cooled down to its initial temperature. Flow resumes through the micro-capillary grill and the pressure returns to a level incapable of droplet formation. 
     Referring to FIG. 3, one can appreciate that the spacing between adjacent nozzle openings  60  on a print head must be greater than the diameter of inner wall  70  of the circular opening through back substrate  48 . While this spacing would probably be appropriate for most applications, it is to be noted that the micro-capillary for each of a plurality of nozzles can be fabricated as an array of aligned grill passages  72  through back substrate  48 ′, as illustrated in FIG.  5 . Each array of aligned grill passages has an associated heater, or heaters,  74 . A row or rows of nozzle openings can be positioned orthogonal to the array of grill passages such that the nozzle spacing is reduced.