CELL APPARATUS FOR METERING LIQUID FLOW IN THE RANGE OF LESS THAN 10 ML/MINUTE

Abstract: Apparatus and method for accurately metering liquid flow based on the injection of a brief heat pulse into the flowing stream, e.g., via an electrically insulated thermistor (16), and detection of an electronic time derivative of temperature downstream with, e.g., a sec­ ond electrically insulated thermistor (20). This detection triggers a subsequent heat pulse and the cycle repeats, with pulse total corresponding to elapsed liquid through­ put, and pulse frequency to flow rate.

Description: METHOD AND APPARATUS FOR METERING LIQUID FLOW IN THE RANGE OF LESS THAN 10 CC/MINUTE In order to determine molecular weight or size distribution of separated particles in GPC (Gel Permeation Chromatography) and EDC (Hydrodynamic Chromatography), peak composition is inferred from its elution volume. Elution volume has been determined in chromatography by measuring the. transit time of an unretarded marker species to which the detector is sensitive and relating solute position to marker position. Use of a marker is quite typical since even premium quality liquid chromatographic pumps are generally not capable of better than 0.3% flow stability over-repeated analyses. For this reason, the practice of assuming constant flow and measuring elution time would frequently result in unacceptable uncertainties in the determination of latex particle diameters as an illustrative example. Another flow related source of error for concentration-sensitive detectors (Ultra Violet = Infra Red = IR, Refractive Index = RI, Conductivity) in Liquid Chromatography (LC) is the inverse proportionality between peak area id flow rate, e.g., a 0.5 percent flow decrease produces a 0.5 percent area increase. The most troublesome flow fluctuations are those with periods on the order of peak widths since these cause individual peak areas to change Such fluctuations can occur, e.g., with reciprocating piston pumps because check valve leakage rates tend to change for subsequent pump strokes, and stroke volumes are typically 50 to 500 micro-liters (yl). Present methods for measuring elapsed flow include collecting a volume of eluent in a graduated cylinder, measuring the movement of a bubble injected into the flowing liquid, or accumulating the total number of dumps of a siphon dump counter, all techniques which can be somewhat imprecise or erratic. Other classical flow measuring devices, generally for higher ranges of liquid flow, include the following: 1. Coriolis flow meter, measures mass flow as a function of gyroscopic torque forces. This method is complex and expensive; accuracy is t 0.4 percent 2. Ultrasonic flow meter, suited for gallons per-minute flow; accuracy is i 0.5 percent. 3. Differential Pressure (D/P) flow cell, measures pressure drop across an orifice. This cell is prone to plugging, drift; and is viscosity dependent. 4. Turbine meter, target meter, venturi meter, rotameter, Pitot tube, all principally applicable to flow rates in excess of 50 cc/min. 5. Continuous heat addition flow meter, heats eluent and measures downstream temperature continuously. Result varies with the specific heat of the metered liquid and ambient temperature fluctuations. 6. Self-heating thermistor, undergoes cooling proportional to flow. Nonlinear and result varies with specific heat of solution and ambient temperature variations. The invention relates to a non-invasive liquid metering method and apparatus for determining liquid movement with an attainable precision of i 0.1% under typical LC conditions. The invention particularly satisfies the technical need for an improved liquid metering method and apparatus for accurately metering liquids in the 0.1 to 10 cc/minute range where metering precision becomes extremely important. The inventive method and apparatus uses the principle of injecting a heat pulse into the flowing stream via, e.g., a miniature thermistor (or semiconductor) operated in the self-heating mode and detecting the pulse downstream with, e.g., a second microprobe or fast response thermistor. Pulse detection triggers a subsequent heat pulse upstream and the process is repeated. Salient keys to achieving this technical advance in flow metering include particularly: 1. minimizing the thermal mass of the heat "pulses" and "sensor through the application of semiconductor pulsing and sensing elements; 2. electronically time-differentiating the sensor output to reject characteristically slower ambient thermal drift and to minimize response time in preparation for subsequent pulse detection; 3. application of a flow metering scheme which uses an improved method for high precision flow measurements and flow cell calibration; and 4. development of a flow cell and method, which by component selection and operation, is highly independent of temperature and liquid composition variables. While the general principle of heat pulse injection is not entirely new to liquid metering, being applied previously in the form of what is known as "Knauer Electronic Volumeter distributed through Utopia Instrument Company, Joliet, Illinois, none of the recited technical improvements (1-4) are embodied in this prior liquid flow meter. Among major expressed differences in utility between the invention and the prior flow meter, as taken from the manufacturer's literature, is the development of a successful two-probe metering flow cell (Knauer teaching utility only with respect to a 4 probe device); as well as the extended utility to meter aqueous solvents, a field of utility disclaimed by Knauer. The invention resides in a flow cell for metering liquid flow comprising: (a) a flow cell body having a passageway for flow of a liquid therethrough, said passageway forming a flow through chamber of fixed dimensions; (b) a resistance heating means encapsulated in an electrical insulator which is exposed to the liquid flowing through the passageway; and (c) a heat sensor encapsulated in an electrical insulator which is exposed to the flow of liquid in the passageway in a spaced apart relationship with respect to the resistance heating means. The invention further resides in an apparatus for electronically metering liquid flow, which comprises: (a) a flow cell having a passageway which forms a. flow through chamber of fixed dimensions; (b) a resistance heating means encapsulated in an electrical insulator and a circuit to operate the resistance heating means; (c) a heat sensor encapsulated in an electrical insulator and a circuit to monitor the temperature of the liquid and to measure rate of change of temperature of the liquid, and heat sensor being positioned in said passageway in a fixed, spaced relationship with respect to the resistance heating means; ; (d) a time-differentiating circuit for generating an electrical signal which in magnitude is proportional to dRt/dt, or a time derivative thereof, wherein dRt/dt is the time rate of change of the resistance of the heat sensing thermistor with pulse temperature or during its encounter with the pulse of heated liquid conveyed through said passageway; (e) said circuit means for operating the resistance heating means comprising a timer circuit which is activated by detection of each pulse (d) to apply a timed voltage pulse to the resistance heating means. The invention further resides in a method for electronically metering the flow of Newtonian liquids comprising the steps of: (a) conveying the liquid to be metered through a flow cell having a passageway which forms a flow through chamber of fixed dimensions, said chamber having a predetermined calibrated volume (Vc) and calibrated time constant (K); (b) applying a heat pulse of constant duration from an upstream probe to the liquid and detecting the pulse with a second probe downstream of the first probe, and wherein each detection event triggers the application of a subsequent heat pulse to produce the condition that pulse frequency is related to liquid flow rate (f); (c) electronically detecting the period (T) between pulses; and (d) determining a measure of flow of the metered liquid based on the application of the relationship T = Vc + K. -f Optimum embodiments of the invention use a self-heating thermistor as the heat pulsing element, in conjunction with a fast response thermistor as the heat sensor, each of which includes an electrical insulator, e.g., of glass, which encapsulates the semiconductor thermistor element. In addition, not less than the second time derivative of the resistance of the heat sensing thermistor is taken and used as the signal to pulse the self-heating thermistor. In respect to the method of the invention, other known forms of electronic flow cells (i.e., "flow cells, the metering principle of which is based on the time of flight of an electrically injected heat pulse) can be. operated by the method to produce an improved measure of flow. The optimum practice of the invention uses the inventive electronic flow cell. The term Newtonian liquids as used herein refers to a liquid, the viscosity of which at the metered flow condition is substantially constant. While the invention has been described with regard to applications where actual data is desired to show, as a measure of flow, instantaneous or averaged flow rate or total flow volume with time, the invention can additionally be applied in the form of a control method or instrument, e.g., to regulate a chromatographic or other liquid metering pump, e.g., by continually detecting flow rate and relaying a signal (measure of flow) to the pump to adjust its flow to a metered setting. It is also apparent that while the major expressed technical need is for an improved apparatus and method to meter flow in the range of less than 10 cc/minute, the principles of the invention are extendable to measuring a considerably higher range of flow rates as demonstrated by Example 3 below. Features and advantages of the invention will be apparent from the "Detailed Description of the Invention", below, taken with the accompanying drawings wherein: Figure 1 is an exploded, part cross-sectional view of a preferential flow cell design for metering liquid according to the principles and teachings of this invention; Figure 2 is a top view showing the cell body of the Figure 1 flow cell; Figure 3 is a schematic of a preferred electronic circuit for operating the flow cell according to the principles of the invention; and Figure 4 is a graph associated with the calibration of the flow cell as described in Example 1. Referring to Figures 1 and 2, a preferred embodiment of the apparatus of the invention is illustrated comprising an electronic flow cell 10 for accurately metering liquid movement (herein meaning the range of flow from 0.1 to 10 cc/min). Flow cell 10 comprises a body 14 having a flow-through passageway 12 through which the liquid to be metered flows. The size or internal volume of the flow cell (calibrated) is fixed and within the range of from 0.01 to 0.5 cc, preferably from 0.01 to 0.25 cc. A thermistor 16 (or its equivalent as described hereinafter) is mounted in the body 14 to extend into the passageway and which is designed to be used in the self-heating mode to impart sensible heat pulses of short time duration to the liquid to be metered. The self-heating thermistor includes a heat emitting surface 18 which is exposed in the passageway for making direct contact with the flowing liquid to be metered. Preferably, the heat emitting surface is centered in the passageway. Spaced at a fixed distance from the self -heating thermistor is a second thermistor 20 which, in relative terms, is a fast response thermistor, preferably of a smaller mass, designed for use in the heat sensing mode. The heat sensing thermistor includes a heat sensing surface 22 which extends into the flow channel or passageway 12 for making direct contact with the flowing liquid to be metered (downstream from the self -heating thermistor). The heat sensing thermistor is also preferably centered in the passageway. Preferentially used for the self-heating thermistor is what is referred to as a "standard-probe" thermistor, various commercial types of which are known in the art. These standard probe thermistors include a glass bulb or probe 24 which comprises the heat emitting surface of the thermistor. Encased in the glass probe is a semiconductor element 26 which is thus protected and electrically insulated from direct contact with the liquid to be metered. The probe 24 of a preferred thermistor measures 0.254 cm (0.100 inch) in diameter. It can be used to develop a pulse power of approximately 50-150 milliwatts over extended periods of use without apparent deterioration or alteration of its electrical properties. The small thermal mass of the probe indicated by its Time Constant rating (T.C.) in air of between 14-22 seconds is found generally sufficient to permit rapid enough pulsing in a liquid to be suitable for applications in accordance wth the invention. Its power output is sufficient to develop sensible heat pulses in conjunction with the heat sensing capability of thermistor 20. The heat sensing thermistor 20 is a "fast response" glass probe thermistor and also comprises a semiconductor element 28 encased in glass 30. Thermistor 20, due to a much smaller thermal mass, has a T.C rating in air of about 5 seconds or less The commercial heat sensing thermistors described generally have a 3-4 percent negative temperature coefficient This range of sensitivity has been found quite suitable for use in the invention. A lesser temperature coefficient for the heat sensing thermistor would be operable so long as a sufficient resistance change is registered to.sense the heat pulses in the liquid. The temperature coefficient of the self -heating thermistor is largely an unimportant parameter since the thermistor is used in a self-heating mode; it being preferred, however, to use a self-heating thermistor with a negative temperature coefficient to minimize possible thermistor damage due to inadvertent excessive heating, e.g., in the event the apparatus is abused or operated improperly. However, either a negative or a positive temperature coefficient thermistor may be used as a heat sensing thermistor. The invention also contemplates the use of devices which are equivalent to the self-heating thermistor. These would be based on the substitution for thermistor element 16, of a semiconductor based heating element which differs in that it does not possess the temperature coefficient property which characterizes a thermistor element The term "semi- conductor" is intended to define a material which has a resistivity in the range of from 103 to 1013 micro -ohm-centimeters, preferably, from 104 to 106 micro -ohm-centimeters. Marginally useful as element 26 are resistance heating elements, the resistivity of which falls within the transition range between conductors and semiconductors, i.e., from 750-1000 micro-ohm -centimeters. The term "semiconductors", as used. in this disclosure, is by definition intended to include such latter materials having a resistivity within the defined transition range (e.g, certain carbon based materials); and which may be suitably fabricated into resistance heating elements useful for the purposes of the invention. An advantageous feature of the flow cell 10 of this invention is its simplicity in design and fabrication. A preferred flow cell is constructed using a machinable block of glass-filled Teflons to fabricate the cell body 14. Ordinary drilling methods may be used to provide the passageway 12. Threaded openings 32, 34 are provided at each end of the cell body in communication with passageway 12 for the attachment of chromatographic tube end fittings 36, 38 for passing liquid to be metered through passageway 12. Similar threaded openings t40, 42 are provided in the cell body at positions perpendicular to the passageway 12 for threadably mounting the thermistors 16, 20, respectively. Due to the relatively larger size of the self-heating thermistor 16, a shallow extension 44 of the bore is provided in the cell body 14 extending below the passageway or to provide a space for the lower tip of the heat emitting surface 18 of the probe 16. The extension 44 permits the heat emitting surface of the self-heating thermistor to be adjustably moved for centering along the axis of fluid flow in the passageway 12 and for alignment with the heat sensing surface 22 of the heat sensing thermistor 20 (which is similarly desirably centered along the axis of the passageway). Where relative dimensions of the thermistors require it, the flow channel can be enlarged at the position of either or both thermistors 16, 20 to produce a coaxially enlarged cavity in which the heat emitting and heat sensing surfaces of the thermistors are placed in a centered alignment with the axis of the passageway. The small size flow cells maybe fabricated by mounting thermistors 16, 20 on opposite sides of cell body 14 whereby through the offset, a closer spacing and thus shorter flow channel length dimension can be obtained using essentially the same flow cell design as illustrated in the drawing A preferred arrangement for threadably mounting the thermistors 16, 20 in the cell body 14 employs hollow threaded plugs 46, 48, preferably of plastic, through which the electrical lead wires of the thermistors 16, 20 are passed. Elastic O-rings 50, 52, suitably of Kalrez , are seated in the threaded openings 40, 42, respectively, and are compressed by the plugs to form a liquid tight seal about the body of each thermistor. A terminal strip (not shown) may be attached, e.g., by machine screws, to the cell body. The lead wires of the thermistors are fastened, e.g., by standard electrical contact screws, to the terminal strip, Obviously, considerable variation in this simple cell design is possible without changing it functionally. For example, the cell body may be composed of several joined components (as opposed to the unitary block construction shown). In addition, the cell flow channel may be defined using, e.g., a narrow diameter plastic tube (an embodiment described in the teaching of Example 3, below). A flow restrictor 56 is connected by end fitting 38 to the opening 34 of flow cell 10. The flow restrictor suitably comprises an appropriate length of capillary tubing which restricts fluid flow to produce a back pressure sufficient to avoid microscopic degassing of the metered liquid. The flow restrictor is beneficially used whenever the flow cell is located in a position of back pressure insufficient to avoid detrimental degas sing phenomena. Any alternative device such as a common restrictor valve may be substituted for the illustrated capillary tube. The use of the flow restrictor, while optional, produces optimum levels of liquid metering precision in combination with flow cell 10 when used, e.g., to monitor chromatographic column effluent flow (where characteristically low back pressure leads to detrimental degassing of the meter liquid). A preferred design of an electronic circuit for operating flow cell 10 is shown in Figure 3 and comprises a circuit 58 for operating thermistor 20 in the heat sensing mode. Circuit 58 comprises a standard voltage divider circuit consisting of a potentiometer 60 and a series resistor 62 divided at juncture (A) from thermistor 20 and series resistors 64 and 65. The total resistance of the circuit is sufficient to produce negligible current pulse surges due to pulse resistance decreases of the thermistor, and hence, non-detrimental self-heating of the heat sensing thermistor. The terminals of a common power source are connected across the voltage divider circuit to provide an energizing voltage within the equilibrium range of thermistor 20. A capacitor 67 stabilizes the voltage at juncture (A) from rapid transients in the positive voltage supply level Pulse temperature changes in the metered liquid are electronically sensed in the form of positive voltage pu1seswhich are proportional to a change in the resistance of thermistor 20 with a change in temperature (this circuit being designed for and assuming the use o± a negative temperature coefficient heat sensing thermistor). The generated voltage pulses pass through a series-connected current limiting resistor 66 and are amplified by a non-inverting amplifier 68 set for a gain of 50 by the selected resistance ratio of resistors 70, 72 which are connected in a voltage divider circuit mode on the negative feedback of amplifier 68 (in the standard arrangement). A representative pulse wave form of a pre-amplified and amplified voltage pulse is shown in Inset A-B. This pulse is fed to a preferably two stage differentiating amplifier circuit 74, 74a. A first stage 74 of the differentiating circuit comprises a capacitor 76 connected in series with a current limiting resistor 78 and connected to the inverting;.input of an operational amplifier 80. A feedback resistor 82 returns the input signal to zero following each pulse signal. A capacitor 84 is connected in parallel with resistor 82 to filter high frequency ambient electrical noise. The pulse signal from amplifier 80 is both inverted and proportional to the time rate of change of this pulse (of inset A-B), the pulse is shown in inset (C). Since the amplified (inset A-B) voltage pulse is proportional to the electrically sensed resistance of the heat sensing thermistor, the pulse produced by amplifier 80 (inset C) is thus equivalently considered as the amplified time rate of change (or first time derivative) of the resistance change of thermistor 20 with pulse temperature changes in the metered liquid. The time rate of change pulse signal is conducted to the second stage 74a of the differentiating circuit, which consists of the common elements (with amplifier 80) given like reference numerals. Additionally, the non-inverting input of the second stage amplifier 80a is provided with a zero adjustment biasing circuit 84 which is connected to the referenced power supply outputs in order to trim output of the voltage pulse signal of amplifier 80a. An approximate form of the amplifier 80a output is shown for exemplary purposes in inset D; and is the amplified, electronically derived, second time derivative of the resistance of the heat sensing thermistor 20 with pulse temperature changes in the metered liquid. The second derivative voltage pulse is fed through a current limiting resistor 86 to the non -inverting input of an operational amplifier 88 which is connected to a capacitor 90 and resistors 92, 94 to produce high gain amplification with additional high frequency filtering. An output signal is thus amplified, e.g., 500 times, and is generated by amplifier 88 and filtered through a low pass filter consisting of a resistor 96 and capacitor 98 connected to the power supply common. The total amplification and derivatization functions produce a square wave voltage pulse which is shown in inset (E). The voltage pulse of inset (E) is fed to a timer circuit 100 for pulsing the self-heating thermistor, and which includes a current limiting resistor 102, connected to the base of a switching transistor 104, for switching its collector terminal 106 from +15 volts (power supply level) to zero upon arrival of the output of each inset (E) voltage pulse With each such triggering f the collector terminal 106, a voltage pulse from +15 to zero is produced The collector terminal at rest is biased at +15 volts by a voltage divider circuit consisting of a resistor 108 and the switching transistor 104. ' A second voltage divider 110, 112 produces a highly positive voltage level. The two voltages are placed across a capacitor 114 such that the capacitor is at an elevated voltage on both plates. The switching of the collector terminal voltage rapidly reduces the voltage at capacitor 114, whereby capacitor plate 116 is biased to zero for a brief period of time until the second voltage divider returns to the original voltage level. Consequently, the voltage pulse width generated at the collector terminal is reduced to a voltage spike, which i-s fed to pin #2 of a timer 118 which is the time cycle reset pin; The timer generates a voltage pulse at pin #3, the duration of which is determined by an external variable resistor 120 in combination with an external capacitor 122 connected to pins #6 and #7. The time interval is adjustably changed in this circuit between the limits of 0.1 to 1.0 second. Pins *1 and *8 are connected to common and the +15 volts power supply, respectively. An output voltage of fixed duration is fed from pin #3 to a relay 124, which is a double pole, single throw relay which completes the contact between the power supply, a series resistor 126, and the heating thermistor 16. Leads 128, 130 from the relay are connected to an external data collector 132, e.g+, a computer, which records each activation event of the self-heating thermistor (in order to derive T). The circuit is initially activated by a manual switch 134. A single 100 ma-rated t 15 volts regulated power supply may be used to operate the entire circuit The liquid metering process is initiated by pushbutton activation of a thermal pulse at Rh (the self-heating thermistor). The -4 percent per OC temperature coefficient of the heat sensing thermistor (Rt) produces a positive-going voltage at juncture (A) as the warm liquid pulse traverses the sensing zone. This signal is amplified at (B) and connected through capacitor 76 to the inverting input of amplifier 80 of the first stage differential amplifying circuit 74. This circuit yields a voltage pulse at (C) equivalent to the amplified inverted time derivative at (B). Output at (C) is proportional to dRt/dt and thus slow temperature changes yield essentially zero response in contrast to heat pulses generated in situ by the self-heating thermistor. A single derivative pulse output returns to baseline too slowly to be optimally prepared for sub- sequent pulses. Most preferably, therefore, an inverted second derivative is produced at the second stage amplifier 80a resulting in the approximate pulse output form shown in inset (D) and which is proportional to d2Rt/dt2 This voltage pulse form is amplified at (E) to drive the transistor triggered timing circuit that applies power to the reed relay. This relay supplies a 30 volt D*C. pulse for a fixed time interval (generally from OcT to 1.0 second) to both the pulse counter (i.e., computer), and self-heating thermistor 16. Metering precision is improved through the use of a D.C. pulse forum, as opposed to an A.C. voltage pulse to heat thermistor 16 The- 2K ohm resistor 126 protects the self-heating thermistor from overheating damage as it undergoes self-heating and its resistance declines. A calculated maximum of 113 mW of power is dissipated at Rh during application of the 30 volts D.C. using the standard probe thermistor. The rate of flow and/or total flow of the metered liquid is electronically computed based on the pulse data collected by the electronic circuit, and by applying the following generic mathematical expression: T = Vc/f + K where: T = time period between pulses (e.g., in seconds); Vc = calibrated cell volume constant (e.g., in cubic centimeters); f = flow rate (e.g., in cubic centimeters per second); and K = calibrated time constant (e.g., in seconds). The values 7c and K may be determined, e.g., by the exemplary flow cell calibration procedure described in Example 1. T is the pulse period data collected, whereas f is solved to derive the flow rate of the metered liquid Since the value Vc/f is shown to be characteristically linear with T over a wide flow rate range (See Example 1), the computation of f may be straightforwardly performed electronically; and by a chart recorder or other device displayed visually in any desired form, e.g., to display either or both the instantaneous or averaged flow rate, or to produce based on total pulse count (IT), total flow of the metered liquid over any elapsed period of time. Example 1 This Example describes a preferential calibration method suitable to determine the calibration constants Vc and K. These constants are described with respect to a given flow cell, electronic circuit, and electronic settings. In this study, the flow cell is of a design in which the thermistors 16, 20 are set apart (in center-to-center spacing) approximately 1-1/2 inches (3.8 cm); and are used in conjunction with a flow channel 12 of approximately 1/16 inch (0.159 cm) in diameter. Timer 118 is set to produce 0.8 second pulse heating time; and potentiometer 60 is adjusted to provide a steady state 50 mV positive baseline voltage on which the positive-going-voltage pulses of the heat sensing thermistor are imposed. The zero adjust biasing circuit 84 is adjusted to produce zero voltage at (D) during the absence of pulsing. The apparatus used to calibrate the flow cell consists of a Constametric I pump from LDC Corporation. The pump withdraws liquid (water) from a chromatographic reservoir, and. advances it at a preset rate of flow through, sequentially, a pressure gauge, pulse dampening coil, and ultimately the flow cell, using standard 1/16 inch (0.159 cm) O.D. chromatographic tubing to convey the liquid. The discharge from the flow cell is fed through a back pressure-applying capillary coil E3 inches x 0.005 inches (7.62 cm x 0.127 cm) I.D capilIary to a collection vessel. A- timer is used with a high precision balance to verify liquid flow rates. The data generated are compiled in Table I, below, wherein: f is the averaged flow rate in cc/minute determined from the precision balance and timer; and T is the averaged time period in seconds between pulsing of the self-heating thermistor as determined from relay 124. TABLE I Experiment 1/f T Run Number cc/min (seconds/cc) (seconds) 1 5 30 11.321 1.1826 2 4.78 12.552 1.2384 3 4.25 14 118 1.3078 4 3.74 16.043 1.3987 5 3.20 18.750 1.5240 6 2.64 22.727 1.7020 7 2.125 28.235 1.9729 8 1.61 37.267 2.4327 9. 1.06 56.604 3.3449 Knowing f and T from any two sets of data points, taken from Table 1, the equation T = Vc/f + K can be solved to yield the calibration constants Vc and K, using simultaneous equation solving methods to determine the two unknowns. equation solving flow metering system described, and using the Table I data, the calibrated cell volume Vc is computed to be 0.048 cc; and the calibration constant K is computed to be 0.630 second. Hence, flow in cc/second is determined according to this flow cell, using the expression T = 0.048 cc + 0.630 sec. sec The validity of the above equation is further established by making the plot illustrated as Figure 4. The data points of multiple solutions to the equation at varying Tsec and fcc/min produce the straight line (slope of Vc) which is projected to intercept the ordinate axis at the value K. Thus, the equation shows that the linear y = mx + b relationship is closely followed The correlation coefficient for this data is calculated to be 0.99989. Use of the mathematical basis described above to calibrate the flow cell constants produces exceptional liquid metering precision as shown in Example 2. Nevertheless, liquid flow may be alternatively measured using the flow cell with conventional calibration methods, e.g., by equating total pulse count and pulse frequency data, taken from relay 124, to preknown accumulated liquid volumes or flow rates, as applies. These latter calibration methods can be applied, for example, in order to use the flow-cell for metering accurately non-Newtonian fluids. Example 2 The precision of an electronic flow cell of the same design as used in Example 1 is studied by connecting the cell to an elevated eluent reservoir through 5 feet (1.524 meters) of standard wall 1/16 inch (0.159 cm) Ovid. chromatographic tubing. Liquid (water) is fed by gravity feed through the flow cell under a hydrostatic head pressure (total) of 6 inches (15.24 cm) of water. The water is discharged ultimately to a collection vessel through tubing [also 1/16 inch (0.159 cm) O.D.] which has its end immersed in water in the collection vessel. Initial liquid flow is at approximately 1 cc/minute, and diminishes very slightly during the course of the experiment. The time value of each pulse T produced at relay 124 is electronically stored in the memory bank of a Microcomputer. At the completion of data collection, the computer electronically generates a linear regression curve and computes the standard deviation of T to be 2.973 milliseconds. The observed standard deviation in the measurement was calculated to be 0.092 percent at the 63 percent confidence level (f 1 sigma). Since it is assumed that actual flow varied randomly (in very small amounts), due solely to the imperfect characteristics of the testing apparatus, observed precision is thus determined to be no worse than 0.092% in this experiment and quite likely true precision is better. Example 3 The various flow cells used in this study essentially differ only in respect to calibrated cell volume (vac) Flow cells Nos. 1 and 2 of Table II, below, are constructed using 24 and 12 inches (61 cm and 30.5 Cm), respectively, of 0.031 inch. (0.79 mm) I.D. tubing which is connected between flow cell. blocks each singularly mounting a thermistor. These are the relatively large volume cells. Cell Nos. 3 and 4 are smaller volume cells of the design shown in Figures 1 and 2; flow cell No. 3 being that used in the preceding Example 1. A variable liquid chromatographic metering pump is used to determine the dynamic flow range specific to each cell design, the observed results being reported in Table II. TABLE II Observed T Average In Flow Vc/Vg* Calculated Seconds & ommat; Cell K c g Flow Range Flow Range No. in seconds in cc in cc/min Limits 1 0.687 0.492/0.424 9.84+ 3.69 & ommat; flow minimum 2 0.689 0.219/0.225 4.56-11.0 3.63 - 1.88 3 0.630 0.048/0.075 l.05- 5.30 3.34 - 1.18 4 0.-653 0.017/0.025 0.20- 2.17 5.72 - 1.12 ;t = geometric cell volume The largest volume cell No. 1 shows a threshold (minimum) flow detection limit at about 10 cc/minute, its upper limit not being tested due to the limitations of the pumping apparatus used in the experiment. This flow cell. demonstrates the feasibility- of extending the liquid flow metering principles. of the invention to the metering of considerably greater than 10 cc/minute flow rates. Flow cells Nos. 1-3 collectively demonstrate the utility of the invention for metering liquid across essentially the entire practical scope of the sub-10 cc/minute flow range. This experiment is not intended to be construed to represent an optimization study of flow cell dynamic operating range as to any given cell design used in the experiment. A point to be noted is that the K values determined for the various flow cells 1-4 are not identical. The slight discrepancies between the observed K values can probably be attributed to small differences in the electrical characteristics of the thermistors 16, 20 of each flow cell which, while of identical manufacturing source and part description, would be expected. to vary slightly in thermal mass and/or electrical properties.

Claims: CLAIMS 1. A method for electronically metering the flow of Newtonian liquids comprising the steps of: (a) conveying the liquid to be metered through a flow cell having a passageway which forms a flow through chamber of fixed dimensions, said chamber having a predetermined calibrated volume (Vc) and calibrated time constant (K); (b) applying a heat pulse of constant duration from an upstream probe to the liquid and detecting the pulse with a second probe downstream of the first probe, and wherein each detection event triggers the application of a subsequent heat pulse to produce the condition that pulse frequency is related to liquid flow rate (f); (c) electronically detecting the period (T) between pulses; and (d) determining a measure of flow of the metered liquid based on the application of the relationship, T=V +K c f 2. The method of Claim I wherein the flow rate of the metered liquid is in a range of less than 10 ccjminute andthe calibrated volume (Vc) is from 0.01 to 0.5 cc. 3. The method of Claim 1 or 2, including the step of using a thermistor operating as a resistance heater in the self-heating mode to generate heat pulses into the metered liquid, and wherein the heat pulsing event is activatedbyan electronically time differe'ntiated electricalpulse,said pulse being a time differentiated response of a heat sensing thermistor to pulSe temperature change in the metered liquid. 4. The method of Claim 3 wherein said activating electrical pulse response comprises no less than the second time differential of the electrical pulse response of the heat sensing thermistor to pulse temperature change in the metered liquid. 5. The method of any one of Claims 1 to 4 including the step of feeding the outflow of the flow cell through a flow restrictor means. 6. An apparatus for electronically metering liquid flow, which comprises: (a) a flow cell having a passageway which forms a flow through chamber of fixed dimensions; (b) a resistance heating means encapsulated in an electrical insulator and a circuit to operate the resistance heating means; (c) a heat sensor encapsulated in an electrical insulator and a circuit to monitor the temperature of the liquid and to measure rate of change of temperature of the liquid, and heat sensor being positioned in said passageway in a fixed, spaced relationship with respect to the resistance heating means; ; (d) a time-differentiating circuit for generating an electrical signal which in magnitude is proportional to d,Jdt, or a time derivative thereof, wherein dRt/dt is the time rate of change of the resistance of the heat sensing thermistor with pulse temperature or during its encounter with the pulse of heated liquid conveyed through said passageway; (e) said circuit means for operating the resistance heating means comprising a timer circuit which is activated by detection of each pulse (d) to apply a timed voltage pulse to the resistance heating means. 7. The apparatus of Claim 6 in which the resistance heating means and the heat sensor, respectively, is a thermistor encapsulated in an electrical insulator in the form of probes exposed in fixed, spaced relationship in the chamber, and circuit means to operate said thermistor in the self-heating mode. 8. The apparatus of Claim 6 or 7 in which the timedifferentiating circuit generates an electrical pulse which in magnitude is proportional to d2Rt /dt2, wherein d2Rt/dt2 is the second time rate of change of the resistance of the heat sensing thermistor with pulse temperature changes in the liquid to be metered. 9. Theapparatus-of Claim 8 inwhich the volume of the chamber is equivalent to acalibrated volume (Vc) of between 0.01 to .5 cc. 10. The apparatus of Claim I, 8 or 9 in which the heat sensing thermistor has a Time Constant in air of less than 5 seconds and the self-heating thermistor has a Time Constant in air of less than 22 seconds. 11. The apparatus of any one Claims 6 to 10 including a flow restrictor in the form of a capillary tube in communication with the passageway for the application of back pressure on the liquid to be metered. 12. A flow cell for metering liquid flow comprising; (a) a flow cell body having a passageway for flow of a liquid therethrough, said passageway forming a flow through chamber of fixed dimensions; (b) a resistance heating means encapsulated in an electrical insulator which is exposed to the liquid flowing through the passageway; and (c) a heat sensor encapsulated in an electrical insulator which is exposed to the flow of liquid in the passageway in a spaced apart relationship with respect to the resistance heating means. 13. The flow cell of Claim 11 wherein the flow through chamber has a volume which is equivalent to a calibrated volume (Vc) of from 0.01 to 0.5 cc. 14. The flow cell of Claim 12 or 13, wherein the resistance heating means is a thermistor adapted to operate in a self-heating mode, said heat sensor is a heat sensing thermistor, and wherein the thermistors are in the form of probes which are exposed to liquid flow in a fixed, spaced relationship in the passageway. 15. The flow cell of Claim 14 wherein the heat sensing thermistor has a Time Constant in air of less than about 5 seconds, and the self-heating thermistor has a Time Constant in air of less than about 22 seconds. 16. The flow cell of any one of the preceding Claims 12 to 15, including a flow restrictor means in communication with the passageway for applying back pressure on the liquid to be metered.

Inventors: MILLER, THEODORE EDWARD, JR., SMALL, HAMISH
Applicants: THE DOW CHEMICAL COMPANY
Application year: 1982
Main classification: G01F1
IPC codes: G01F1, G01F11, G01F13