Heating system and method

Abstract

Microfluidic strip 114 is positioned within diagnostic reader 112. A resistor (14, Fig. 1) is adhered to a surface of the strip in thermal contact with reaction zone 124. A capacitor of capacitance C

Description

FIELD OF THE INVENTION The present invention relates to systems and methods for generating heat such as to heat an object and / or composition of matter. RELATED APPLICATION U.S. patent application no. 17 / 860,933, titled "Fluid Control in Microfluidic Devices" and filed July 8, 2022 ("the '933 Application") is incorporated herein in its entirety. BACKGROUND OF THE INVENTION Microfluidic devices, e.g., microfluidic strips, such as disclosed in the '933 Application may be used to determine the presence and / or amount of one or more targets in a liquid sample. Typically, such microfluidic devices define a microfluidic network therein having an application zone for introducing a sample and one or more channels and chambers through which the sample is moved. The microfluidic network may include reagents configured to react with the one or more targets to facilitate the determination thereof. The microfluidic network may include valves configured to permit or obstruct the passage of sample and / or gases through portions of the microfluidic network. Other components of microfluidic networks may include sources of gas pressure configured to move samples therein. In some cases, the reaction of samples with reagents, the operation of valves, or the gas pressure-induced movement of samples may be facilitated or accomplished by heating a portion of the microfluidic network. For example, the temperature of a mixture of sample and one or more reagents may be raised above ambient temperature to facilitate one or more reactions. A valve may include a temperature sensitive material that is heated to change the shape or phase of the material thereby opening or closing the valve. Sample movement can be induced by heating a volume of gas within a chamber of a microfluidic device thereby increasing the pressure of the gas acting on the sample. The operation of such thermally actuated microfluidic components and processes would be a heating system capable of delivering a known and reproducible amount of energy and / or power to a location of a microfluidic device associated with the component or process. SUMMARY OF THE INVENTION In embodiments, a heating system includes an electrical circuit comprising first and second circuit leads and a resistive element and a capacitive element in, e.g., series between the first and second circuit leads, a power supply comprising first and second supply leads and being configured to provide a constant potential VPS across the first and second supply leads, a switch system having (1) a first position in which the first supply lead is in electrical communication with the first circuit lead and the second supply lead is in electrical communication with the second circuit lead and (2) a second position in which the first supply lead is in electrical communication with the second circuit lead and the second supply lead in electrical communication with the first circuit lead, and a switch system controller configured to cause the switch system to alternate between the first and second positions. At least the power supply and the switch system may be implemented as one or more integrated circuits, such as an integrated circuit(s) including two or more ½ H-bridge drivers or at least one H-bridge driver. A switch system typically includes at least first and second switches. In embodiments of the heating system, the resistive element consists essentially of a single resistive element, e.g., a single resistor. In other embodiments, the resistive element includes two or more resistive elements, e.g., two or more resistors, arranged to provide a total resistance. In embodiments of the heating system, the capacitive element consists essentially of a single capacitive element, e.g., a single capacitor. In other embodiments, the capacitive element includes two or more capacitive elements, e.g., two or more capacitors, arranged to provide a total capacitance. In any of the embodiments, the capacitive element may be configured as any of the capacitive elements disclosed herein. For example, the capacitive element(s) may be a non-polarized capacitor having a low temperature coefficient such that the capacitance exhibits low variation as a function of the temperature of the capacitor. Exemplary capacitive elements, individually or in combination, may be formed, e.g., of polyester, polypropylene, ceramic, and combinations thereof. In any of the embodiments of the heating system, the resistive element(s) may have a total resistance R, the capacitive element(s) may have a total capacitance C, and the electrical circuit has an RC time constant given by the product R x C. The RC time constant is typically between about 1 ms and about 100 ms, between about 3 ms and 50 ms, between about 5 ms and about 25 ms, between about 7.5 and about 15 ms. The resistance R of the RC circuit may be essentially determined by the resistance of the resistive element(s), e.g., the RC circuit may exclude other sources of resistance that contribute substantially to the total resistance of the RC circuit. The capacitance of the RC circuit may be essentially determined by the capacitance of the capacitive element(s), e.g., the RC circuit may exclude other sources of capacitance that contribute substantially to the capacitance of the RC circuit. In any of the embodiments of the heating system, the controller may be configured to (i) cause the switch system to switch to the first position and to maintain the switch system in the first position for a time Tist before causing the switch system to switch to the second position, (ii) maintain the switch system in the second position for a time T2nd, and (iii) repeat steps (i) and (ii). The duration of T1sr and T2nd are each typically between about RC and 20 x RC, between about 2 x RC and about 10 x RC, between about 3 x RC and about 7 x RC, e.g., about 4 x RC, wherein RC is the RC time constant of the RC circuit. The controller may be configured to repeat step (iii) a total number N times per second, wherein N is between about (0.5 x RC)1 and about (40 x RC)1, e.g., about (8 x RC)-1. In embodiments, for example, N may be between about 5 and 500, between about 10 and 200, or between about 15 and 100. In any of the embodiments of the heating system, the controller may be configured to (i) place the switch system in the first position for a period of time sufficient to charge the capacitive element to a potential of at least about 0.5 x VP$, at least about 0.80 x VPS, at least about 0.95 x VPS, or at least about 0.98 x VPS and with a first polarity, (ii) cause the switch system to switch to the second position and to maintain the switch system in the second position for a time sufficient to discharge the capacitive element and then charge the capacitive element to a potential of at least about 0.5 x VPS, at least about 0.80 x VPS, at least about 0.95 x VPS, or at least about 0.98 x VPS, with a second polarity opposite to the first polarity, (iii) cause the switch system to switch to the first position and to maintain the switch system in the first position for a time sufficient to discharge the capacitive element and then charge the capacitive element to a potential of at least about 0.5 x VPS, at least about 0.80 x VPS, at least about 0.95 x VPs, or at least about 0.98 x VPS, with the first polarity, and (iv) repeat steps (ii) and (iii). The controller may be configured to repeat step (iii) a total number N times per second, wherein N is between about (0.5 x RC)1 and about (40 x RC)4, e.g., about (8 x RC)4. In embodiments, for example, N may be between about 5 and 500, between about 10 and 200, or between about 15 and 100. In embodiments, a diagnostic reader may include any of the foregoing embodiments of the heating system. The diagnostic reader is configured to operate a diagnostic device, such as a microfluidic device, e.g., a microfluidic device, to perform a diagnostic assay(s) on a liquid sample applied to the diagnostic device. The reader includes the resistive element positioned so that the resistive element is in thermal communication with a region of the microfluidic device when the device is disposed in an operative position with respect to the reader. For example, the reader may include a platen incorporating the resistor. A diagnostic device inserted in an operative position with respect to the reader is disposed in thermal communication with the platen. During operation, the reader operates the heating system to dissipate heat over the resistor and thereby heat a region of the diagnostic device. In embodiments, a diagnostic system may include any of the foregoing embodiments of the heating system. The diagnostic system typically includes a diagnostic device, such as a microfluidic device, e.g., a microfluidic strip, and a diagnostic reader configured to operate the diagnostic device to perform a diagnostic assay(s) on a liquid sample applied to the diagnostic device. For example, the diagnostic assay may be performed to determine the presence and / or amount of a target(s) present in the liquid sample. In the diagnostic system, the resistive element of the heating system is disposed in thermal communication with a region of the diagnostic device so as to heat the region of the diagnostic device. For example, the region of the diagnostic device may include, a reaction zone, valve, or a gas-pressure chamber, e.g., a gas-pressure chamber configured to move liquids and / or gases within the device. An exemplary valve includes a temperature sensitive material that is heated to change the shape or phase of the material thereby opening or closing the valve. In a reaction chamber, the temperature of a mixture of sample optionally including one or more reagents may be raised above ambient temperature to facilitate one or more reactions and / or mixing. A volume of gas disposed in a gas chamber may be heated thereby increasing the pressure of the gas and inducing movement of a sample or other material in gaseous communication therewith. The diagnostic device may include the resistive element. For example, the resistive element may be disposed on a surface of the diagnostic device in thermal communication with the region to be heated. The surface may be an external surface, e.g., a surface which is not in direct contact with liquids or other materials that are manipulated within the diagnostic device. Alternatively, at least a portion, e.g., all, of the resistive element may be disposed within the diagnostic device in direct contact with liquids or other materials within the diagnostic device. The resistive element may include an electrically insulating layer, e.g., a coating, to prevent shorting in the presence of liquids, other materials, or other electrical elements of the diagnostic device. Exemplary resistive elements suitable for use with a diagnostic device include carbon-based resistive elements, e.g., carbon ink-based resistive elements, silver-ink based resistive elements, metal oxide, e.g., silver oxide, resistive elements, and combinations thereof. Such resistive elements may be, e.g., printed or otherwise deposited on the diagnostic device. The diagnostic device and diagnostic reader may be configured and include features of microfluidic strips and readers disclosed in the '933 Application. In embodiments, a heating method includes using any of the foregoing heating systems, including any diagnostic reader incorporating such heating systems or diagnostic systems incorporating such heating systems, to heat a composition of matter, article of manufacture, or combination thereof. For example, the heating method may be included within a diagnostic method including the determination of the presence and / or amount of one or more targets within a sample. The heating method may include, for example, heating a thermally actuated valve to open or close the valve, heating a sample, optionally including one or more reagents in combination therewith, to facilitate a reaction or mixing of the sample and / or reagent(s), and / or heating a volume of gas such as to exert a motive pressure on a liquid or other material to be moved within a microfluidic network of a diagnostic device. In embodiments, a heating method includes providing an electrical circuit comprising first and second circuit leads and a resistive element and a capacitive element between the first and second circuit leads. Typically, the resistive element and capacitive element are arranged in series. The method includes providing a power supply having first and second supply leads and configured to generate a constant potential VPS therebetween. The method further includes, alternatingly, (1) connecting the first supply lead to the first circuit lead and the second supply lead to the second circuit lead and (2) connecting the second supply lead to the first circuit lead and the first supply lead to the second circuit lead. In performing the heating method, the resistive element may have a resistance R, the capacitive element may have a capacitance C, and the electrical circuit may have an RC time constant R x C. The method may include performing step (1) and maintaining the connecting for a duration Tist, performing step (2) and maintaining the connecting for a duration T2nd, and sequentially repeating steps (1) and (2). The duration of Tist and T2nd are each typically between about RC and 20 x RC, between about 2 x RC and about 10 x RC, between about 3 x RC and about 7 x RC, e.g., about 4 x RC, wherein RC is the RC time constant of the RC circuit. The controller may be configured to repeat each of steps (1) and (2) a total number N times per second. Number N is typically between about (5 x RC)1 and about (0.5 x RC) S e.g., about (2 x RC)1. In embodiments, for example, N may be between about 10 and 500, between about 25 and 250, between about 50 and 200, e.g., about 70. Performing the heating method may include (i) performing step (1) and maintaining the connecting for a period of time sufficient to charge the capacitive element to a potential of at least about 0.5 x VPS, at least about 0.80 x VPS, at least about 0.95 x VPS, or at least about 0.98 x VPS and with a first polarity, (ii) performing step (2) and maintaining the connecting for a period of time sufficient to discharge the capacitive element and then charge the capacitive element to a potential of at least about 0.5 x VPS, at least about 0.80 x VPS, at least about 0.95 x VPS, or at least about 0.98 x VPS and with a second polarity opposite to the first polarity, (iii) performing step (1) and maintaining the connecting for a time sufficient to discharge the capacitive element and then charge the capacitive element to a potential of at least about 0.5 x VPS, at least about 0.80 x VPS, at least about 0.95 x VPS, or at least about 0.98 x VPS, with the first polarity, and (iv) repeating steps (ii) and (iii). In the heating method, the resistive element and / or capacitive element may be configured as any of the resistive elements and / or capacitive elements disclosed herein. A diagnostic method may include any of the foregoing heating methods. The diagnostic method may include disposing a liquid sample within a reaction zone of a microfluidic device, the reaction zone being in thermal communication with the resistive element and performing the heating method to heat the liquid sample within the rection zone. The diagnostic method may alternatively or in combination include heating a thermally actuated valve within a microfluidic device thereby opening or closing the valve. The diagnostic method may alternatively or in combination include heating a gas chamber within a microfluidic device so as to exert a motive pressure on a liquid and / or other material within a microfluidic network of the microfluidic device. In embodiments, a heating method includes providing an electrical circuit comprising first and second circuit leads and a resistive element and a capacitive element arranged in series between the first and second circuit leads; providing a power supply having first and second supply leads and generating a potential VPS therebetween; and alternatingly: (1) (a) flowing electrons out of the first circuit lead and into the first supply lead and (b) flowing electrons out of the second supply lead and into the second circuit lead, thereby charging the capacitive element to a potential Vi with a first polarity and wherein a ratio Vi / VPs is between about 0.5 and 1, e.g., between about 0.8 and 1, between about 0.95 and 1, or between about 0.98 and 1; and (2) (a) flowing electrons out of the second supply lead and into the first circuit lead and (b) flowing electrons out of the second circuit lead and into the first supply lead, thereby charging the capacitive element to a potential V2 with a second polarity opposite to the first polarity and wherein a ratio V2 / VPS is between about 0.5 and 1, e.g., between about 0.8 and 1, between about 0.95 and 1, or between about 0.98 and 1. In performing the heating method, the resistive element may have a resistance R, the capacitive element may have a capacitance C, and the electrical circuit may have an RC time constant R x C. The method may include performing step (1) and maintaining the connecting for a duration Tist, performing step (2) and maintaining the connecting for a duration T2nd, and sequentially repeating steps (1) and (2). The duration of Tut and T2nd are each typically between about RC and 20 x RC, between about 2 x RC and about 10 x RC, between about 3 x RC and about 7 x RC, e.g., about 4 x RC, wherein RC is the RC time constant of the RC circuit. The controller may be configured to repeat steps (1) and (2) a total number N times per second, wherein N is between about (0.5 x RC)1 and about (40 x RC)-1, e.g., about (8 x RC)-1. In embodiments, for example, N may be between about 5 and 500, between about 10 and 200, or between about 15 and 100. In embodiments, a heating method includes providing an electrical circuit comprising first and second circuit leads and a resistive element and a capacitive element having a capacitance C arranged in series between the first and second circuit leads; performing repeated cycles each comprising (i) charging the capacitor to a potential V with a first polarity by passing electrical current through the electrical circuit in a first direction and (ii) charging the capacitive element to the potential V with a second polarity opposite to the first polarity by passing electrical current through the electrical circuit in a second direction opposite to the first direction, thereby dissipating an amount of energy in the resistive element equal to C x (2 x V)2 during each cycle, wherein a difference between a maximum potential and a minimum potential applied to the first and second leads is no greater than about 1.2 x V, no greater than about 1.1 x V, no greater than about 1.05 x V, e.g., is about V. In any embodiment of the heating system, heating methods, and diagnostic readers and systems and methods incorporating such heating systems and methods, the power supply may include a single source of electrical potential that is applied to the RC circuit of the heating system. Such a system would not include, for example, in which two or more sources of electric potential were alternatingly used to apply electrical potential to the RC circuit. In any embodiment of the heating system, heating methods, and diagnostic readers and systems and methods incorporating such heating systems and methods, the constant electrical potential provided by the power system, e.g., VPS, may be, e.g., between about 5 V and about 50 V, e.g., about 12 V. BRIEF DESCRIPTION OF THE DRAWINGS FIGURE 1 is a schematic illustrating a heating system of the present invention; FIGURE 2 illustrates the time dependence of an electrical potential applied to an RC circuit of the heating system of FIGURE 1 during the operation thereof and, in response to the applied electrical potential: (i) the time dependence of an electrical potential drop across a resister of the RC circuit and (ii) the time dependence of an electrical potential drop across a capacitor of the RC circuit; FIGURE 3 illustrates an exemplary output of a prior art alternating current power supply in the form of a square wave oscillating between a maximum potential V and a negative potential -V; FIGURE 4 illustrates an exemplary implementation of the heating system of FIGURE 1 for heating a reaction zone of a microfluidic device; and FIGURE 5 illustrates a temperature vs time plot obtained for each of two resistors using a heating system of the invention and as described in the Example; each row of the chart represents a 5 °C temperature difference and each column of the chart represents a 30 s time interval. DETAILED DESCRIPTION With reference to FIGURE 1, a heating system 10 includes an RC circuit 12, a DC power supply 22, a first switch 28, and a second switch 40. A controller 11, e.g., an electronic processor, is configured to operate DC power supply 22 and first and second switches 28,40. Controller 11 may be in direct electrical and / or wireless communication with heating system 10. RC circuit 12 includes a resistor 14 and a capacitor 16 arranged in series between a first RC circuit lead 18 and a second RC circuit lead 20. DC power supply 22 and first and second switches 28,40 may be implemented using, e.g., an integrated circuit such as one providing at least two K H-bridge drivers or at least one H-bridge driver. An exemplary integrated circuit is the DRV8844PWP quad ½ H-bridge driver manufactured by Texas Instruments. (RTM). In use, resistor 14 is disposed in thermal communication with a location 52 to be heated. Location 52 may be, e.g., a region of a microfluidic network of a microfluidic device, such as a thermally controlled valve, source of gas-pressure, or reaction chamber thereof. Controller 11 actuates DC power supply 22 and first and second switches 28,40 thereby applying a timedependent electrical potential 200 across RC circuit 12 (FIGURE 2). The application of timedependent electrical potential 200 repeatedly charges and discharges capacitor 16 with all of the charging and discharging current flowing through resistor 14. As discussed below, the current flow through resistor 14 dissipates a known amount of energy at a known rate, i.e., power, through resistor 14 thereby providing controllable heating of location 52. The heating can also be efficient because heating system 10 can maximize the relative amount of electrical potential difference generated by power supply 22 that is converted to thermal energy, i.e., heat. Resistor 14 has a resistance R. In an exemplary embodiment in which heating system 10 is used to heat a region of a microfluidic network of a microfluidic device, R is, e.g., between about 25 Q and about 500 Q, e.g., about 150 Q. Capacitor 16 has a capacitance F. In such exemplary embodiment, F is, e.g., between about 20 pF and about 100 pF, e.g., about 50 pF. RC circuit 12 is typically formed so that resistance R of resistor 14 accounts for substantially all, e.g., essentially all, of the resistance of circuit 12 and so that the capacitance F of capacitor 16 accounts for substantially all, e.g., essentially all, of the capacitance of circuit 12 when determined at frequencies of less than 200 Hz. Together, resistance R and capacitance C determine the RC time constant of RC circuit 12. For example, for R = 150 Q and F = 50 p.F, RC = 7.5 ms. Resistor 14 may be formed as a resistive element adhered to a surface of the microfluidic device, e.g., to an external surface of the microfluidic device or to an internal surface a microfluidic network of the microfluidic device, e.g., to an internal surface of a channel, valve, or chamber thereof. Exemplary resistive elements include carbon ink-based resistive elements, silver ink-based resistive elements, metal oxide, e.g., silver oxide, resistive elements, and combinations thereof. Such resistive elements may be, e.g., printed or otherwise deposited on the diagnostic device. In some instances, the manufacturing process is imprecise so that the resistance of any one resistive element is unknown unless determined by measurement. However, the range of resistances resulting from such manufacturing processes may be empirically determined to fall between upper and lower bounds. Accordingly, it is possible to predict that any one manufactured resistive element will have a resistance greater than the minimum bound and less than the maximum bound. Capacitor 16 is typically a non-polarized capacitor having a low temperature coefficient such that the capacitance exhibits low variation as a function of the temperature of the capacitor. To further reduce a temperature dependence of the capacitance, two or more capacitors may be combined, with a first one of the capacitors having a negative dependence on temperature and a second one of the capacitors having a positive dependence on temperature. In combination, such capacitors form a capacitive element with a combined capacitance with a reduced temperature dependence. Suitable capacitors, individually or in combination, may be formed, e.g., of polyester, polypropylene, ceramic, and combinations thereof. As used herein, the term capacitive element means an electronic element such as a capacitor or combination of capacitors having a suitable capacitance, polarization characteristics (e.g., being non-polarized), and low temperature coefficient. DC power supply 22 includes a first power supply lead 24 and a second power supply lead 26. First power supply lead 24 bifurcates at location 25 into a first power supply sub-lead 24', which terminates at a first power supply switch contact 42, and a first power supply sub-lead 24", which terminates at a first power supply switch contact 36. Second power supply lead 26 bifurcates at location 27 into a second power supply sub-lead 26', which terminates at a second power supply switch contact 32, and a second power supply sub-lead 26", which terminates at a second power supply switch contact 46. First RC circuit lead 18 bifurcates at a location 19 into a first RC circuit sub-lead 18', which terminates at a first RC switch contact 44, and a first RC circuit sub-lead 18", which terminates at a first RC switch contact 48. Second RC circuit lead 20 bifurcates at a location 21 into a second RC circuit sub-lead 20', which terminates at a second RC switch contact 30, and a second RC circuit sub-lead 20", which terminates at a second RC switch contact 34. First switch 28 includes a bridging contact 38. In a first switch position as illustrated in FIGURE 1, bridging contact 38 provides electrical connectivity between second RC switch contact 30 of second RC circuit sub-lead 20' and second power supply switch contact 32 of second power supply sub-lead 26'. In a second switch position as illustrated by arrow 28', bridging contact 38 provides electrical connectivity between second RC switch contact 34 of second RC circuit sublead 20'' and first power supply switch contact 36 of first power supply sub-lead 24". Second switch 40 includes a bridging contact 50. In a first switch position as illustrated in FIGURE 1, bridging contact 50 provides electrical connectivity between first RC switch contact 44 of first RC circuit sub-lead 18' and first power supply switch contact 42 of first power supply sub-lead 24'. In a second switch position as illustrated by arrow 40', bridging contact 50 provides electrical connectivity between first RC switch contact 48 of first RC circuit sub-lead 18"and second power supply switch contact 46 of second power supply sub-lead 26". DC power supply 22 is configured to supply a constant electrical potential VPS between location 25 of lead 24 and location 27 of lead 26. However, direction of the electrical potential drop across RC circuit 12 depends on the positions of first and second switches 28,40. Referring also to FIGURE 2, time-dependent electrical potential 200 illustrates the electrical potential drop across RC circuit 12 as would be observed with a voltmeter having its positive contact disposed at location 19 of first RC circuit lead 18 and its negative contact disposed at location 21 of second RC circuit lead 20. When first and second switches 28,40 are each in the first switch position (FIGURE 1), the electrical potential drop across RC circuit 12 so measured between first RC circuit lead 18 and second RC circuit lead 20 is VPS (FIGURE 2, during, e.g., a pulse 200' between times Ti and t2). When first and second switches 28,40 are each in the second switch position (as indicated by respective arrows 28’,40' in FIGURE 1), the electrical potential drop so measured across RC circuit 12 between first RC circuit lead 18 and second RC circuit lead 20 is -VPS (FIGURE 2, during, e.g., a pulse 200" between times t3 and t4). A pulse period tp is typically the same for each of the pulses. Between successive pulses, e.g., between time t2 (the end of pulse 200') and time t3 (the start of pulse 200"), both switches 28,40 are in an open position and the electrical potential drop across RC circuit 12 between first RC circuit lead 18 and second RC circuit lead 20 is 0. However, the open period is not illustrated in FIGURE 2 because the duration of the open period is typically substantially smaller than the pulse period tp. For example, the ratio of the open period to the pulse period may be, e.g., about 0.01 or less, about 0.005 or less, or about 0.001 or less. Although first and second switches 28,40 permit the polarity of the electrical potential drop across RC circuit 12 to be reversed as shown in FIGURE 2, the output of DC power supply 22 remains constant, i.e., VPS. When DC power supply 22 is off, i.e., not generating any potential, the output is zero volts (FIGURE 2, between times t0 and t3). Accordingly, the difference between the maximum potential and the minimum potential generated by DC power supply is VPS. In contrast, as seen in FIGURE 3, a zero-centered square-wave output by an alternating current power supply (not shown) is not constant and instead oscillates between a maximum potential VAc and a minimum potential -VAC. The difference between the maximum potential VAC and the minimum potential -VAC output by such alternating current power supply is 2VAC. Heating system 10 may be configured and operated, e.g., as follows. Resistor 14 is positioned in thermal communication with location 52 to be heated. As discussed above, the RC time constant for RC circuit 12 is 7.5 ms for R = 150 Q and F - 50 pF. In addition to illustrating time dependent electrical potential 200 across RC circuit 12, FIGURE 2 illustrates a time dependent electrical potential drop 202 across resistor 14, e.g., between location 19 of first circuit lead 18 and location 23 intermediate resistor 14 and capacitor 16, and a time dependent electrical charge of capacitor 16, e.g., between location 23 and location 21 of second circuit lead 20. Prior to initiating heating, DC power supply 22 is off so that the electrical potential drop across RC circuit 12 between first RC circuit lead 18 and second RC circuit lead 20 is 0 (time t0). At time Ti, controller 11 actuates DC power supply 22 to a voltage VPS, e.g., 12 V DC, positions switches 28,40 in the first position (FIGURE 1) and then maintains the switches in the first position for pulse period tp thereby generating voltage pulse 200' (FIGURE 2). A ratio of pulse period Tpto the RC time constant (tp:RC) is 4 (tp = 30 ms). During pulse 200', the electrical potential drop across resistor 14, as illustrated by a segment 202' of time dependent electrical potential 202, decreases exponentially from VPS at time toward 0 V at time t2. Capacitor 16 charges exponentially from 0 V at time Ti toward VPS at time t2 as illustrated by a segment 204' of time dependent electrical potential 204. Because tp is long with respect to time constant RC, the potential drop across resistor 14 decreases essentially to 0 V and capacitor 16 charges essentially to VPS by the end of pulse 200' (time t2). For example, the potential drop across resistor 14 decreases to eA(—tP / RC) x Vps = 0.018 x VPS and capacitor charges to an electrical potential given by 1 - eA(—tP / RC) x Vps = 0.982 x VPS. The amount of energy dissipated by resistor 14 during pulse 200' is 0.5 x C x (0.98 x VPS)2 = 3.45 mJ, which is essentially equal to 0.5 x C x (VPS)2 - 3.6 mJ. At time t2, controller 11 switches switches 28,40 from the first to the second position (as indicated by arrows 28',40' in FIGURE 1) thereby reversing the polarity of the electrical potential applied to RC circuit 12. The output of DC power supply 22 itself remains constant at VPS. Controller 11 then maintains the switches in the second position for period tp generating a voltage pulse 200'' beginning at time t3 and ending at time t4 (FIGURE 2). During the transition between pulses 200' and 200", the switches are briefly in the open position as discussed above. At time t3, the electrical potential drop across resistor 14, as illustrated by a segment 202" of time dependent electrical potential 202, is given by the sum of the electrical potential of charged capacitor 16 and the electrical potential applied by DC power supply 22, i.e., essentially -2VPs. During pulse 200", the electrical potential drop across resistor 14 increases exponentially from essentially -2VPS at time t3 toward 0 V at time t4. Capacitor 16 discharges exponentially from essentially VPS at time t3 through 0 V at the midpoint of pulse 200" toward - VPS at time t4 as illustrated by a segment 204" of time dependent electrical potential 204. By the end of pulse 200" (time t4), the potential drop across resistor 14 increases essentially to 0 V, i.e., to -eA(—tP / RC) x VPS = -0.018 x VPS and capacitor 16 charges essentially to- VPS, i.e., to an electrical potential given by -[1 - eA(—tP / RC) x VPS] = -0.982 x VPs. The amount of energy dissipated by resistor 14 during pulse 200" is 0.5 x C x (2 x 0.98 x VPS)2 = 13.8 mJ, which is essentially equal to 2 x C x (VPS)2 = 14.4 mJ. The amount of energy dissipated during pulse 200" is four times (4x) greater than the energy dissipated during the initial pulse 200' because capacitor 16—which was first charged to essentially VPS during pulse 200'—combines with the electrical potential applied by DC power supply 22 to increase the electrical potential drop over and the resulting current flowing through resistor 14 during pulse 200". At time t4, controller 11 switches switches 28,40 from the second to the first position (FIGURE 1) thereby reversing the polarity of the electrical potential applied to RC circuit 12. The output of DC power supply 22 itself remains constant at VPS. Controller 11 then maintains the switches in the first position for period tp generating a voltage pulse 200'" beginning at time x5and ending at time t6 (FIGURE 2). During the transition between pulses 200" and 200'", the switches are briefly in the open position as discussed above. At time t4, the electrical potential drop across resistor 14, as illustrated by a segment 202'" of time dependent electrical potential 202, is given by the sum of the electrical potential on capacitor 16 and the electrical potential applied by DC power supply 22, i.e., essentially 2VPS. During pulse 200'", the electrical potential drop across resistor 14 decreases exponentially from 2VPs at time t5 toward 0 V at time t6. Capacitor 16 discharges exponentially from essentially -VPS at time t5 through 0 V at the midpoint of pulse 200'" toward VPS at time t6 as illustrated by a segment 204'" of time dependent electrical potential 204. By the end of pulse 200'" (time t6), the potential drop across resistor 14 has decreased essentially to 0 V, i.e., to eA(—tP / RC) x Vps = 0.018 x VPS and capacitor 16 has charged essentially to V, i.e., to an electrical potential given by 1 -eA(—tP / RC) x V = 0.982 x VPS. The amount of energy dissipated by resistor 14 during pulse 200'" is the same as the energy dissipated during pulse 200". Following pulse 200'" at time t7 controller 11 switches switches 28,40 from the first to the second position thereby again reversing the polarity of the electrical potential applied to RC circuit 12. Controller 11 then maintains the switches in the second position for period tp generating a voltage pulse 200"" beginning at time t7 and ending at time t8 (FIGURE 2). The behavior of the electrical potentials and energy dissipation during pulse 200"" are the same as during pulse 200". The process of switching the electrical potential applied to RC circuit 12 can be repeated for a number of times necessary to achieve a desired heating of object 52. For example, the electrical may be switched a number N times per second, wherein N may be between about (0.5 x RC)1 and about (40 x RC)-1, e.g., about (8 x RC) T In embodiments, for example, N may be between about 5 and 500, between about 10 and 200, or between about 15 and 100. As discussed above, the average power dissipated by resistor 14 during initial pulse 200' in which capacitor 16 first becomes charged depends on the square of the input potential: 0.5 x C x (VPS)2 / tp = 0.12 W. In contrast, during each subsequent pulse, e.g., pulses 200"—200"" and each pulse thereafter, the charged capacitor contributes to the electrical potential drop experienced by resistor 14. Therefore, the average power dissipated by resistor 14 during each subsequent pulse depends on the square of twice the input potential VPS: 0.5 x C x (2 x VPS)2 / tp - 2 x C x (VPS)2 / tp = 0.48 W. Heating system 10 efficiently converts the difference between the maximum and minimum electrical potential generated by DC power supply 22 (VPS) to energy and power dissipated by resistor 14. The average power dissipated is inversely proportion to the duration of the period of each pulse as well as the number of pulses generated per second. However, the energy and power dissipated are independent of the resistance of resistor 14. Referring to FIGURE 4, includes a diagnostic reader 112 and a microfluidic strip 114. Diagnostic reader 112 is configured to operate microfluidic strip 114 to perform a diagnostic assay for a target present in a liquid sample applied to the strip, e.g., as disclosed in the '933 application. Diagnostic strip 114 includes a microfluidic network 116 having a sample application zone 118 and a microchannel leading to a reaction zone 124, e.g., a detection zone. Microfluidic strip 114 may be configured and include features of microfluidic strips, e.g., reagents, gas chambers (gas bladders), and electrical sensing elements disclosed in the '933 application. Microfluidic strip 114 further includes a resistive element 124 disposed in thermal communication with reaction zone 124. For example, resistive element 124 may be formed from carbon ink-based resistive elements, silver ink-based resistive elements, metal oxide, e.g., silver oxide, resistive elements, and combinations thereof, printed or otherwise deposited on an external or internal surface of strip 114. Resistive element 124 is connected via a first lead 126 to a first terminal 126' and by a second lead 128 to a second terminal 128'. When strip 114 is inserted into a receiving slot 113 of reader 112, terminals 126',128' engage with corresponding connectors within the reader providing electrical communication therebetween. Remaining portions of the heating system, e.g., a DC power supply, capacitor, and switching assemblies are housed within the reader. The resistive element of the microfluidic strip 114 and the capacitor within the reader form a series RC circuit as disclosed herein. In use, strip 114 is inserted into receiving slot 113 and a liquid sample applied to application zone 118. The sample flows along microfluidic network 116 and is manipulated by reader 112 such as to move the liquid sample and mix the sample with reagents. The heating system is actuated to heat reaction zone 122 to facilitate a desired reaction or condition of the liquid sample and reagents therein. The capacitance of the capacitor, the DC voltage of the power supply, and other operating conditions, e.g., pulse period and frequency, of the of the heating system are chosen to produce a desired level of heating in the reaction zone. In some cases, the process for manufacturing such resistive elements leads to elements having a resistance that is not known with specificity. However, the range of resistances, e.g., with 99% confidence or more, can be determined. Typically, the duration tp of pulses generated by the heating system are determined based on the largest likely resistance of such resistive element such that tp >RC time constant, e.g., so that the ratio tp:RC is between about 3 and 10, between about 3 and 7, between about 3 and 6, e.g., about 4. EXAMPLE A heating system was prepared to assess the capability of generating the same amount of heat from resistive elements having different resistances. A first test RC circuit was prepared by connecting a 27 Q resistor and a 47 pF non-polarized capacitor connected in series (RC = 1.27 ms). A second test RC circuit was prepared by connecting a 150 Q resistor and a 47 pF nonpolarized capacitor connected in series (RC = 7.05 ms). Each resistor was a 1 / 8 W carbon film resistor. Each RC circuit included a first circuit lead corresponding to first circuit lead 18 of RC circuit 12 and a second circuit lead corresponding to second circuit lead 20 of RC circuit 12. The first circuit lead of each test RC circuit was connected to output 2 of a DRV8844PWP quad % H-bridge driver ("driver") manufactured by Texas instruments (rtmj and the second circuit lead of each test RC circuit was connected to output 1 of the driver. A constant (DC) power supply was used to input an electrical potential of 12 V to the driver. A switch system controller (an electronic processor) was used to input control signals to the driver thereby switching the state of the internal switches. In response to the control signals, the driver simultaneously alternated the polarity of the electrical potential (12 V) applied across the respective leads of each RC circuit as described for heating system 10. The pulse period tp was 28.2 ms, which is four times the length of the longest RC time constant of the two test RC circuits. The current and electrical potential capacities of the driver were sufficient to simultaneously operate each RC circuit without overloading the driver. Approximately 35 pulses per second were simultaneously delivered to each circuit. The temperature of each resistor was monitored by a respective thermocouple placed in thermal communication the resistor. The resistors were thermally isolated from one another, but exposed to the same ambient environment. With reference to temperature vs time chart of FIGURE 5, the temperature of each resistor increased from the ambient temperature (about 26 °C) to about 65 °C within about two minutes. At all times, the measured temperatures of the respective resistors are within about 1 °C of one another. The similar temperature profiles demonstrate the capability of the system to dissipate a constant average power from a resistor independently of its resistance. The ripples in the temperature vs time curves are believed to be due to air currents created by a computer cooling fan. After turning off the power to the heating system, the temperature of each resistor returned to ambient temperature within about 2.5 minutes. The respective 1 / 8 W resistors have a much larger thermal mass than ink-based resistive elements deposited on a surface of a diagnostic device. Accordingly, such diagnostic device resistive elements are expected to heat and cool much more rapidly than the 1 / 8 W test resistors employed in this Example.

Claims

What is claimed is:

1. A method of heating a reaction zone of a microfluidic strip, comprising:positioning a microfluidic strip in an operative position within a diagnostic reader, wherein the microfluidic strip comprises: (i) a microfluidic network comprising a reaction zone and (ii) a resistor adhered to a surface of the microfluidic strip in thermal communication with the reaction zone, wherein the resistor has a resistance R;connecting, in series, the resistor of the microfluidic strip and a capacitor disposed within the diagnostic reader to form an RC circuit having first and second RC circuit leads, wherein the capacitor has a capacitance C and the RC circuit has an RC time constant = trc;preparing a reaction mixture within the reaction zone of the microfluidic strip, wherein the reaction mixture comprises a liquid sample and at least one reagent;generating and maintaining a constant electrical potential VPS between first and second electrical supply leads disposed within the diagnostic reader; andwhile maintaining the constant electrical potential VPS between the first and second supply leads, heating the reaction zone by alternatingly and repeatedly performing the following steps to thereby dissipate an average power 2 x C x (VPS)2 / tp over the resistor:(1) connecting the first supply lead to the first RC circuit lead and the second supply lead to the second RC circuit lead for a time period tp of about 4 x trc; and(2) connecting the second supply lead to the first RC circuit lead and the first supply lead to the second RC circuit lead for the time period tp.

2. The method of claim 1, comprising performing the step of heating the reaction zone for a period of between about 10 s and 6000 s.

3. The method of claim 1 or 2, wherein the step of heating the reaction zone comprises performing each of the steps of (1) connecting and (2) connecting between about 10 and 50 times per second.

4. The method of any of claims 1—3, wherein VPS is between about 5 and 25 volts, e.g., about 12 volts.

5. The method of any of claims 1—4, wherein the resistance of the resistor is between about 20 O and about 200 Q.

6. The method of any of claims 1—5, wherein the capacitance of the capacitor is between about 20 p.F and about 75 p.F.

7. The method of any of claims 1—6, comprising dissipating between an average power of between about 0.2 and about 1.0 W over the resistor.

8. The method of any of claims 1—7, wherein the RC time constant is 7.5 ms, tp = 30 ms, VPS = 12 V, and the average power dissipated is about 0.48 W.

9. The method of any of claims 1—8, wherein the step of heating comprises heating the reaction mixture to a temperature of between about 40 °C and about 100 °C.

10. The method of any of claims 1—9, wherein a temperature of ambient gas surrounding the microfluidic strip is between about 20 °C and about 30 °C and the step of heating comprises heating the reaction mixture to a temperature of between about 20 °C and about 80 °C greater than the ambient temperature.

11. The method of any of claims 1—10, wherein the resistor is a carbon ink-based resistor, a silver ink-based resistor, a metal oxide strip or a combination thereof.

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