Abstract:
A microfluidic device and method for assessing properties of a fluid. The device includes a base supported by a substrate and a tube extending from the base and spaced apart from the substrate surface. The tube has an internal passage, first and second portions adjacent the base and defining, respectively, an inlet and outlet of the passage, and a distal portion. A drive electrode is located on the substrate surface adjacent the distal portion of the tube. Sensing electrodes are located on the substrate surface adjacent the first and second portions of the tube, and are adapted for sensing deflections of the first and second portions when vibrated with the drive electrode and from which the fluid property is determined. A pair of electrodes is located on the substrate surface between the drive and sensing electrodes, and are operated to enhance the performance of the microfluidic device, such as by supplementing the drive or sensing electrodes.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 60/756,488 filed Jan. 6, 2006, and U.S. Provisional Application No. 60/786,882 filed Mar. 30, 2006, the contents of which are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention generally relates to devices and methods for measuring properties of fluids. More particularly, this invention relates to a microfluidic device equipped with a microchannel through which a fluid flows and means for ascertaining properties of the fluid while flowing through the microchannel. 
     Fluid delivery devices, systems, and methods involve technologies under constant development. Examples of fluid delivery systems of particular current interest include drug infusion systems and fuel cell systems, both of which require devices capable of delivering relatively small amounts of a fluid. While fuel cells have been used for many years to provide electrical power, currently there is increased interest for their use in consumer products such as automobiles, computers, cellular phones, personal digital assistants (PDA&#39;s), camcorders, and other portable devices. Fuel cell systems typically employ a small electrically powered fluid pump to deliver fluids to various parts of the system, such as water, fuels, and fuel cell solutions, examples of which include mixtures of water and fuels such as methanol, ethanol, ethylene glycol, isopropyl alcohol (IPA), formic acid, sulfuric acid, gasoline, diesel fuel, and other organic liquids. The solution is delivered to a fuel cell, such as a reformed fuel cell, direct methanol fuel cell (DMFC), or proton exchange membrane (PEM) fuel cell (or PEMFC), which can be adapted to provide power to a vehicle or other device that requires electrical power. 
     As well known in the art, in a fuel cell system it is important to know the concentration of a fuel in fuel cell solution to optimize the efficiency of the system. For example, DMFC&#39;s often employ a fuel cell solution of methanol mixed with water to reduce membrane crossover problems and boost the efficiency of the fuel cell. If the methanol concentration is too high, crossover problems can occur, whereas low methanol concentrations reduce the power output of the fuel cell. Consequently, various concentration sensors for fuel cell systems have been proposed, including electrolytic, refractometer, ultrasonic, electrochemical, electromagnetic, and electromechanical sensors. An example is an electromechanical system disclosed in commonly-assigned U.S. patent application Publication No. 2006/0213552 to Sparks et al., which makes use of a Coriolis-based fluid sensing device preferably of a type disclosed in commonly-assigned U.S. Pat. No. 6,477,901 to Tadigadapa et al., whose contents relating to the fabrication and operation of a Coriolis-based sensor are incorporated herein by reference. Sparks et al. teach that chemical concentrations, including those of fuel cell solutions, can be measured by sensing changes in fluid density as a fluid sample flows through a microchannel within a resonating tube of a Coriolis-based fluid sensing device. 
     A fluid sensing device  10  of a type disclosed by Tadigadapa et al. and Sparks et al. is represented in  FIGS. 1 and 2 . The device  10  is represented as including a micromachined tube  14  extending from a base  28  on a substrate  12  and having a freestanding portion  16  above a surface  18  of the substrate  12 . Drive and sensing electrodes  22  and  24  are located on the surface  18  beneath the freestanding portion  16  of the tube  14 , and bond pads  32  (only one of which is shown) are provided for transmitting input and output signals to and from the device  10 . The drive electrode  22  can be, for example, capacitively coupled to the tube  14  for capacitively (electrostatically) driving the freestanding portion  16  at or near resonance, while the sensing electrodes  24  sense (e.g., capacitively, optically, etc.) the deflection of the tube  14  relative to the substrate  12  and provide feedback to enable the vibration frequency induced by the drive electrode  22  to be controlled with appropriate circuitry. With a fluid entering the device  10  through an inlet port  26  and flowing through an internal passage  20  within the tube  14 , the freestanding portion  16  can be vibrated at or near resonance by the drive electrode  22  to ascertain certain properties of the fluid, such as flow rate and density, using Coriolis force principles. In particular, as the freestanding portion  16  is driven at or near resonance by the drive electrode  22 , the sensing electrodes  24  sense a twisting motion of the freestanding portion  16 , referred to as the Coriolis effect. Because the twisting motion is more readily detectible along the parallel legs of the freestanding portion  16 , the sensing electrodes  24  may be positioned along the entire lengths of the legs. The degree to which the freestanding portion  16  deflects during a vibration cycle as a result of the Coriolis effect can be correlated to the mass flow rate of the fluid flowing through the tube  14 , while the density of the fluid is proportional to the frequency of vibration at resonance. Notable advantages of the device  10  include the extremely miniaturized scale to which it can be fabricated and its ability to precisely analyze very small quantities of fluids. In  FIG. 2 , the device  10  is schematically shown as enclosed by a cap  30  to allow for vacuum packaging that further improves the performance of the device  10  by reducing air damping effects. 
     During fuel cell power generation processes, carbon dioxide and other gases are generated that can form bubbles within the fuel cell solution. Any air dissolved in the solution can also form bubbles under high temperature or low pressure conditions. Bubbles present in a liquid can cause errors in chemical concentration outputs based on density, as well as density measurements made by measuring speed of sound (ultrasonic measurements), refractive index, and other methods. Sensing errors can also occur over time as a result of films and residues building up on sensing elements such as tubes and windows, resulting in an offset shift in the chemical concentration output. For resonating tubes of the type employed by Sparks et al., bubbles present in the liquid being evaluated will increase the resonant frequency of the resonating tube, and build up of a film or residue on the internal surfaces of the tube will lower the resonant frequency of the tube, resulting in errors in density measurements. 
     The ability to detect potential measurement errors of the types noted above is complicated by other potential sources of sensor output drift, including imperfections due to manufacturing variations and defects, particles (or other second phases) in the fluid being sensed, differences in materials that lead to different responses to temperature and mechanical stress, charge buildup, and others. Therefore, while sensors of the type taught by Tadigadapa et al. and used by Sparks et al. have proven to be extremely precise in their ability to measure properties of fluids, further improvements capable of addressing the above-noted issues would be desirable. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention provides a microfluidic device and method for assessing properties of a fluid. The invention provides the capability of improving the performance of a microfluidic device, such as by improving the sensitivity of the device, and/or detecting potential measurement errors attributable to, for example, second phases such as gas bubbles in the fluid being evaluated, film buildup on the surfaces of the device contacting the fluid, and manufacturing and material variations and defects of the device itself. 
     According to a first aspect of the invention, a microfluidic device is provided that is operable to determine at least one property of a fluid. The device includes a structure comprising a base supported by a substrate and a tube extending from the base and spaced apart from a surface of the substrate so as to be capable of vibrating in a plane normal to the surface of the substrate. The tube has a continuous internal passage, a first portion adjacent the base and defining a fluid inlet of the passage, a second portion adjacent the base and defining a fluid outlet of the passage, and a distal portion relative to the base. A drive electrode is located on the surface of the substrate adjacent the distal portion of the tube, and is adapted for vibrating the tube. Sensing electrodes are located on the surface of the substrate adjacent the first and second portions of the tube. The sensing electrodes are adapted for sensing deflections of the first and second portions of the tube when vibrated with the drive electrode, and for producing outputs corresponding to the sensed deflections and from which the property of the fluid is determined. A pair of electrodes is located adjacent the tube and on the surface of the substrate between the drive electrode and the sensing electrodes. According to this aspect of the invention, the location of the sensing electrodes is preferably chosen to enhance the sensitivity and overall performance of the microfluidic device, and the pair of electrodes can be operated to supplement the drive or sensing electrodes, compensate for manufacturing and material variations and defects within the device, or otherwise promote the performance of the device. 
     According to a second aspect of the invention, a method is provided by which a microfluidic device is operated to sense the density of a fluid. A structure of the microfluidic device is vibrated as the fluid flows through a microchannel within the structure, a series of outputs is produced corresponding to the vibration frequency of the vibrating structure, and the density of the fluid flowing through the microchannel of the vibrating structure is determined on the basis of at least a first set of the outputs. In determining the fluid density, any outputs altered by a second phase in the fluid are excluded from the determination, and/or the density for any film build-up within the microchannel is offset from the fluid density. According to this aspect of the invention, the accuracy of the measurements performed by the microfluidic device is promoted by detecting sources of potential measurement errors attributable to, for example, second phases such as gas bubbles in the fluid being evaluated, film buildup on the surfaces of the device contacting the fluid, and manufacturing and material variations and defects of the device itself. 
     Other objects and advantages of this invention will be better appreciated from the following detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1 and 2  are perspective and cross-sectional views, respectively, of a microfluidic device with a resonating micromachined tube through which a fluid flows in accordance with the prior art. 
         FIG. 3  is a plan view of a microfluidic device with a resonating micromachined tube in accordance with a first embodiment of this invention. 
         FIG. 4  is a plan view of a microfluidic device with a resonating micromachined tube in accordance with a second embodiment of this invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIGS. 3 and 4  represent microfluidic devices  40  similar in construction and operation to the prior art microfluidic device  10  of  FIGS. 1 and 2 , but modified to exhibit improved operating characteristics. In  FIGS. 3 and 4 , consistent reference numbers are used to identify functionally equivalent structures. Each device  40  is represented as being fabricated on a substrate  42 , which can be formed of silicon or another semiconductor material, quartz, glass, ceramic, metal, or a composite material. A tube  44  is cantilevered from a base  46  bonded to the substrate  42 , such that the tube  44  is suspended above a surface  48  of the substrate  42 . In  FIG. 3 , the surface  48  is defined by a single recess in the substrate  42  underlying the entire tube  44 , while in  FIG. 4  the surface  48  is defined by multiple recesses  50  and  52  in the substrate  42 . The tube  44  is generally U or C-shaped, resulting in the tube  44  having legs with proximate portions immediately adjacent the base  46  and a distal portion interconnecting the legs. Furthermore, the base  46  is between the proximate portions of the legs of the tube  44 , and the proximate portions are coaxial. While the shape of the tube  44  shown in  FIGS. 3 and 4  is preferred, other shapes—both simpler and more complex—are also within the scope of the invention. The tube  44  defines a continuous microchannel  54  through which a fluid can flow into the tube  44  from the base  46 , and is then returned to the base  46  as it exits the tube  44 . Fluid preferably enters and exits the device  40  through a fluid inlet  56  and outlet  58  defined in the substrate  42 . 
     The tube  44  and its base  46  are preferably micromachined from silicon, doped silicon, or another semiconductor material, quartz, glass, ceramic, metal or composite material. As used herein, micromachining is a technique for forming very small elements by bulk etching a substrate (e.g., a silicon wafer), or by surface thin-film etching, the latter of which generally involves depositing a thin film (e.g., polysilicon or metal) on a sacrificial layer (e.g., oxide layer) on a substrate surface and then selectively removing portions of the sacrificial layer to free the deposited thin film. The tube  44  and base  46  can either be fabricated entirely from layers of the chosen materials deposited on the substrate  42 , or fabricated in part by etching the substrate  42 . The shape and size of the tube  44  can be chosen to provide an adequate flow capacity for the fluid and to have suitable vibration parameters for the intended fluids to be evaluated with the device  40 . Because micromachining technologies are employed to fabricate the tube  44 , the size of the tube  44  can be extremely small, such as lengths of about 0.5 mm and cross-sectional areas of about 250 μm 2 , with smaller and larger tubes also being within the scope of this invention. Particularly suitable configurations and processes for fabricating resonant mass flow and density sensors using micromachining techniques are disclosed in commonly-assigned U.S. Pat. No. 6,477,901 to Tadigadapa et al., commonly-assigned U.S. Pat. No. 6,647,778 to Sparks, and commonly assigned U.S. patent application Publication No. 2006/0175303 to Sparks et al. 
     According to Tadigadapa et al., each of the micromachined tubes  44  shown in  FIGS. 3 and 4  can be vibrated at or near resonance to determine the mass flow rate and density of a fluid flowing through the tube  44  using Coriolis force principles. As such, the devices  40  are suitable for use in chemical concentration applications, including but not limited to drug infusion systems, fuel cell systems, and drug and chemical mixing systems. Coriolis force principles can also be used to ascertain the viscosity, lubricity, and other properties of a fluid flowing through the tube  44 . As in Tadigadapa et al., the tube  44  is vibrated in a direction perpendicular to the surface  48  of the substrate  42 , preferably at or near its resonant frequency. During half of the vibration cycle in which the tube  44  moves upward, the tube  44  has upward momentum as the fluid travels around the tube bends, and the fluid flowing out of the tube  44  resists having its vertical motion decreased by pushing up on the leg of the tube  44  nearest the fluid outlet  58 . The resulting force causes the tube  44  to twist. As the tube  44  moves downward during the second half of its vibration cycle, the tube  44  twists in the opposite direction. This twisting characteristic is referred to as the Coriolis effect, and the degree to which the tube  44  deflects during a vibration cycle as a result of the Coriolis effect can be correlated to the mass flow rate of the fluid flowing through the tube  44 , while the density of the fluid is proportional to the frequency of vibration at resonance. 
     Similar to the device  10  of the prior art, the microfluidic device  40  can be enclosed by a capping wafer to form a sensing package. The use of a capping wafer allows for vacuum packaging that reduces air damping of the tube vibration. A variety of package and wafer-level methods exist to vacuum package devices. These include solder or weld hermetic packages, and wafer bonding using glass frit, solder, eutectic alloy, adhesive, and anodic bonding. A preferred material for the capping wafer is silicon, allowing silicon-to-silicon bonding techniques to be used, though it is foreseeable that a variety of other materials could be used, including metals and glass materials, the latter including borosilicate glass (e.g., Pyrex). In preferred embodiments of the invention, the bond between the capping wafer and substrate  42  is hermetic, and the resulting enclosure is evacuated to enable the tube  44  to be driven efficiently at high quality (Q) factor values without damping. In such an embodiment, a getter material is preferably placed in the enclosure to assist in reducing and maintaining a low cavity pressure. As an alternative to a hermetically sealed package, the tube  44  could be enclosed such that a vacuum can be drawn when desired through the use of a pump. 
     In addition to the density of the fluid within its microchannel  54 , the resonant frequency of the tube  44  is influenced by its mechanical design (shape, size, construction and materials). Resonant frequencies will generally be in the range of about 1 kHz to about 100 kHz for tubes of the type fabricated in accordance with Tadigadapa et al. The amplitude of vibration is preferably adjusted through means used to vibrate the tube  44 . As shown in  FIGS. 3 and 4 , a drive electrode  60  is located on the surface  48  of the substrate  42  beneath the distal portion of the tube  44 . If formed of an electrically-conductive material, such as doped silicon, the tube  44  can serve as an electrode that can be capacitively coupled to the drive electrode  60 , enabling the electrode  60  to electrostatically drive the tube  44 . However, it is foreseeable that the tube  44  could be formed of a nonconductive material, and a separate electrode formed on the tube  44  opposite the electrode  60  for vibrating the tube  44  electrostatically. An alternative driving technique is to provide a piezoelectric element on an upper surface of the tube  44  to generate alternating forces in the plane of the tube  44  that flex the tube  44  in directions normal to the plane of the tube  44 . Other alternatives are to drive the tube  44  magnetically, thermally, piezoresistively, thermally, optically, or by another actuation technique. 
     Also shown in  FIGS. 3 and 4  is a pair of sensing electrodes  62  that sense the deflection of the tube  44  relative to the substrate  42 , as well as provide feedback to the drive electrode  60  to enable the vibration frequency to be controlled with any suitable on-chip or remote microprocessor or microcontroller  70 . The sensing electrodes  62  can sense the proximity or motion of the tube  44  capacitively, electrostatically, magnetically, piezoelectrically, piezoresistively, thermally, optically, or in any other suitable manner capable of sensing the proximity or motion of the tube  44 . Furthermore, the degree to which the tube  44  twists during a vibration cycle as a result of the Coriolis effect can be detected by the sensing electrodes  62  on the basis of the amplitude of the deflection and/or the phase difference between the respective sides (legs) of the tube  44  nearest the electrodes  62 . Input and output signals to the electrodes  60  and  62  (and electrodes  64  of  FIG. 4 ) are made through bond pads  66  along an edge of the substrate  42 , and are transmitted to the microcontroller  70  with appropriate signal conditioning circuitry  68 , as schematically represented in  FIGS. 3 and 4 . Finally, ground contacts  74  are shown as being formed in the same metal layer as that used to form the electrodes  60  and  62  and bond pads  66 , and by which an electrical ground to the tube base  46  is provided to enable the tube  44  or an electrode formed on the tube  44  to be capacitively coupled to the drive electrode  60 . 
     As previously discussed in reference to the prior art of  FIGS. 1 and 2 , the ability to accurately measure properties of a fluid flowing through the resonating tubes  44  of  FIGS. 3 and 4  is degraded by the presence of gas bubbles or another second phase within the fluid, the build up of films on the internal walls of the tubes  44 , structural imperfections due to manufacturing variations and defects, differences in materials that lead to different responses to temperature and mechanical stress, charge buildup, and other sources. With particular respect to bubbles, the presence of bubbles or another unintended low density second phase within the fluid under evaluation affects the output of the resonating tube  44  by increasing its resonant frequency. The change in resonant frequency due to a lighter second phase can be sufficient to cause an error in liquid chemical concentration applications. For example, in a fuel cell system in which a solution of water and alcohol (e.g., methanol or ethanol) is used, gas bubbles in the solution will yield a false reading that a higher concentration of alcohol is present. 
     According to a first aspect of the invention, in addition to increasing the resonant frequency of the tube  44 , the presence of bubbles or another low density second phase in the fluid under evaluation can be detected as a result of measurably lowering the peak gain and Q factor of the tube  44  via two-phase damping. As such, by also monitoring the peak gain and/or Q factor associated with the output of the tube  44 , a lower gain signal or Q factor value can be used to indicate that gas bubbles, and not a higher alcohol concentration in the fluid, are increasing the resonant frequency of the tube  44  and thus yielding an inaccurate density/chemical concentration measurement. A low gain or Q factor reading that falls outside (below) a predetermined threshold value can be used to initiate a computational algorithm with the microcontroller  70  that compensates for the presence of gas bubbles passing through or trapped within the tube  44 . For example, the drive signal to the drive electrode  60  can be increased to ensure that the gain of the tube  44  is maintained so that a clear signal output is obtained with the device  40  until the low gain or Q factor reading falls within a empirically or theoretically expected range for the tube  44  and fluid under evaluation. An alternate method is to monitor the tube  44  for readings indicating a sharp increase in resonant frequency coinciding with a sharp decrease in peak gain or Q factor, and then employ an algorithm to filter out any such frequency readings, for example, by using a previous frequency reading, until the peak gain or Q value again falls within an empirically or theoretically expected range for the tube  44  and fluid under evaluation. A lower gain value or Q factor reading can also be used by the microcontroller  70  to trigger a high pressure pulse in the fluid to help flush out any gas bubble that might be trapped in the tube  44 . 
     The gradual build up of a film on the internal walls of the tube  44  often manifests itself as output drift over time. In addition to altering the resonant frequency of the tubes  44  for the devices  40  shown in  FIGS. 3 and 4 , film build up can also attenuate signals of optical and infrared (IR) sensors and change the speed of sound of ultrasonic sensors. If the build up of certain chemicals in a fluid under evaluation is predictable, such as a fuel cell solution with a fairly constant mixture ratio and by-product formation rate, then the output drift of the device  40  can be empirically or theoretically predicted for periods of time under different temperature conditions. Therefore, by monitoring the temperature of the tube  44  over measured time periods, the microcontroller  70  can be programmed to include a frequency offset algorithm, such that the predicted drift in the mass of the tube  44  due to film build up can be removed from the chemical concentration calculation. This functionality has the capability of significantly reducing measurement errors, and also enables the microfluidic device  40  to operate for longer periods of time without the need to remove the film build-up within the internal microchannel  54  of the tube  44 . 
     For monitoring temperature, the devices  40  of  FIGS. 3 and 4  are represented as being equipped with a temperature sensing element  72 . A suitable construction for the sensing element  72  can make use of one or more metal layers of the type employed to form the electrodes  60  and  62  and their associated conductive runners. For example, a resistive-based temperature sensing element  72  can be formed by a thin-film metal layer of platinum, palladium, nickel, or another metal or alloy, in accordance with known practices. With the temperature sensing element  72 , changes in mechanical properties of the tube  44  and properties of the fluid therein attributable to temperature changes can be compensated for with the signal conditioning circuitry  68 . 
     The above-noted algorithms and functionalities of the microcontroller  70  can be implemented in any suitable manner known in the art, including fuzzy logic algorithms and statistical and probability-based algorithms capable of estimating whether the output of the tube  44  is attributable to changes in the chemical concentrations within the fluid, or gas bubbles present in the fluid, or a film build up on the internal walls of the tube  44 . The algorithms can be loaded into the microprocessor  70  using the device  40 , in which case the output of the device  40  would be processed by a system computer and the effects of bubbles and/or film build-up removed from the raw sensor output signal. The use of algorithms in the manners described above to compensate for bubbles and film build-up in sensing devices with microchannels is not limited to the embodiments represented in  FIGS. 3 and 4 , but can also be applied to liquid concentration sensors employing optical or transparent tubes, channels, walls, and windows, ultrasonic/speed-of-sound windows, tubes, and channels, x-ray transmitted sensors, capacitive monitors, heat monitoring sensors, sensors that take resistive measurements through a wall and/or fluid path, and sensors that send a beam or wave through a liquid or monitor the wall of a fluidic channel. 
     According to another aspect of the invention, the vibration motion induced in the tube  44  by the drive electrode  60  can interfere with the ability of the sensing electrodes  62  to detect the twisting motion of the tube  44  induced by the Coriolis effect. In particular, finite element modeling (FEM) of resonant tube devices configured similarly to that shown in  FIG. 3  have evidenced that the amplitude of the drive motion is much greater than that of the twisting motion of the Coriolis flow mode. In particular, FEM analysis has evidenced that the drive motion is greatest at the distal portion of the tube  44  farthest from the base  46  and immediately above the drive electrode  60 , and smallest within the proximate portions of the tube  44  immediately adjacent the base  46 , where the greatest sensitivity to the twisting motion is also observed as a result of the fluid entering and exiting the tube  44  from the base  46 . In response to this analysis, the embodiment of  FIG. 4  represents the sensing electrodes  62  as being reduced in size and location for the purpose of sensing the deflection of only the proximate portions of the tube  44  immediately adjacent the base  46 , thereby reducing the drive motion of the tube  44  sensed by the sensing electrodes  62 . In particular, whereas the sensing electrodes  62  of  FIG. 3  extend the entire length of each leg of the tube  44 , the sensing electrodes  62  of  FIG. 4  extend less than half the length of each leg, i.e., less than half the distance from the base  46  to the distal portion of the tube  44 . Computer simulations and empirical test results have evidenced that limiting the size and location of the sensing electrodes  62  in the manner represented in  FIG. 4  enhances the resolution of the device  40  for sensing mass flow rate and density of a fluid flowing through the tube  44 . 
     The sensing electrodes  62  are also represented in  FIG. 4  as being within the recesses  50 , which are preferably formed in the surface  48  of the substrate  42  so as to be shallower than the recesses  52  in which the drive electrode  60  is formed. As such, the gap between the tube  44  and the drive electrode  60  is sufficiently large to accommodate the increasingly greater motion of the tube  44  corresponding to increasing distances from the base  46 , whereas the smaller gap between each sensing electrode  62  and the tube  44  enables the sensing electrodes  62  to exhibit increased sensitivity to the deflection of the tube  44 .  FIG. 4  also represents the device  40  as having a second set of electrodes  64  located between the drive and sensing electrodes  60  and  62  and within the deeper recesses  52 . The electrodes  64  can be used as drive electrodes along with or instead of the drive electrode  60 , or used as sensing electrodes to supplement the sensing electrodes  62 . If the electrodes  64  are used for sensing, either set of the sensing electrodes  62  and  64  can operate on the basis of phase difference and/or amplitude measurement. For example, the phase difference approach can be used by the electrodes  64 , while the amplitude measurement approach is used by the electrodes  62  nearest the base  46  where the Coriolis flow effect is most pronounced. 
     The second set of electrodes  64  can also be employed as balancing electrodes to compensate for errors leading to output drift of the device  40 . For example, a bias can be applied to the electrodes  64  to compensate for a twist that is present in the tube  44  as a result of manufacturing or material variations that can cause a zero-flow offset error in the sensor output. A balance control loop can be incorporated into the microcontroller  70  that uses the outputs of the sensing electrodes  62  to vary the balance voltage over temperature and time to compensate for this offset difference between the legs of the tube  44 . This compensation can greatly improve the basic noise floor of the device  40 , enhancing output resolution and accuracy. Offset compensation can be accomplished with a two-step process. During sensor calibration, any offset error or difference can be nulled out by adjusting the bias of the balance electrodes  64  to provide rough balancing or compensation. The balance control loop can then be employed to perform any further adjustments to the bias of the balance electrodes  64  to complete the compensation process, and allow for corrections to be made during the operation of the device  40 . 
     The electrodes  64  can also be employed to compensate for damping due to a two-phase condition, such as where bubbles, solid particles, an emulsion phase, etc., is present in the fluid being evaluated. When a reduced gain or Q factor condition is detected as discussed previously with respect to  FIG. 3 , the microcontroller  70  can operate the electrodes  64  as additional drive electrodes to increase the amplitude of the tube  44 , with the intent of dislodging and expelling the bubbles, solid particles, emulsion phase, or other second phase that caused the increased damping condition. 
     As noted above, the shallower recesses  50  in which the sensing electrodes  62  are formed results in smaller gaps being present between the sensing electrodes  62  and the proximate portions of the tube  44  as compared to the gap between the electrodes  60  and  64  and the remaining portions of the tube  44 , thereby providing the sensing electrodes  62  with greater sensitivity (higher sensor gain) to the twisting motion of the tube  44  as compared to the electrodes  64 . The shallower gap between the tube  44  and sensing electrodes  62  is preferably in a range of about 0.1 microns to about 4 microns, with the gaps between the tube  44  and drive electrode  60  and between the tube  44  and the electrodes  64  being greater. While the recesses  50  and  52  are represented as being etched into the surface  48  of the substrate  42 , it should be understood that the same affect can be obtained by micromachining the tube  44  so that the gaps between the tube  44  and sensing electrodes  62  are less than the gaps between the tube and the electrodes  60  and  64 . Furthermore, it should be understood that the electrodes  62  and  64  could be spaced the same distance from the tube  44 , though with reduced sensitivity to the twisting motion of the tube  44 . 
     It should be noted that the relative lengths of the tube  44  associated with sensing electrodes  62  as compared to the second set of electrodes  64  can vary. While the electrodes  64  are represented in  FIG. 4  as being larger than the sensing electrodes  62 , and therefore associated with longer lengths of the tube  44  than the sensing electrodes  62 , in some cases it may be preferable that the sensing electrodes  62  are larger than the electrodes  64 . 
     While the invention has been described in terms of certain embodiments, it is apparent that other forms could be adopted by one skilled in the art. Therefore, the scope of the invention is to be limited only by the following claims.