Fully Integrated Mass Flow, Pressure, Density and Viscosity Sensor for Both Liquids and Gases T.V.P

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FULLY INTEGRATED MASS FLOW, PRESSURE, DENSITY AND VISCOSITY SENSOR FOR BOTH LIQUIDS AND GASES T.V.P. Schut1, D. Alveringh1, W. Sparreboom2, J. Groenesteijn2 R.J. Wiegerink1, and J.C. Lötters1,2 1 MESA+ Institute for Nanotechnology, University of Twente, Enschede, THE NETHERLANDS 2 Bronkhorst High-Tech BV, Ruurlo, THE NETHERLANDS

ABSTRACT This paper reports on a fluid viscosity sensor consisting of pressure sensors fully integrated with a Coriolis mass flow sensor. The sensor is capable of measuring viscosities of both liquids and gases through a mathematical model. For liquids, this model is simply the Hagen-Poiseuille equation. For gases, a more elaborate model is derived, taking into account compressibility and additional pressure losses due to channel geometry. Viscosities of (mixtures of) water and isopropanol were measured and correspond well with values found in literature. Viscosities of nitrogen and argon were measured with accuracies of ∼0-12%, depending on input pressure and mass flow rate. Improvement of the Figure 1: Overview of the sensor. Pressure sensors upstream mathematical model could lead to higher accuracy and less and downstream of a Coriolis mass flow sensor are used to determine the pressure drop over the channel. Various fluid dependence on mass flow or pressure. parameters can be determined using the sensor. INTRODUCTION In many applications, knowledge of flow rate and fluid composition is of great importance, e.g. mixing of chemicals in (bio)chemical processes. Fluid composition can be determined from parameters such as pressure, mass flow rate, density and viscosity. In this paper, a sensor is presented which can measure all of the above mentioned Figure 2: Schematic representation of the sensor modes. Left: Actuation/Twist mode. Right: Detection/Swing mode. properties. The sensor consists of a micro Coriolis mass flow sensor integrated with resistive pressure sensors. drop over a Coriolis mass flow sensor, taking into account A micro Coriolis mass flow sensor [1] measures both compressibility and the aforementioned additional losses. mass flow and fluid density. The relation between mass flow and pressure drop over the channel can be used to determine DESIGN fluid viscosity. This is the most straightforward way to obtain An overview of the sensor is presented in Figure 1. viscosity [2] although other techniques have been proposed, The figure describes how the various fluid parameters are e.g. [3–5]. Lötters et al. presented a Coriolis-based multi- determined. parameter sensor [6] with external pressure sensors which Coriolis mass flow sensor could measure viscosities of liquids and gases within 10% accuracy. However, the gas viscosities were determined only The Coriolis mass flow sensor design is based on the for low flows, where compressibility could be neglected. sensor presented in [1]. The sensor has been characterized A subsequent sensor was presented in [7] with integrated in this paper by Sparreboom et al. The sensor works by capacitive pressure sensors. In [8], it was proposed to bringing it into resonance in the twist mode, see Figure integrate resistive pressure sensors with a Coriolis mass 2. When a flow is introduced, this results in a vibration flow sensor. Combining the latter sensor with a new model in the swing mode. The amplitude of this vibration is a for the pressure drop gives a means of measuring viscosities measure for the flow and can be measured with comb C , C of liquids and gases for the full laminar flow range. In drive capacitors ( 1 2) positioned at the free end of the case of liquids, the Hagen-Poiseuille equation is applicable channel. The density of the fluid inside the channel can be and pressure drop is directly proportional to viscosity. For determined from the resonance frequency. gases, a more elaborate model is needed. This is because: Pressure sensors 1) gases are compressible, i.e. gas density will change over The pressure sensors consist of resistive strain gauges the length of the channel, and 2) kinetic energy losses due patterned on top of the channel upstream and downstream of to sharp bends in the channel cannot be neglected due the Coriolis mass flow sensor (see Figure 1). The design and to high(er) flow velocities. A model was derived which characterization of the pressure sensors has been presented can be used to determine gas viscosity from the pressure in [8]. The operation of the sensors is explained in Figure 3. that the density will also vary throughout the channel. Furthermore, sharp bends and junctions in the channel introduce additional pressure drop. Due to high(er) flow velocities in gas flow, this effect cannot be neglected. A relation for the pressure drop over a straight channel can be derived from the basic energy relations for flow [10, 11]: u v dP + du + δU = 0 (4) β dis

Figure 3: Schematic representation of the pressure sensors. Where the first term represents a change in energy contained A pressure inside the channel results in deformation of the in a volume (per unit mass) of fluid v due to a change roof and elongation/compression of the strain gauges. The in pressure dP. The second term represents a change in resistances R R will decrease while R R increase. 1 & 4 2 & 3 kinetic energy, where u is the flow velocity and β is a MATHEMATICAL MODEL correction factor. The value of β depends on the flow regime Density (Turbulent: β = 1, Laminar: β = 0.5). Finally, the third and The actuation mode of the Coriolis mass flow sensor last term represents the dissipated energy due to friction. can be modelled as a second order system with resonance Laminar flow is assumed, Re < 2000 & β = 0.5, where Re frequency: is the Reynolds number. After various steps of substitution r k and integration, equation 4 becomes: ω0 = (1) m 2 2 2 2 P − P φm P1 l φm With k the modal spring constant and m the modal mass. The 2 1 + 2 ln + 2 f = 0 (5) 2RT A P r A relation between resonance frequency, pressure and density 2 is different for liquid- and gas flow due to compressibility. Where A is the cross sectional area of the channel and f is This leads to two expressions for the resonance frequency: the friction factor, which is dependent on viscosity: s s k(P) k + αP 8 4µπr ω = = 0 f = = (for Re < 2000) (6) liquid Re φm ρflVch + mch ρflVch + mch (2) s s Where µ is the dynamic viscosity. Thus, the dynamic k(P) k0 + αP ωgas = = viscosity of a gas flowing through a straight channel can be ρ (P)V + m PV /RT + m fl ch ch ch ch determined with equation 5. However, as already mentioned, the channel contains sharp bends and junctions which Where k(P) is the pressure dependent spring constant, k0 introduce additional pressure drop. This additional pressure is the spring constant at atmospheric pressure, ρfl is the drop due to these bends and junctions can be characterized density of the fluid inside the channel, Vch is the inner by a loss coefficient κ [9]: volume of the channel and mch is the mass of the channel itself. For gas, ρ = P/RT according to the ideal gas fl 1 1 κφ2 RT law [9], with pressure P, specific gas constant R and ∆P = ρu2κ = m (7) 2 2 PA2 temperature T. The spring constant is pressure dependent due to deformation of the channel by an applied pressure. Where ∆P is the pressure drop over the turn/junction and The resulting pressure dependency coefficient α can be fitted P is the pressure just before the turn/junction. The channel from measurement data. When α is known, fluid density can contains junctions where it splits into three equally large easily be determined from the resonance frequency. channels and it contains junctions where these channels Viscosity are joined back together. These junctions can be modelled The viscosity of the fluid inside the channel can as sudden expansion/contraction of the channel. These be determined from the relation between mass flow and junctions and the 90 degree bends are characterized each by pressure drop. For liquid flow, this relation is simply the their own loss coefficient. Table 1 shows the loss coefficient Hagen-Poiseuille equation: for each situation. Now the total pressure drop over the channel can be 8l estimated. Equation 5 can be used to calculate the pressure P − P = ηφm · (3) 2 1 πr4 drop over the straight channel sections. By combining equations 5 and 7, the pressure drop over the junctions/turns Where P1/2 is the up-/downstream pressure, η is the kinematic viscosity, φm is the mass flow rate and l, r are Symbol Description Value the channel length and effective radius respectively. κse Sudden expansion of the channel 0.44 κ Sudden contraction of the channel 0.28 For gas flow, the relation between pressure drop and sc κturn 90 degree turn in the channel 0.40 viscosity is not linear. The pressure throughout the channel is not constant. Since gas is compressible, this means Table 1: Loss coefficients for the different situations. [9] 1000

950 ) 3 900

850

Density (kg/m Literature Sensor at 3 bar 800 Sensor at 4 bar Sensor at 5 bar Sensor at 6 bar 750 0 20 40 60 80 100 Percentage of isopropan-2-ol (%) Figure 4: Scanning electron microscope image of the sensor. Figure 6: Measured densities of the liquids in comparison with experimentally determined values from [13]. ) −1

K 300 −2 s 2 275

250

225

200

175 N2: Literature Ar: Literature Measured Measured Figure 5: Schematic representation of the measurement 150 setup. Specific gas constant (m 5 6 7 8 Applied pressure (bar) can be calculated. Since the pressure drop over a section Figure 7: Measured specific gas constants of nitrogen and depends on its input pressure, this calculation needs to be argon at applied pressures of 5 to 8 bar with zero flow in done going along the channel section by section. Summing comparison with theoretical values [14]. The error bars the pressure drops over the separate sections gives the total represent 3σ, where σ is the standard deviation. pressure drop. Viscosity measurement FABRICATION The Hagen-Poiseuille equation is used to determine The sensor was fabricated according to the process the liquid viscosities. Again, an initial calibration is done 4 presented in [12]. An SEM image of the sensor is displayed with water to determine the constant l/r in Equation 3. in Figure 4. To reduce pressure drop, the channel is split The measured liquid viscosities are displayed in Figure into three equally large channels at each side of the Coriolis 8. As can be seen from the literature data, temperature mass flow sensor. Resistive strain gauges are patterned on greatly influences viscosity. Unfortunately, temperature of each of the channels. The capacitive readout structure is the liquids was not measured. Joule heating will occur due visible in the top of the image. to Lorentz actuation. As a result, the temperature of the liquids can be assumed to be 1 to 2 degrees above room EXPERIMENTAL temperature. The measurement data seems to correspond The measurement setup is displayed in Figure 5. A fluid well with this assumption. It is difficult to determine the is fed into the chip via a chosen input pressure. A Bronkhorst accuracy from this data, since the exact temperature during Cori-Flow mass flow controller is used to control the mass the measurement was unknown. flow through the chip. The pressure drop is measured For gas, it was mentioned that a more elaborate model for various combinations of input pressure and mass flow is used to determine the viscosities. Before the viscosities rate. These measurements are done with liquids as well as can be determined, the model must first be validated. The gases. The following liquids are used: water, isopropanol pressure drop is approximated using the model based on and mixtures with ratios 25/75, 50/50 and 75/25 (vol%). equations 5 and 7 with theoretical dynamic viscosities Nitrogen and argon are used during the gas measurements. [14]. Figure 9 shows the approximated pressure drop and Density measurement measured pressure drop in relation to the mass flow. The After initial calibration measurements with water, the pressure drop is approximated with and without taking into constants in equation 2 are determined. Using the model account additional losses. As can be seen from the figure, with these constants, the liquid densities and the specific the curves all have similar shape. However, when additional gas constants are obtained. Figure 6 shows the densities of losses are not taken into account, there is a large difference the various liquids. The input pressure hardly affects the between the measured and modelled pressure drop. The determined density and the accuracy is very high with a additional losses must thus be taken into account. The maximum error of approximately 1%. curve corresponding to the additional loss model is still The measured specific gas constants are displayed in not 100% accurate. This is most likely due to inaccuracy Figure 7. The accuracy of these is slightly lower, with a in the loss coefficients in Table 1. The gas viscosities are maximum error of approximately 4.5%. determined from the measurement data using a total fitted 4.5 30

/s) 25 2 3.5 Pa s)

T=293.15K µ 3 20 T=298.15K

2.5 T=303.15K 15 2 N : Literature Ar: Literature 1.5 Literature 10 2 Flow ≈ 2 g/h Dynamic viscosity ( Flow ≈ 2 g/h Flow ≈ 2 g/h Kinematic Viscosity (mm 1 Flow ≈ 3 g/h Flow ≈ 3 g/h Flow ≈ 3 g/h Flow ≈ 4 g/h Flow ≈ 4 g/h Flow ≈ 4 g/h 5 0.5 4 5 6 7 8 9 0 20 40 60 80 100 Pressure (bar) Percentage of IPA (%) Figure 10: Measured dynamic viscosities of the gases in Figure 8: Measured kinematic viscosities of the liquids in comparison with theoretical values [14]. The error bars comparison with literature [13]. The input pressure for this represent 3σ, where σ is the standard deviation. particular measurement is 4 bar, similar data is obtained for other input pressures. The error bars represent 3σ, where ACKNOWLEDGEMENTS σ is the standard deviation. The authors gratefully acknowledge ﬁnancial support 4 by the Eurostars Programme through the TIPICAL project Measured pressure drop 3.5 Approximation straight channel (E!8264) and R.G.P. Sanders for technical support. Appr. including additional losses 3

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2 [1] W. Sparreboom et al., “Compact mass ﬂow meter based on a micro coriolis ﬂow sensor,” Microma- 1.5 chines, vol. 4, no. 1, pp. 22–33, 2013.

Pressure drop (bar) 1 [2] J. J. Singh et al., “Measurement of viscosity of gaseous mixtures at atmospheric pressure,” 1986. 0.5 [3] M. Andrews et al., “Damping and gas viscosity 0 measurements using a microstructure,” Sensors and 0 1 2 3 4 5 Actuators A: Physical, vol. 49, pp. 103–108, 1995. Mass flow (g/h) [4] J. Van Baar et al., “Micromachined two dimensional Figure 9: The measured and modelled pressure drop in resistor arrays for determination of gas parameters,” relation to mass flow rate. Nitrogen is used as a flow medium, in Transducers, 12th International Conference, vol. 2. at an input pressure of approximately 7 bar. IEEE, 2003, pp. 1606–1609. [5] R. Dias et al., “Gas viscosity mems sensor based on Transducers, 17th International Confer- loss coefficient with the corresponding pressure in equation pull-in,” in ence. IEEE, 2013, pp. 980–983. 7 being the average pressure inside the channel. Figure 10 [6] J. C. Lotters et al., “Integrated multi-parameter flow shows the measured dynamic viscosities of the gases in measurement system,” in MEMS, 27th International comparison with values from literature [14]. Conference. IEEE, 2014, pp. 975–978. [7] J. C. Lötters et al., “Fully integrated microfluidic The accuracy ranges from ∼0-12%. This variation in measurement system for real-time determination of accuracy most likely due to the fact that in fitting the total gas and liquid mixtures composition,” in Transducers, loss coefficient, the average pressure was used as a reference 18th Int. Conference. IEEE, 2015, pp. 1798–1801. et al. pressure. This is a rough approximation. By improving the [8] D. Alveringh , “Resistive pressure sensors integrated with a coriolis mass flow sensor,” in Transduc- approximation of the additional losses, the model can be ers, 19th Int. Conf. IEEE, 2017, pp. 1167–1170. improved and thus the accuracy. [9] F. White, Fluid Mechanics 4th edition, Chapter 6, ser. International editions. McGraw-Hill, 2003. [10] J. Douglas, Fluid Mechanics, Chapters 10 and 17. CONCLUSION Pearson/Prentice Hall, 2005. A Coriolis-based multi-parameter sensor has been [11] J. Coulson et al., Chemical Engineering: Vol. 1, Fluid realized, which is capable of measuring viscosities of both flow, heat transfer and mass transfer, chapters 2 & 4. Pergamon Press, 1990. liquids and gases. Measured liquid viscosities correspond [12] J. Groenesteijn et al., “A versatile technology platform well with values from literature. However, integration of for microfluidic handling systems, part i: fabrication temperature sensing is necessary to accurately determine and functionalization,” Microfluidics and Nanoflu- fluid composition. Gas viscosities have been determined idics, vol. 21, no. 7, p. 127, 2017. et al. ∼ [13] F.-M. Pang , “Densities and viscosities of aqueous through a newly derived model. The accuracy is 0-12%. solutions of 1-propanol and 2-propanol at tempera- The relatively low accuracy and variation in accuracy is due tures from 293.15 k to 333.15 k,” Journal of Molecular to assumptions made in the approximation of the additional Liquids, vol. 136, no. 1, pp. 71–78, 2007. ® pressure loss. The approximation of additional losses can [14] “Bronkhorst FLUIDAT , flow property calculation be perfected by investigating the effect of junctions/turns system.” [Online]. Available: http://www.fluidat.com experimentally or through simulation. Thus, the accuracy CONTACT of the sensor can be improved simply by improving the Thomas Schut model, without making any changes to the sensor itself. [email protected]