A microfluidic study of transient flow states in permeable media using fluorescent particle image velocimetry

Jindi Sun, Ziqiang Li, Frederico Furtado, Saman A. Aryana

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Velocity fields in flow in permeable media are of great importance to many subsurface processes such as geologic storage of CO2 , oil and gas extraction, and geothermal systems. Steady-state flow is characterized by velocity fields that do not change significantly over time. The flow field transitions to a new steady state once it experiences a disturbance such as a change in flow rate or in pressure gradient. This transition is often assumed to be instantaneous, which justifies the expression of constitutive relations as functions of instantaneous phase saturations. This work examines the evolution of velocity fields in a surrogate quasi-2D permeable medium using a microfluidic device, a microscopy system, and a high-speed camera. Tracer particles are injected into the medium along with Deionized water. The evolution of the velocity field is examined by tracing these particles in the captured images using the standard high-density particle image velocimetry algorithm founded on cross-correlation. The results suggest that the transition between steady states for an incompressible fluid takes a finite and non-negligible amount of time that is independent of the magnitude of the change in pressure gradient. The existence of transient states and the nature of the response during these states are readily interpreted by the principle of least action where flow gradually establishes an optimal configuration such that energy dissipation is minimized. The findings provide evidence against the applicability of the assumption that flowing phases relax instantaneously to their steady states and, hence, against the accuracy of the classical multiphase extension of Darcy’s law.

Cited as: Sun, J., Li, Z., Furtado, F., Aryana, S. A. A microfluidic study of transient flow states in permeable media using fluorescent particle image velocimetry. Capillarity, 2021, 4(4): 76-86, doi: 10.46690/capi.2021.04.03


Particle image velocimetry, transition state, permeable media, microfluidics

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Adrian, R. J. Twenty years of particle image velocimetry. Experiments in Fluids, 2005, 39: 159-169.

Adrian, R. J., Westerweel, J. Particle Image Velocimetry. Cambridge, U.K., Cambridge University Press, 2011.

Aryana, S. A., Kovscek, A. R. Experiments and analysis of drainage displacement processes relevant to carbon dioxide injection. Physical Review E, 2012, 86: 066310.

Aryana, S. A., Kovscek, A. R. Nonequilibrium effects and multiphase flow in porous media. Transport in Porous Media, 2013, 97: 373-394.

Barenblatt, G. I., Patzek, T. W., Silin, D. B. The mathematical model of nonequilibrium effects in water-oil displacement. Paper SPE 75169 Presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, Oklahoma, 13-17 April, 2002.

Berkowski, K. L., Plunkett, K. N., Yu, Q., et al. Introduction to photolithography: Preparation of microscale polymer silhouettes. Journal of Chemical Education, 2005, 82(9): 1365-1369.

Cai, J., Jin, T., Kou, J., et al. Lucas-washburn equation-based modeling of capillary-driven flow in porous systems. Langmuir, 2021, 37(5): 1623-1636.

Chung, B. G., Flanagan, L. A., Rhee, S. W., et al. Human neural stem cell growth and differentiation in a gradient-generating microfluidic device. Lab on a Chip, 2005, 5: 401-406.

Dullien, F. A. L. Porous Media: Fluid Transport and Pore Structure. San Diego, USA, Academic Press, 2012.

Elsinga, G. E., Scarano, F. Characterization of PIV systems. Measurement Science and Technology, 2014, 25: 080301.

Ergin, F. G., Watz, B. B., Gade-Nielsen, N. F. A review of planar PIV systems and image processing tools for lab-on-chip microfluidics. Sensors, 2018, 18(9): 3090.

Erickstad, M., Gutierrez, E., Groisman, A. A low-cost low-maintenance ultraviolet lithography light source based on light-emitting diodes. Lab on a Chip, 2015, 15: 57-61.

Guo, F., Aryana, S. A. An experimental investigation of nanoparticle-stabilized CO2 foam used in enhanced oil recovery. Fuel, 2016, 186: 430-442.

Guo, F., Aryana, S. A. An experimental investigation of flow regimes in imbibition and drainage using a microfluidic platform. Energies, 2019, 12(7): 1390.

Hain, R., Kähler, C. J. Fundamentals of multiframe particle image velocimetry (PIV). Experiments in Fluids, 2007, 42: 575-587.

Hosseini, H., Guo, F., Barati Ghahfarokhi, R., et al. Microfluidic fabrication techniques for high-pressure testing of microscale supercritical CO2 foam transport in fractured unconventional reservoirs. Journal of Visualized Experiments, 2020, 161: e61369.

Hubbert, M. K. Darcy’s law and the field equations of the flow of underground fluids. Transactions of the AIME, 1957, 207(1): 222-239.

King, M. J., King, P. R., McGill, C. A., et al. Effective properties for flow calculations. Transport in Porous Media, 1995, 20: 169-196.

Kubitscheck, U. Fluorescence Microscopy: From Principles to Biological Applications (2nd Edition). New Jersey, USA, Wiley-Blackwell, 2017.

Kvon, A., Lee, Y. H., Cheema, T. A., et al. Development of dual micro-PIV system for simultaneous velocity measurements: Optical arrangement techniques and application to blood flow measurements. Measurement Science and Technology, 2014, 25: 075302.

Li, J., Liu, J., Pei, J., et al. Experimental study of human thermal plumes in a small space via large-scale TR PIV system. International Journal of Heat and Mass Transfer, 2018, 127: 970-980.

Lima, R., Wada, S., Tanaka, S., et al. In vitro blood flow in a rectangular PDMS microchannel: Experimental observations using a confocal micro-PIV system. Biomedical microdevices, 2008, 10: 153-167.

Liu, Y., Kaszuba, J., Oakey, J. Microfluidic investigations of crude oil-brine interface elasticity modifications via brine chemistry to enhance oil recovery. Fuel, 2019, 239: 338-346.

Mijatovic, D., Eijkel, J. C. T., Van den Berg, A. Technologies for nanofluidic systems: Top-down vs. bottom-up—a review. Lab on a Chip, 2005, 5: 492-500.

Murray, C. D. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proceedings of the National Academy of Sciences of the United States of America, 1926, 12(3): 207-214.

Northrup, M. A., Kulp, T. J., Angel, S. M. Fluorescent particle image velocimetry: Application to flow measurement in refractive index-matched porous media. Applied Optics, 1991, 30: 3034-3040.

Prevost, J. H. Wave propagation in fluid-saturated porous media: An efficient finite element procedure. International Journal of Soil Dynamics and Earthquake Engineering, 1985, 4: 183-202.

Rousseeuw, P. J., Leroy, A. M. Robust Regression and Outlier Detection. New York, USA, John Wiley & Sons, 1987.

Santiago, J. G., Wereley, S. T., Meinhart, C. D., et al. A particle image velocimetry system for microfluidics. Experiments in Fluids, 1998, 25: 316-319.

Shinohara, K., Sugii, Y., Aota, A., et al. High-speed micro-PIV measurements of transient flow in microfluidic devices. Measurement Science and Technology, 2004, 15: 1965.

Tabeling, P. Introduction to Microfluidics. New York, USA, Oxford University Press, 2005.

Tauro, F., Pagano, C., Porfiri, M., et al. Tracing of shallow water flows through buoyant fluorescent particles. Flow Measurement and Instrumentation, 2012, 26: 93-101.

Thielicke, W., Stamhuis, E. J. PIVlab—towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. Journal of Open Research Software, 2014, 2: 30.

Unadkat, H., Rielly, C. D., Hargrave, G. K., et al. Application of fluorescent PIV and digital image analysis to measure turbulence properties of solid-liquid stirred suspensions. Chemical Engineering Research and Design, 2009, 87: 573-586.

Wang, Y., Aryana, S. A., Allen, M. B. An extension of Darcy’s law incorporating dynamic length scales. Advances in Water Resources, 2019, 129: 70-79.

Wang, Y., Aryana, S. A., Furtado, F., et al. Analysis of nonequilibrium effects and flow instability in immiscible two-phase flow in porous media. Advances in Water Resources, 2018, 122: 291-303.

Wang, Y., Mckinzie, J., Furtado, F., et al. Scaling analysis of two-phase flow in fractal permeability fields. Water Resources Research, 2020, 56: e2020WR028214. Westerweel, J., Scarano, F. Universal outlier detection for PIV data. Experiments in Fluids, 2005, 39: 1096-1100.

Whitaker, S. Flow in porous media I: A theoretical derivation of Darcy’s law. Transport in Porous Media, 1986, 1: 3-25.

Yi, Y., Blois, G., Kazemifar, F., et al. A particle-based image segmentation method for phase separation and interface detection in PIV images of immiscible multiphase flow. Measurement Science and Technology, 2021, 32: 095208.

FLUIGENT. LineUp Flow EZ. Accessed September 21, 2021.


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