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Effect of capillary number and viscosity ratio on multiphase displacement in microscale pores

Samantha A. McBride1,*, Fernando Temprano-Coleto1,2,*, Paul R. Kaneelil1,3, Reese Knopp1, Aubrey J. Taylor1, Mariko A. Storey-Matsutani1, Jessica L. Wilson1, Mohammad Sadeq Saleh1, Andrew R. Konicek4 et al.

Arben Jusufi4, Mohsen S. Yeganeh4, and Howard A. Stone1,†

  • 1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
  • 2Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 08544, USA
  • 3John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
  • 4ExxonMobil Technology and Engineering Company, Annandale, New Jersey 08801, USA

  • *These authors contributed equally to this work.
  • †Contact author: hastone@princeton.edu
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Phys. Rev. Fluids 10, 054201 – Published 5 May, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.054201

Abstract

Understanding the dynamics of fluid transport and trapping within microscale cavities is important for a range of environmental, industrial, and research applications. Using PDMS microfluidic channels, we explore the displacement and retention of (wetting) oil by an invading flow of (nonwetting) water at low Reynolds number (Re≪1) in noncontiguous pores, and examine the influence of trapping velocity, viscosity ratio, and pore aspect ratio. We find that increasing capillary numbers lead to a greater amount of oil trapped per cavity. This is contrary to findings for interconnected porous media in which the availability of multiple pathways for fluid flow leads to more displacement with increased flow rates. This result can be attributed to a dynamic transition from a meniscus displacement to a viscous fingering displacement, by which the advancing water front shifts from a discrete triple contact line at channel walls to a continuous layer of oil enveloping the water. Data from all pore geometries can be collapsed onto a single trend by subtracting the amount of oil captured in the zero capillary number limit, indicating that increased oil retention at higher values of capillary number is not dependent on pore geometry. A model for steady-state, three-dimensional flow based on the long-wave approximation was developed to analyze the amount of fluid retained as a function of capillary number and viscosity ratio. Model predictions are qualitatively consistent with several experimental observations, including the shape of the interface of the trapped oil and the trend that increasing capillary number leads to greater oil trapping per pore. Our results highlight the need to quantitatively investigate the transient dynamics of fluid invasion in multiphase systems that exhibit localized entrapment.

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Phys. Rev. Fluids 10, 054201– Published 5 May, 2025
  • Received 27 July 2023
  • Accepted 4 March 2025
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