Hypothesis: The effects of mutual transfer of momentum between two immiscible flowing fluids in porous media are not well understood nor predictable yet. From considerations at the pore-scale, it should be possible to determine whether and to what extent interfacial viscous coupling effects are significant.
Experiments: We visualize the velocity distributions inside immobile globules of wetting phase (water) while a non-wetting phase (oil) is injected. We investigate viscous coupling effects and their relationship with the viscosity ratio and the capillary number.
Findings: Four regimes of viscous dissipation are identified: (i) a regime for which the fluid-fluid interface acts as a solid wall; (ii) a regime where the wetting phase is dragged in the direction of the imposed flow; (iii) and (iv) two regimes for which the trapped globule of water shows a recirculating motion due to the shear stress at the oil/water interface. We demonstrate the significant role of the lubricating effect and of the topology of the pore space on the magnitude of viscous dissipation. Importantly, for a viscosity ratio close to one and low capillary number, we demonstrate that viscous coupling effects should be incorporated into the existing Darcy's law formulation for two-phase flow in porous media.
Keywords: Capillary forces; Microfluidics; Porous media; Two-phase flow; Viscous coupling.
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