Interfacial tension and viscosity-contrast driven moving-contact-line-hydrodynamics along tortuous pathways

In this article, we report the influence of interfacial tension and the viscosity-contrast on the moving contact line (MCL) hydrodynamics of two immiscible fluids, flowing within a periodic tortuous or porous domain. The motion of the driving fluid is generated by an externally applied pressure gradient, and a displacing-displaced type flow occurs. The surface wettability of the pores is determined by a predefined static contact angle. We investigate the combined effects of interfacial tension, pore packing fraction, viscosity-contrast, and substrate wettability on interfacial and MCL dynamics using the Cahn-Hilliard-Navier-Stokes phase field formalism. Depending on the viscosity and the interfacial tension, two distinct spatiotemporal regimes emerge: the entrapment of displaced phase between successive pores (forming a liquid bridge), or the merging of MCL after traversing the pores (resulting in complete interface recovery). We observe complete interface recovery for the combinations of n(A)=0.15-0.6 and theta=45(degrees)- 75(degrees) when Ca=1.2x10(-5) and eta(R)=1. A similar phenomenon is also observed for n(A)=0.15-0.30 and theta=75(degrees)- 135(degrees). When Ca=1.2x10(-3) and eta(R)=100, complete interface recovery is observed for n(A)=0.15 and theta=45(degrees)- 60(degrees), and under all other wettability and porosity conditions, a liquid bridge forms. Our results reveal the complex mechanisms by virtue of which interfacial tension at the fluid-fluid interface influences the dynamic evolution of MCL and, consequently, the geometries and dimensions of the trapped displaced phase within the liquid bridge. We also demonstrate, via detailed regime maps, that the likelihood of liquid bridge formation and complete recovery is strongly affected by viscosity contrasts, along with relevant surface properties and governing parameters. We also report how the velocity of the MCL on the pore surface varies with changes in the viscosity contrast and interfacial tension. Finally, we also pin-point a new mechanism of liquid entrapment in such scenarios, where both upstream and downstream pores play a role.