Mechanism Driving Fluid Circulation in a Microcavity Junction Due to Immiscible Displacement Flow

Understanding the fluid dynamics of displacement of a non-wetting phase by a wetting continuous phase is relevant for a wide range of applications including oil recovery, environmental remediation, and droplet-based microfluidics. In this study, we investigate fluid circulation patterns due to an immiscible displacement flow occurring at a micrometer-scale cavity located at a channel bifurcation. Using particle-image velocimetry, we map both the direction and strength of fluid circulation as a function of the capillary number. At low capillary numbers, we find that fluid circulation is in a direction that is opposite of what is expected for lid-driven single-phase cavity flow. However, at higher capillary numbers, the circulation direction is the same as that of single-phase cavity flow. We explain these counterintuitive observations by considering the competition between viscous stresses—1) shear stress at the cavity entrance due to the displacement flow, and 2) shear stress along the perimeter of the non-wetting phase within the cavity due to continuous-phase gutter flows—as well as the dependence of gutter size on capillary number. We propose a scaling analysis that can qualitatively describe the cavity circulation direction and strength as a function of capillary number. Our study highlights the importance of gutter flows associated with immiscible displacement flows in non-circular microchannels. The boundary-driven advection of fluid by the gutter flows could potentially be harnessed as a new hydrodynamic mechanism for pumping out fluid trapped in microcavities and porous media.