Numerical simulation of drops inside an asymmetric microchannel with protrusions

• A 3D immersed-boundary method is developed for two fluids in arbitrary geometries.
• Dynamics of a drop through a channel with asymmetric constriction is studied.
• Interior asymmetric flow pattern depends on the viscosity ratio and channel shape.
• Flow pattern found in the drop may enhance drop-based mixing.

Microfluidic channels with asymmetric protrusions have been utilized previously to enhance mixing in the drops that travel through the channels. To study the flow pattern in the drops and help explain the mixing phenomenon, in this work an immersed-boundary method is developed to simulate dynamics of a drop in arbitrary channel geometries. In this method, the fluid–solid interface is handled by the sharp-interface approach in which the interface maintains its singularity and the boundary conditions are satisfied at the exact location of the interface. On the other hand, the fluid–fluid interface is handled by a diffuse-interface approach in which the interfacial discontinuities are regularized by an approximated delta function. The simulation results show that for the drop in a channel with bumps on one side, the flow pattern inside the drop largely depends on the viscosity ratio and the geometry of the bumps. When the viscosity ratio or the curvature of the bumps is increased, the vortex pair inside the drop become skewed or even reduce to one single circulation. In three dimensions, the circulations in the spanwise direction are also developed. The mixing enhancement of these flow patterns is demonstrated by simulating the passive tracers in the drop.