Morphology and kinematics of a train of power-law droplets in a corrugated microchannel

Abstract

We numerically investigate the deformation of a train of power-law droplets in a highly viscous suspending medium in nonlinear microfluidic geometry. We examine how viscous stresses conspire against surface tension in two-dimensional incompressible liquid–liquid flow in a corrugated microchannel using the finite volume technique with the volume of fluid method. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices (n) is varied from 0.7-1.3. We validate our numerical model with the available literature data in good agreement. Interestingly, the corrugated cavities are found to have an elongating effect on the non-Newtonian droplets, whereas literature delineates a compressive effect of the nonlinear geometry on bubbles. Specific orbital trajectories are found in the (droplet length A, spacing B) space with dispersed and synchronized orbitals at low and high capillary number for all power-law droplets, respectively. Furthermore, the hysteresis in the droplet shape is found to increase with the capillary number. Consequently, the hysteretic area Ap revealed that the slope increases with (n). An interesting finding is elucidated where the hysteresis loops are found to rotate from low capillary to high capillary number for all power-law droplets. A new finding is reported where the evolution of the droplet perimeter revealed the development of secondary peaks as the capillary number increases. The power-law droplets are found to pack themselves up in the corrugated section in two distinct regimes: smaller droplets obey the linear deformation regime. In contrast, large droplets lie in the flow-induced deformation regime. The instantaneous cap velocities produce a nonmonotonic behavior for the front velocity as the capillary number increases for all power-law droplets. We develop functional relationships between flow parameters of segmented flows at the pore scale for every non-Newtonian droplet. Given the implications of this setup with industrial and biomedical applications, the illustrations shown herein could be beneficial in tackling problems at the pore scale with nonlinear fluids.