(498g) Numerical Investigation of Deformable Drops in Three-Dimensional Microchannels Using a Moving-Frame Boundary-Integral Method

The study of deformable drop motion in microchannels has a wide range of applications, such as drug targeting, micro-chemical reactors, and generation of emulsions with low polydispersity. Fundamental understanding of the physics of drop motion in bounded domains plays an important role in designing such systems. An approach commonly used to analyze drop motion and fluid flow at low Reynolds numbers is the boundary-integral method, reducing the problem to solving integral equations on the entire domain boundary. The economical, “Moving-Frame” (MF) version [1,2] of this method was previously developed to simulate solid particle [1] and deformable drop [2] motion in a channel of infinite depth with bifurcations. Here, the boundary-integral equations are solved at each time step within a moving frame travelling with the particle/drop; this frame, much larger than the particle/drop size, can still be made much smaller than the entire channel size with acceptable accuracy, resulting in much faster simulations. However, the assumption of an infinite channel depth is often too restrictive for practical channels. In the present work, the MF boundary-integral method is developed for finite-depth channels of arbitrary profile with bifurcations and applied to tight deformable drop motion through such channels. The difficulty of dynamical meshing for the front and back panels of the evolving moving frame is overcome by a novel algorithm, which is a combination of Monte Carlo techniques and 2D Voronoi tessellation to efficiently triangulate these panels at each time step with high resolution.

We first apply this moving-frame approach to the drop motion in long, straight microchannels of rectangular cross-section, where we analyze the effect of the physical parameters (capillary number, viscosity ratio), confinement ratio and the channel finite depth on the drop steady-state velocity. An increase in capillary number allows the droplet to attain higher velocities, whereas higher drop-to-medium viscosity ratios slow down the droplet. The presence of the front and back panels, in contrast to previous results for infinite-depth channels, also decreases the drop velocity and produces multi-lobed, tail-like instabilities for more deformable drops. In addition, we investigate drop motion in bifurcating channels, such as Y-shaped and T-shaped channels, where we determine drop sorting and break-up conditions. Namely, the change in the flow-rate conditions and geometrical parameters of such channels can alter the interplay between sorting and breakup trajectories. A simplified approach is also used to probe inertial effects (previously neglected in the analysis) on drop motion in bifurcating channels of finite depth. To this end, full Navier-Stokes equations are first solved for the entire channel without the drop, and this tabulated solution is then used as the boundary condition on the MF surface for the Stokes flow with the drop inside the MF.

[1] Zinchenko, A. Z., Ashley, J. F., & Davis, R. H. (2012). A moving-frame boundary-integral method for particle transport in microchannels of complex shape. Physics of Fluids, 24(4), 043302.

[2] Navarro, R., Zinchenko, A. Z., & Davis, R. H. (2020). Boundary-integral study of a freely suspended drop in a T-shaped microchannel. International Journal of Multiphase Flow, 130, 103379.