Cross-streamline migration and near-wall depletion of elastic fibers in micro-channel flows

Abstract

The complex dynamics of elastic fibers in viscous fluids are central to many biological and industrial systems. Fluid–structure interactions underlying these dynamics govern the shape and transport of flexible fibers, and understanding these interactions can help tune flow properties in applications such as microfluidic separation, printing and clogging. In this work, we use slender-body theory to study micromechanical dynamics that arise from the coupling between the elastic backbone of a fiber and the local straining flow that contributes to filament flipping and cross-streamline migration. The resulting transverse drift is unbiased in either direction in simple shear flow. However, a non-uniform shear rate results in bias towards regions of high shear, which we connect to the shape transitions during flips. We discover a depletion layer that forms near the boundaries of pressure-driven channel flow due to the competition between such a cross-streamline drift and steric exclusion from the walls. Finally, we develop scaling laws for the curvature of filaments during flip events, demonstrating the origin of the drift bias in non-uniform flows, and confirm this behavior from our simulations. Put together, these results shed light on the role of a local and dominant coupling between elasticity and viscous resistance in dictating long-term dynamics and transport of elastic fibers in confined flows.