# Shear induced migration of microswimmers in a two-dimensional Taylor-Green vortex flow

Diptiman Pati

Mechanical second year undergraduate, School of Mechanical Sciences, IIT Bhubaneswar, at- Argul, Jatni, Khordha, Bhubaneswar 752050 [Orissa]

Professor Ganesh Subramanian

Professor, Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientiﬁc Research, Rachenahalli Lake Rd, Jakkur, Bengaluru, Karnataka 560064

## Abstract

The migration of micron-sized self-propelled particles subjected to an imposed shearing flow has been the subject of a considerable number of theoretical and experimental investigations for somany years. These self-propelled particles convert ambient or internal free energy into continual swimming motion that may be further modiﬁed depending on the imposed forcing and inter-swimmer interactions. The present work aims to investigate the shear-induced migration of micro-swimmers subjected to a steady two-dimensional Taylor-Green vortex ﬂow ﬁeld via Langevin Simulations. The motion of each micro-swimmers in a shear-induced ﬂow involves a combination of convection by the ambient ﬂow, swimming, rotation by the ambient velocity gradient and stochastic changes in the swimmer orientation (that in turn affect swimming motion) due to either run-and-tumble motion or active Brownian motion. The positions of the micro-swimmers are a function of Peclet number, Pe = A/ Dr ( where A is a characteristic inverse ﬂow time scale and Dr is the rotary diffusivity), the aspect ratio $\kappa$  of the swimmer, and the flow-type parameter which, for the case considered, is the aspect ratio of the Taylor-Green vortex, R = H1 / H2. Insights from these simulations may enable us to characterize novel migration patterns of swimmer suspensions. At least from analyzing swimmers in a pressure-driven channel flow, we know that the interplay between flow and swimmer geometry results in high- and low-shear regimes.This in turn can enable segregation and shape-based sorting of micro-swimmers and/or characterize preferential accumulation/retardation of the swimmers in certain regions of the flow field.

Keywords: self-propelled particles, Newtonian ﬂuid, Brownian dynamics, TaylorGreen vortex, aspect ratio, rotary diffusivity

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