Emergent rheotaxis of shape-changing swimmers in Poiseuille flow
Benjamin J. Walker, Kenta Ishimoto, Clément Moreau, Eamonn A. Gaffney, Mohit P. Dalwadi
Abstract
A simple model for the motion of shape-changing swimmers in Poiseuille flow\nwas recently proposed and numerically explored by Omori et al. (2022). These\nexplorations hinted that a small number of interacting mechanics can drive longtime behaviours in this model, cast in the context of the well-studied alga Chlamydomonas and its rheotactic behaviours in such flows. Here, we explore this model\nanalytically via a multiple-scale asymptotic analysis, seeking to formally identify\nthe causal factors that shape the behaviour of these swimmers in Poiseuille\nflow. By capturing the evolution of a Hamiltonian-like quantity, we reveal the\norigins of the long-term drift in a single swimmer-dependent constant, whose sign\ndetermines the eventual behaviour of the swimmer. This constant captures the\nnonlinear interaction between the oscillatory speed and effective hydrodynamic\nshape of deforming swimmers, driving drift either towards or away from rheotaxis.