Active Particle Dynamics in a Cubic Poiseuille Field

Abstract We investigate the dynamics arising from an idealized model of a spherical active particle immersed in a cubic Poiseuille field inspired by fluid flow through an equilateral triangular duct. Starting from a general Hamiltonian formulation, we describe the equations of motion, analyse equilibrium points and their stability and classify trajectories based on their initial position. Motion of an active particle within the Poiseuille flow of an equilateral triangular duct is an interesting case to examine given its symmetry group and a velocity field described by a cubic polynomial. In addition to trajectory types previously identified in other duct geometries, including central and vertical swinging, tumbling, off-centred trapping and wandering, we observe some exotic orbits within the triangular geometry. We also examine the chaotic behaviour by using Poincaré maps and Lyapunov exponents over a range of parameter values and initial conditions. This work enhances the broader understanding of idealized microswimmer motion via a case where the fluid flow has a straightforward closed-form description.