(504f) Cross-Stream Migration of an Elastic Particle in a Steady Pressure-Driven Flow

A deformable elastic particle can migrate cross-stream in a pressure-driven Stokes flow by breaking the flow reversibility. Theories for quantifying the particle deformation and cross-stream migration exist but they are limited to linear deformation of the particle. In this work, using regular perturbation method, we calculate the weakly nonlinear deformation and cross-stream migration of a deformable elastic particle in a steady pressure-driven Stokes flow. The particle is modeled as a neo-Hookean solid and is spherical in shape without external perturbation. We report two new findings. First, we show that a neo-Hookean particle could deform with new harmonic modes in the weakly nonlinear regime compared to the linear regime. Second, we demonstrate that, because of the new modes of deformation, cross-stream migration of a neo-Hookean particle in the weakly nonlinear regime could be qualitatively different from that in the linear regime. Our results here could be employed to design cross-stream migration of elastic particles in dilute suspensions, which is central to applications such as particle sorting and additive manufacturing.