On the deformation of an elastic particle under pressure-driven axisymmetric channel flow #

Simon M Finney, Matthew G Hennessy, Andreas Muench, Sarah Waters

11:30 Tuesday in 2Q49.

Part of the IMA Lighthill-Thwaites prize session.

Abstract #

We study an elastic particle translating axially along the center-line of a rigid cylindrical tube filled with a Newtonian fluid. The flow is pressure-driven and an axial body force is applied to the particle. We consider the regime in which the viscous flow leads to small elastic strains in the particle. In this case, there is a one-way decoupling of the fluid-structure interaction problem. The leading-order fluid problem is shown to be pressure-driven Stokes flow past a rigid sphere, and is solved using a semi-analytical method, known as the method of reflections. The traction exerted by the fluid on the particle can be computed and used to formulate a pure solid-mechanics problem for the deformation of the particle, which can be solved analytically. The next-order correction to the translational velocity of the particle is shown to be zero. This framework is used to investigate the role of the background flow, an axial body force, and the tube wall on the particle’s translational velocity, induced solid stress, and incurred deformation. Depending on the magnitude of the dimensionless body force, the particle can either have a bullet-like shape, an anti-bullet shape, or retain its original spherical shape. A finite element implementation is also presented to validate the method of reflections for solving the leading-order fluid and solid problems.