Modelling of an Internally Actuated Weakly Elastic Sphere

Analysing the dynamics of smart polymer beads encapsulated with magnetic particles is important in biomedical applications. To analyse the dynamics of such particles, one must understand the force distribution acting on them. We analytically examine the dynamics of an internally actuated weakly elastic spherical particle moving in different ambient flows: (i) when the particle translates parallel to the rigid wall in a quiescent fluid, and (ii) when the particle translates in a general unbounded quadratic flow. The motion of the particle is constrained by applying an external point force and a point torque at the centre of its undeformed shape. The particle and the fluid are modelled using the Navier elasticity equations and the Stokes equations, respectively. The domain perturbation method is used to capture the particle deformation. In the first case, we have used the method of reflections to capture the wall effects and observed that the particle experiences a wall-induced elastic lift force. In the second case, the point force and torque due to the elastic effects appear at O(α). Here, α is the measure of particle elastic strain due to fluid viscous stress. The results are simplified for the particle motion along the centreline in the quadratic components of Poiseuille flows.

Keyword: Low-Reynolds number flows