(354a) Elastohydrodynamic Collisions in Viscous Shear Flows

Elastic deformation of particles place a significant role in the dynamics of sheared suspensions of spheres with finite elastic modulus. We analyze the full elastohydrodynamic equations for the deformation of a Hookean elastic solid and a Newtonian viscous fluid in the limit of small deformation. The formulation for the elastic deformation leads to an integral equation for the half space while the fluid equations reduce to the classic lubrication equation in the fluid phase. Results are presented for Galerkin finite element solutions, and an efficient approximate solution procedure is presented in terms of a orthogonal expansion for the deformation. Results show that the deformation/velocity history for both approach and withdrawal may be well captured with as few as 3 terms in the orthogonal expansion. This makes the method suitable for use in large scale many particle simulations. Comparisons are made between the history dependent force and instantaneous predictions based on rigid body and Hertz contact force approximations.