A fast algorithm for approximating hydrodynamic lubrication interactions between elastic particles

We present in this work a fast nonlinear method which approximately solves an integro-partial differential equation that describes the dominant elastohydrodynamic lubrication interaction between two elastic spheres in a Newtonian fluid. This governing equation was given by Christensen [7], Goddard [13], and Davis, Serayssol, and Hinch (DSH) [8]. Our approximate method is intended for inclusion in highly accurate, large-scale simulations of concentrated suspensions of deformable particles. This method inherits all of the assumptions made in the derivation elastohydrodynamic equation, including the restriction to linearly-elastic deformation of smooth particles in a Newtonian fluid with no-slip boundary conditions, and consideration of relative motion only along the axis of symmetry. The approximate solutions are characterized by a variable number of parameters, whose number may be chosen to balance accuracy and speed. This method shows good accuracy and stability over a wide range of conditions.;We present selected simulation results which provide a qualitative understanding of hydrodynamic collisions of elastic spheres. These interactions differ markedly from those between rigid spheres. They are strongly dependent on deformation history and display a short-lived "sticking" behavior, which in extreme cases takes the form of a unique "peeling" separation process. *Please refer to dissertation for references.