A fast algorithm for approximating hydrodynamic lubrication interactions between elastic particles

Elastohydrodynamic;Elastic Particle;Lubrication;Suspension;Integro-differential;Algorithm

Higa, Kenneth F.

关键词: Elastohydrodynamic;    Elastic Particle;    Lubrication;    Suspension;    Integro-differential;    Algorithm;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16742/1_Higa_Kenneth.pdf?sequence=2&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We present in this work a fast nonlinear method which approximately solves anintegro-partial differential equation that describes the dominant elastohydrodynamiclubrication 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 considerationof relative motion only along the axis of symmetry.The approximate solutions are characterized by a variable number of parameters, whose number may be chosen tobalance 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.