A fast algorithm for approximating hydrodynamic lubrication interactions between elastic particles
Higa, Kenneth F.
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https://hdl.handle.net/2142/16742
Description
Title
A fast algorithm for approximating hydrodynamic lubrication interactions between elastic particles
Author(s)
Higa, Kenneth F.
Issue Date
2010-08-20T17:56:31Z
Director of Research (if dissertation) or Advisor (if thesis)
Higdon, Jonathan J.L.
Doctoral Committee Chair(s)
Higdon, Jonathan J.L.
Committee Member(s)
Schweizer, Kenneth S.
Rao, Christopher V.
Schroeder, Charles M.
Department of Study
Chemical & Biomolecular Engr
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2010-08-20T17:56:31Z
Keyword(s)
Elastohydrodynamic
Elastic Particle
Lubrication
Suspension
Integro-differential
Algorithm
Abstract
"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."
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