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."

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Chemical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2010

Author dc:creator

• Higa, Kenneth F.

Contributors dc:contributor

• Higdon, Jonathan J.L.
• Schweizer, Kenneth S.
• Rao, Christopher V.
• Schroeder, Charles M.

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

Statement dc:rights

• Copyright 2010 Kenneth F. Higa

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/16742

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F16742