A fast algorithm for approximating hydrodynamic lubrication interactions between elastic particles

Higa, Kenneth F.

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https://hdl.handle.net/2142/16742 Copy

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

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."

Graduation Semester

2010-08

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

Copyright and License Information

Copyright 2010 Kenneth F. Higa

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