title: A liquid-crystal model for friction.
abstract: Rate-and-state friction is an empirical approach to the behavior of a frictional surface. We use a nematic liquid crystal in a channel between two parallel planes to model frictional sliding. Nematic liquid crystals model a wide variety of physical phenomena in systems that rapidly switch between states; they are well studied and interesting examples of anisotropic non-Newtonian fluids, characterized by the orientational order of a director field SE pointing arrow(x,t) interacting with the the velocity field u(x,t). To model frictional sliding, we introduce a nonlinear viscosity that changes as a function of the director field orientation; the specific choice of viscosity function determines the behavior of the system. In response to sliding of the top moving plane, the fluid undergoes a rapid increase in resistance followed by relaxation. Strain is localized within the channel. The director field plays a role analogous to the state variable in rate-and-state friction.
authors.affiliation: Department of Mathematics, University of California, Davis, CA 95616, USA.
authors.forename: C H A
authors.initials: CH
authors.lastname: Cheng
authors.forename: L H
authors.initials: LH
authors.lastname: Kellogg
authors.forename: S
authors.initials: S
authors.lastname: Shkoller
authors.forename: D L
authors.initials: DL
authors.lastname: Turcotte