A liquid-crystal model for friction

C. H.A. Cheng, L. H. Kellogg, S. Shkoller, D. L. Turcotte

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 d(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.

Original languageEnglish
Pages (from-to)7930-7935
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number23
StatePublished - 10 Jun 2008


  • Faulting
  • Rheology


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