A liquid-crystal model for friction

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 d⃗(x⃗,t) interacting with the the velocity field u⃗(x⃗,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.

速率与状态摩擦是一种针对摩擦表面行为的经验性方法。我们在两个平行平面之间的通道中使用向列液晶来模拟摩擦滑动。向列液晶可模拟在状态间快速转换的系统中的多种物理现象；它们是各向异性非牛顿流体的研究充分且有趣的例子，其特征在于指向矢场\(\vec{d}(\vec{x},t)\)与速度场\(\vec{u}(\vec{x},t)\)的取向序相互作用。为了模拟摩擦滑动，我们引入一种随指向矢场取向变化的非线性粘度；粘度函数的具体选择决定了系统的行为。响应顶部移动平面的滑动，流体的阻力迅速增加，随后松弛。应变局限在通道内。指向矢场所起的作用类似于速率与状态摩擦中的状态变量。