Propagation of elastic waves in liquid crystals

Abstract

The model proposed by Maxwell for a visco-elastic medium is generalized by combining the properties of a crystalline solid and an anisotropic fluid. The basic equations are derived taking the elastic constants and the coefficients of viscosity both to be tensors of rank four. Expressions are given for the complex velocity of propagation of elastic waves of small amplitude as a function of direction. The theory is then applied to the 'stepped drop' (goutte a gradins) discovered by Grandjean, which consists of a number of exactly parallel layers, each layer terminating in a sharp step. The layers slide over one another very easily, but in any other direction the drop is extremely viscous. It is shown that for vibrations of frequency less than about 10⁹ s^-1, only the longitudinal wave is propagated normal to the layers, the two transverse waves being heavily damped. In the plane of the layers the longitudinal wave and one transverse component are propagated.