Does Shear-Flow Enhance or Suppress Fluctuations in Shectics?
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DOES SHEAR-FLOW ENHANCE OR SUPPRESS FLUCTUATIONS IN SHECTICS?
R. BRUINSKA* AND Y. RABIN00 *Physics Department, University of California, Los Angeles, CA 90024 "•Physics Department, Bar Ilan University, Ramat-Gan S2900, Israel.
ABSTRACT We investigate the effects of shear-flow on the smectic phase of thermotropic and lyotropic liquid crystals. We show that shear-flow transforms a Smectic-A thermotropic into an orthorombic solid by the suppression of undulation fluctuations. In contrast, the lyotropic L• phase exhibits, in addition, a very striking enhancement of shortwavelength concentration fluctuations - a phenomenon which is closely analogous to a well-known effect in polymer solutions. We demonstrate this result using both hydrodynamic theory as well as a microscopic model based on the Helfrich theory of membranes. The dispersion relation of the concentration fluctuations is in qualitative agreement with recent experiments on the L, phase in shear flow. INTRODUCTION Instabilities triggered by shear-flow have been known since the time of Reynolds [1], following his pioneering study of the effects of flow on spheres suspended in liquids. More recently, this class of instabilities was investigated by Clark and Ackerson [2] in charged colloidal suspensions. Shear-flow triggered instabilities have been also observed in polymer solutions (3] where the flow induces long-wavelength concentration fluctuations as well as spinodal decomposition. The subject is still under active study. [4] The salient characteristics of a two-component liquid required to show this instability - which we will refer to as the "Reynolds effect" - are (I) that the liquid has a strong dependence of viscosity on concentration and (ii) that it has internal elastic degrees of freedom. These characteristics are (to some degree) present in many complex liquids such as dense colloidal suspensions, dense polymer solutions, lyotropic liquid crystals, and membrane systems. The physical mechanism is as follows: The frictional force exerted by the flowing solvent on the elastic degree of freedom has to be balanced by elastic stress-gradients. For shearflow, this viscous stress is of order rl with n the (local) viscosity and y the shear-rate. Now, consider a concentration fluctuation. This fluctuation leads to a corresponding fluctuation in the viscous stress, through the concentration dependence of ri,and thus to a fluctuation in the elastic stress. The resulting elastic stress gradients oppose the chemical potential gradients that normally drive the relaxation of concentration fluctuations (see Fig. i). The fluctuation amplitude is effectively increased because of the increase in lifetime. This mechanism was invoked by Helfand and Frederickson [S) to explain the Reynolds effect in polymer solutions and it is also akin to the Brochard - de Gennes model [6J for the dissolution of polymer droplets. It has been further investigated by Onuki [71 and by Milner [8]. The mechanism is however in no way specific to polymer solutions and it should also be present
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