Orientation effects in extensional and squeezing flows of certain anisotropic fluids (Q1119077)

The Ericksen-Leslie continuum theory of anisotropic fluids is here used to examine the behaviour of the orientation pattern within the bulk of a fluid that is undergoing an extensional-type of flow. The flow (which is irrotational and generally unsteady) is considered to be generated by application of prescribed normal stresses, and the orientation pattern (represented by a director field n) is taken to be spatially homogeneous but time-dependent. By means of a phase-plane analysis it is shown that, in stretching flows, the director eventually aligns parallel to the direction of imposed stretch, whereas in squeezing-type flows it eventually lies in the plane normal to the direction of squeezing. In both cases the lateral components of n may vary non-monotonically in time, before approaching their asymptotic values; also the lateral components of velocity may change sign during flow. A two-parameter classification is given of all possible modes of behaviour of these model fluids in these flows. Also analytical solutions are obtained for certain special cases, such as axisymmetric flow.