TRANSIENT DIRECTOR ORIENTATION PATTERN OF CREEPING PLANE POISEUILLE FLOW OF A NEMATIC POLYMER

Abstract

The time-dependent Leslie-Ericksen equation in numerically solved for creeping plane poiseuille flow of a nematic polymer (Poly Benzyl Glutamate). The Leslie coefficients and Frank orientation curvature elasticity constants of the nematic polymer reported in the literature were used for the computations of three dimensional director time (t) evolution over the two-dimensional (x-y) plane. The flow is along the x-axis, and the thickness axis the y-axis. On the bounding plates assumed strong homeotropic anchoring condition. On the inlet and outlet flow boundaries, zero surface couple condition is used.

Although poiseuille flow has a zero shearing line in the middle with changing sing of shear rate when going through the mid gap region, unlike simple shear flow, directors escape the shear (x-y) plane as flow rate increases, which this computation study shows in accordance with various experimental studies. As the center velocity (U) increases, complex 3-D orientation structure emerges. When U is further increased, tube orientation walls reminiscent of the tube walls of shear flow emerges, not through pinching and reconnection of orientation wall pair, but through emanation from the central backbone orientation wall structure.

Keywords:

• Leslie-Ericksen theory
• nematodynamics
• pattern formation
• poiseuille flow
• polymeric liquid crystals