高分子液晶の二次元流れの数値シミュレーション

Abstract

Finite difference solutions to the Doi equation with a quadratic closure approximation in two-dimensional channel flows, such as inlet developing flow between parallel plates and 2:1 contraction flow, were obtained. In the case of the inlet developing flow, a uniform velocity profile at the channel entrance was once overshot to become a profile similar to a Newtonian Poiseuille flow before reaching a fully-developed flat profile. The developing profile of velocity is in a wavy form because of the effect of molecular orientation. Because of the deceleration of the flow in the vicinity of channel wall near the entrance, the order parameter in the area became small. Afterwards, it recovered to a higher value owing to shear flow in the downstream, and a region of low order parameter was limited near the channel centerline, where the effect of the shear on the molecular orientation is small. In the developing region, the order parameter along the centerline was high because of extensional flow. It is quite interesting that the order parameter in an area between channel wall and the centerline near the entrance was lowered than the value of equilibrium state. For the contraction flow, the curvature of streamlines near the contraction was small compared to Newtonian flow, and resultantly larger vortices occured at channel corners. The order parameter in those regions was low and the effect of the secondary flow was reflected on the preferred angles.