平行平板流动腔中Casson流体脉动流的摄动解

高度远小于横向和纵向几何尺寸的矩形平行平板流动腔是人们用以体外研究细胞在切应力作用下力学行为的主要工具之一，考虑到通常采用的矩形平行平板流动腔内的流动属于小雷诺数流动，本文用雷诺数作为摄动参数求出了矩形平行流动腔内Casson流体脉动流的摄动解，给出了腔内切应力随压力梯度和流量的变化规律。数值结果表明，相同压力梯度下Casson流体和牛顿流体对应的腔内切应力分布无明显不同，而在相同流量条件下，Casson流体和牛顿流体对应的腔内切应力分布有明显差异，本文为Casson流体脉动流条件下平行平板流动腔切应力的确定方法提供了理论依据。

A Perturbation Solution of Pulsatile Casson Flow in the Parallel-Plate Flow Chamber

The parallel-plate flow chamber (PPFC) with rectangular shape, of which the height is far smaller than its own length and width, is one of the main apparatus for in vitro studies of the mechanical behavior of the cells. Considering that the Reynolds numbers of flows in the usually used PPFCs are small, a perturbation solution of laminar pulsatile Casson fluid in the PPFC is presented using Reynolds number as perturbation parameter. Furthermore, the velocities and shear stresses in the PPFC are given. The numerical results demonstrate that under the same pressure gradient the shear stresses are almost identical between Casson fluid and Newtonian fluid, whereas under the same flux the shear stresses are obviously different between Casson fluid and Newtonian fluid. The results in this paper provide a theoretical way to determine the shear stresses in the parallel-plate flow chamber under pulsatile Casson fluid.