[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.