矩形截面管内电流变液的流动

基于伽辽金方法，导出了矩形截面直管内泊肃叶流动的一阶和二阶近似解．在此基础上，研究了电流变单链的变形问题，并得到了描述它形状的多项式函数．

THE FLOW OF ER FLUIDS IN A TUBE OF RECTANGULAR CROSS 1)

The main feature of flows of electrorheological (ER) fluids is the deformation of chain like structures of particles. The simplest of all structures in ER fluids is a single ER chain. There are two kinds of deformation of chains in ER devices: those produced by moving electrodes such as in ER clutches, and those produced by flow such as in ER valves.Due to the relative movement between basic fluids and ER chains, the analysis of ER chains under flow is more challenging. In this paper an analytical study on the deformation of an ER single chain in a tube with rectangular cross is presented. Firstly, a second order approximate solution of the Poiseuille flow in the tube isderived from Galerkin approach. The numerical results show that the Galerkin approximate solution is much simpler than the exact solution,but maintains enough accuracy. Secondly, a balance equation of moment for the ER chain is established to avoid using of point dipole model,which is not accurate enough in the case that dielectric particles are adjacent to each other. Finally we find that the shape of an ER chain deformed by the flow in a square tube is described by a sextic polynomial. This mathematical expression is not only much simpler than an earlier result, but also is in good agreement with the experimental result.