粘滑混合边界条件下平面边界前的Stokes流动

Stokes Flow Before a Plane Boundary With Mixed Stick-Slip Boundary Conditions

对具有粘滑混合边界条件的平面边界,建立一个Stokes流动的一般性定理,利用双调和函数A与调和函数B,表示了3维Stokes流动的速度场和压力场.关于无滑动平面边界前Stokes流动的早期定理,成为该一般性定理的一个特例.进一步地,从一般性定理导出了一个推论,根据该Stokes流函数,给出了粘滑边界条件时刚性平面轴对称Stokes流动问题的解,得到了流体作用在边界上的牵引力和扭矩公式.给出了一个说明性的例子.

A general theorem for Stokes flow about a plane boundary with mixed stick-slip boundary conditions was established. This was done by making use of a representation for the velocity and pressure fields in three-dimensional Stokes flow, in terms of a biharmonic function A and a harmonic function B. The earlier theorem on Stokes flow before a no-slip plane boundary was shown to be a special case of the present theorem, Furthermore, a corollary of the theorem was also derived which offers the solution to a problem of axisymmetric Stokes flow about a rigid plane with stick-slip boundary conditions, in terms of the Stokes stream function. The formulae for the drag and torque exerted by the fluid on the boundary were found. An illus trative example was given.