An analysis on the basis of the Navier-Stokes equations is made of the flow of a liquid in a thin film on a rotating disk. Fluid flows outward in the radial direction due to the centrifugal force. An asymptotic solution valid for small values of the Rossby number is presented. Higher-order terms correcting for the effects of convection, Coriolis acceleration, radial diffusion, surface curvature, and surface tension are found and discussed on a physical basis.
根据Navier-Stokes方程对液体在旋转盘上的薄膜流动进行了分析。由于离心力,流体向径向方向外流。提出了适用于Rossby数较小值的渐近解。找到并讨论了关于对流、科里奥利加速度、径向扩散、表面曲率和表面张力效应的高阶修正项,基于物理基础。