Title: Longitudinal and transversal flow over a cavity containing a second immiscible fluid Show Chinese title

Title: 腔体内含有第二种不相溶流体的纵向和横向流动

Abstract: An analytical solution for the flow field of a shear flow over a rectangular cavity containing a second immiscible fluid is derived. While flow of a single-phase fluid over a cavity is a standard case investigated in fluid dynamics, flow over a cavity which is filled with a second immiscible fluid, has received little attention. The flow filed inside the cavity is considered to define a boundary condition for the outer flow which takes the form of a Navier slip condition with locally varying slip length. The slip-length function is determined from the related problem of lid-driven cavity flow. Based on the Stokes equations and complex analysis it is then possible to derive a closed analytical expression for the flow field over the cavity for both the transversal and the longitudinal case. The result is a comparatively simple function, which displays the dependence of the flow field on the cavity geometry and the medium filling the cavity. The analytically computed flow field agrees well with results obtained from a numerical solution of the Navier-Stokes equations. The studies presented in this article are of considerable practical relevance, for example for the flow over superhydrophobic surfaces. Show Chinese abstract

Abstract: 一个关于包含第二种不混溶流体的矩形凹槽上的剪切流场的解析解被推导出来。 虽然单相流体在凹槽上的流动是流体力学中研究的标准情况，但凹槽内填充有第二种不混溶流体时的流动却很少受到关注。 凹槽内的流动场被用来定义外流场的边界条件，该条件的形式为具有局部变化滑移长度的Navier滑移条件。 滑移长度函数是从相关的盖驱动凹槽流动问题中确定的。 基于Stokes方程和复变分析，可以为横向和纵向情况下的凹槽上的流动场推导出一个封闭的解析表达式。 结果是一个相对简单的函数，它表现出流动场对凹槽几何形状和填充介质的依赖性。 解析计算得到的流动场与从Navier-Stokes方程数值解中获得的结果相符。 本文中所述的研究具有重要的实际意义，例如对于超疏水表面的流动而言。