Scale Dependence of Contact Line Computations
Scale Dependence of Contact Line Computations
复制标题
接触线计算的尺度依赖性
DOI：
10.1051/mmnp:2008035
复制
发表时间：
2006
影响因子：
2.2
通讯作者：
L. Pismen
中科院分区：
文献类型：
--
作者：
O. Weinstein;L. Pismen
通过求解具有自由界面边界条件的Navier{Stokes方程，计算了液滴的形状和速度。伽辽金有限元法是在二维计算域中用非结构化网格离散的三角单元实现的。网格在角落（接触点）递归地反射。静止滑动速度强烈依赖于网格反射，这是接触线奇异性的结果，接触线奇异性是通过接触点附近的有限元单元的有效滑移来解决的。对于小液滴，使用润滑近似中的多尺度扩展和匹配技术获得的理论估计可以很好地近似这种依赖性，其中角元尺寸用作微尺度参数。对于较大的液滴，其形状也取决于网格的再反射。这就质疑了许多具有移动接触线的∞ow计算的有效性，其中网格总是比解决奇点的分子尺度粗糙得多。建议采用分子尺度的外推法来获得真实的结果。
The shape and velocity of a sliding droplet are computed by solving the Navier{ Stokes equation with free interface boundary conditions. The Galerkin flnite element method is implemented in a 2D computation domain discretized using an unstructured mesh with triangular elements. The mesh is reflned recursively at the corners (contact points). The stationary sliding velocity is found to be strongly dependent on grid reflnement, which is a consequence of the contact line singularity resolved through the efiective slip across the flnite elements adjacent to the contact point. For small droplets, this dependence is well approximated by a theoretical estimates obtained using multiscale expansion and matching technique in lubrication approximation, where the corner element size is used as a microscale parameter. For larger droplets, the shape is also dependent on grid reflnement. This ques- tions the validity of numerous computations of ∞ows with moving contact line where grids are invariably much more coarse than molecular scales on which the singularity is resolved. It is suggested that extrapolation to molecular scales should be used to obtain realistic results.