Department of Chemistry, Tongji University , 1239 Siping Road, Shanghai, P. R. China 200092.
Langmuir. 2014 Jan 14;30(1):83-9. doi: 10.1021/la404125u. Epub 2013 Dec 20.
We investigate theoretically the drainage of a thin liquid film confined between two hydrophobic spheres. Such a problem has been considered in Vinogradova's seminal work, emphasizing the role of slippage. However, it does not include the boundary curvature effects, which may become especially important when the slip lengths are comparable to the sphere radii. We present a reformulation of the hydrodynamic boundary conditions, with the boundary curvature effects fully taken into account. It is shown that such effects not only renormalize the effective slip lengths but also give new contributions to the pressure and drag force, neglected so far. We focus on the symmetric case of two identical spheres with the same radii and slip lengths and obtain analytical expressions for the pressure as well as the drag force. The boundary curvature corrections to the drag force are analyzed and found to be more important for more hydrophobic spheres. The implications of our results are discussed for the coagulation processes of colloids and measurements of surface forces or slip lengths with the drainage technique.
我们从理论上研究了两个疏水球体之间的薄液膜的排水问题。这个问题在 Vinogradova 的开创性工作中已经被考虑到了，强调了滑移的作用。然而，它没有包括边界曲率效应，当滑移长度与球体半径相当时，这些效应可能变得尤为重要。我们提出了一种对流体动力边界条件的重新表述，充分考虑了边界曲率效应。结果表明，这些效应不仅使有效滑移长度正则化，而且对迄今为止被忽略的压力和阻力也有新的贡献。我们集中研究了两个相同半径和相同滑移长度的相同球体的对称情况，并获得了压力和阻力的解析表达式。分析了对阻力的边界曲率修正，并发现它们对更疏水的球体更为重要。我们的结果对胶体的凝聚过程和用排水技术测量表面力或滑移长度的影响进行了讨论。
