Craster R V, Matar O K
Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK.
J Colloid Interface Sci. 2006 Nov 15;303(2):503-16. doi: 10.1016/j.jcis.2006.08.009. Epub 2006 Aug 14.
The spreading of a lens of one liquid on the surface of another liquid is examined. Lubrication theory is used to derive a coupled system of equations for the air-liquid and liquid-liquid interfaces. In the case of highly viscous lenses, extensional stresses are promoted and an additional equation for the lens velocity is derived. The potential singularity at the three-phase line is relieved by a microscopic precursor layer of the spreading fluid assumed to be present ahead of the macroscopic lens. This layer is stabilised via the inclusion of disjoining pressure effects in the lens. The results of our full parametric study show that, for weak gravitational forces, the shape of the lens at equilibrium depends solely on the surface tension ratio for sufficiently deep substrate thicknesses. For thin substrates, the underlying liquid film deforms severely near the point of deposition exhibiting flattening and dimpling.
研究了一种液体透镜在另一种液体表面的铺展情况。利用润滑理论推导了气 - 液和液 - 液界面的耦合方程组。对于高粘性透镜，拉伸应力增强，并推导了透镜速度的附加方程。三相线处的潜在奇点通过假定在宏观透镜前方存在的铺展流体的微观前驱层得以消除。通过在透镜中纳入分离压力效应来稳定该层。我们全面参数研究的结果表明，对于弱重力，在足够深的基底厚度下，平衡时透镜的形状仅取决于表面张力比。对于薄基底，下层液膜在沉积点附近会严重变形，出现变平和凹陷现象。
