We investigate thin film drainage between a viscous oil drop and a mica surface, clearly illustrating the competing effects of Laplace pressure and viscous normal stress (${\tau }_v$) in the drop. ${\tau }_v$ dominates the initial stage of drainage, leading to dimple formation ($h_d$) at a smaller critical thickness with an increase in the drop viscosity (the dimple is the inversion of curvature of the drop in the film region). Surface forces and interfacial tension control the last stage of film drainage. A scaling analysis shows that $h_d$ is a function of the drop size $R$ and the capillary numbers of the film (${\mathrm{Ca}}_f$) and drop (${\mathrm{Ca}}_d$), which we estimate by $h_d=0.5R\sqrt{{\mathrm{Ca}}_f/(1+2{\mathrm{Ca}}_d)}$. This equation clearly indicates that the drop viscosity needs to be considered when ${\mathrm{Ca}}_d>0.1$. These results have implications for industrial systems where very viscous liquids are involved, for example, in 3D printing and heavy oil extraction process.

中文翻译：

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非常粘稠的油滴和云母表面之间的水膜排水

我们研究了粘性油滴和云母表面之间的薄膜排水，清楚地说明了拉普拉斯压力和粘性正应力的竞争效应。${\tau }_v$) 中。 ${\tau }_v$ 主导排水的初始阶段，导致酒窝形成（$H_d$) 在更小的临界厚度下，随着液滴粘度的增加（凹坑是薄膜区域中液滴曲率的反转）。表面力和界面张力控制薄膜排水的最后阶段。规模分析表明，$H_d$ 是液滴尺寸的函数 $\mathrm{电阻}$ 和薄膜的毛细管数（${钙}_F$) 并删除 (${钙}_d$)，我们估计 $H_d=0.5\mathrm{电阻}\sqrt{{钙}_F/(1+2{钙}_d)}$. 这个方程清楚地表明，当${钙}_d>0.1$. 这些结果对涉及非常粘稠液体的工业系统具有影响，例如，在 3D 打印和重油提取过程中。