Water Film Drainage between a Very Viscous Oil Drop and a Mica Surface

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 (${\ensuremath{\tau}}_{v}$) in the drop. ${\ensuremath{\tau}}_{v}$ 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.