The effect of interfacial slip on the drainage time to coalescence between two droplets

A fundamental question that arises in the coalescence of two drops in a flow is the dependence of the drainage time $t_{d}$ prior to film rupture on the capillary number \textit{Ca } and the dimensionless Hamaker constant, which is inversely proportional to the square of the drop radius, $R^{-2}$. Prior investigations from our group have shown that predictions of this relationship based on both scaling theory and numerical simulations deviate qualitatively from experimental data. We believe that a possible explanation for these discrepancies is a breakdown of the continuum flow model for the extremely thin films that are realized prior to film rupture. Such a breakdown would most likely first manifest itself as a violation of the no-slip condition at fluid interfaces. In this work, we examine the effect of interfacial slip on the dependence of the drainage time with capillary number for different \textit{$\lambda $} via boundary integral simulations. Interfacial slip is modeled via the Navier-slip condition, and the slip parameter employed in the simulations is predicted using the work of Goveas and Frederickson [\textit{Eur. Phys. J. B} \textbf{2}, 79--92 (1998) ]. The agreement with the scaling exponents of $t_{d}$ versus \textit{Ca }and$ R$ is improved, but the absolute values of the drainage times are lower than the experimental values. Possible reasons for these deviations are explored.