Buoyancy-driven detachment of a wall-bound pendant drop: interface shape at pinchoff and nonequilibrium surface tension.

Abstract

We present numerical results from phase-field simulations of the buoyancy-driven detachment of an isolated, wall-bound pendant emulsion droplet acted upon by surface tension and wall-normal buoyancy forces alone. Our theoretical approach follows a diffuse-interface model for partially miscible binary mixtures which has been extended to include the influence of static contact angles other than 90^{∘}, based on a Hermite interpolation formulation of the Cahn boundary condition as first proposed by Jacqmin [J. Fluid Mech. 402, 57 (2000)JFLSA70022-112010.1017/S0022112099006874]. In a previous work, this model has been successfully employed for simulating triphase contact line problems in stable emulsions with nearly immiscible components, and, in particular, applied to the determination of critical Bond numbers for buoyancy-driven detachment as a function of static contact angle. Herein, the shapes of interfaces at pinchoff are investigated as a function of static contact angle and distance to the critical condition. Furthermore, we show numerical results on the nonequilibrium surface tension that help to explain the discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart based on a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we show the influence of static contact angle and distance to the critical condition on the temporal evolution of the minimum neck radius in the necking regime of drop detachment.