Related Experiment Video
Updated: Mar 31, 2026

Impacts of Free-falling Spheres on a Deep Liquid Pool with Altered Fluid and Impactor Surface Conditions
Published on: February 17, 2019
Buoyancy-driven detachment of a wall-bound pendant drop: interface shape at pinchoff and nonequilibrium surface
1Department of Civil & Industrial Engineering, University of Pisa, Largo Lazzarino 1, 56122 Pisa, Italy.
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.
Related Concept Videos
Surface Tension of Fluid
Surface tension varies...
Surface Tension, Capillary Action, and Viscosity
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded by other molecules and are attracted equally in all directions by the cohesive forces within the liquid. However, the molecules on the surface of a liquid are attracted only by about one-half as many molecules. Because of the unbalanced molecular attractions on the surface molecules, liquids contract to form a shape that minimizes the number...
Excess Pressure Inside a Drop and a Bubble
Surface Tension and Surface Energy
Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
Buoyancy
Buoyancy and Stability for Submerged and Floating Bodies

