Surface tension

About: Surface tension is a research topic. Over the lifetime, 25410 publications have been published within this topic receiving 695471 citations.

Convergence of the phase field model to its sharp interface limits

Abstract: We consider the distinguished limits of the phase field equations and prove that the corresponding free boundary problem is attained in each case. These include the classical Stefan model, the surface tension model (with or without kinetics), the surface tension model with zero specific heat, the two phase Hele–Shaw, or quasi-static, model. The Hele–Shaw model is also a limit of the Cahn–Hilliard equation, which is itself a limit of the phase field equations. Also included in the distinguished limits is the motion by mean curvature model that is a limit of the Allen–Cahn equation, which can in turn be attained from the phase field equations.

Interfacial tensions at alkane-aqueous electrolyte interfaces

Abstract: Surface tensions of aqueous electrolytes, and their interfacial tensions against n-dodecane, have been determined at 20°C. The salts studied were LiCl, NaCl, KCl, KBr, NaBr, KI and Na2SO4 at concentrations up to about 1 mol kg–1. For the alkali metal chlorides and Na2SO4 the surface and interfacial tension increments are similar for a given electrolyte. The corresponding increments for KBr, NaBr and KI however are found to differ considerably. The results are discussed in terms of both electrostatic theory and dispersion force theory of interfaces. With respect to the latter, it is found that if due allowance is made for the presence of an ion-free layer of water at the interface, an approximate approach in which only a single dominant interaction frequency is considered, gives results in reasonable accord with experiment.

The long-time motion of vortex sheets with surface tension

Abstract: We study numerically the simplest model of two incompressible, immiscible fluids shearing past one another. The fluids are two-dimensional, inviscid, irrotational, density matched, and separated by a sharp interface under a surface tension. The nonlinear growth and evolution of this interface is governed by only the competing effects of the Kelvin–Helmholtz instability and the dispersion due to surface tension. We have developed new and highly accurate numerical methods designed to treat the difficulties associated with the presence of surface tension. This allows us to accurately simulate the evolution of the interface over much longer times than has been done previously. A surprisingly rich variety of behavior is found. For small Weber numbers, where there are no unstable length-scales, the flow is dispersively dominated and oscillatory behavior is observed. For intermediate Weber numbers, where there are only a few unstable length-scales, the interface forms elongating and interpenetrating fingers of fluid. At larger Weber numbers, where there are many unstable scales, the interface rolls-up into a “Kelvin-Helmholtz” spiral with its late evolution terminated by the collision of the interface with itself, forming at that instant bubbles of fluid at the core of the spiral. Using locally refined grids, this singular event (a “topological” or “pinching” singularity) is studied carefully. Our computations suggest at least a partial conformance to a local self-similar scaling. For fixed initial data, the pinching singularity times decrease as the surface tension is reduced, apparently towards the singularity time associated with the zero surface tension problem, as studied by Moore and others. Simulations from more complicated, multi-modal initial data show the evolution as a combination of these fingers, spirals, and pinches.