Stability Of Contact Line Research Articles

Stability of contact lines in 2D stationary Benard convection

Stability of contact lines in 2D stationary Benard convection

Stability of contact lines in fluids: 2D Navier–Stokes flow

In this paper we study the dynamics of an incompressible viscous fluid evolving in an open-top container in two dimensions. The fluid mechanics are dictated by the Navier–Stokes equations. The upper boundary of the fluid is free and evolves within the container. The fluid is acted upon by a uniform gravitational field, and capillary forces are accounted for along the free boundary. The triple-phase interfaces where the fluid, air above the vessel, and solid vessel wall come in contact are called contact points, and the angles formed at the contact point are called contact angles. The model that we consider integrates boundary conditions that allow for full motion of the contact points and angles. Equilibrium configurations consist of quiescent fluid within a domain whose upper boundary is given as the graph of a function minimizing a gravity-capillary energy functional, subject to a fixed mass constraint. The equilibrium contact angles can take on any values between 0 and \pi depending on the choice of capillary parameters. The main thrust of the paper is the development of a scheme of a priori estimates that show that solutions emanating from data sufficiently close to the equilibrium exist globally in time and decay to equilibrium at an exponential rate.

Dynamics and stability of sessile drops with contact points

In an effort to study the stability of contact lines in fluids, we consider the dynamics of a drop of incompressible viscous Stokes fluid evolving above a one-dimensional flat surface under the influence of gravity. This is a free boundary problem: the interface between the fluid on the surface and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the flat surface is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allows us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to a shifted equilibrium exponentially fast.

Stability of Contact Lines in Fluids: 2D Stokes Flow

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary problem: the interface between the fluid in the vessel and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to equilibrium exponentially fast.

The spreading and stability of a surfactant-laden drop on a prewetted substrate

We consider a viscous drop, loaded with an insoluble surfactant, spreading over a flat plane that is covered initially with a thin liquid film. Lubrication theory allows the flow to be modelled using coupled nonlinear evolution equations for the film thickness and surfactant concentration. Exploiting high-resolution numerical simulations, we describe the multi-region asymptotic structure of the spatially one-dimensional spreading flow and derive a simplified ODE model that captures its dominant features at large times. The model includes a version of Tanner's law accounting for a Marangoni flux through the drop's effective contact line, the magnitude of which is influenced by a rarefaction wave in the film ahead of the contact line. Focusing on the neighbourhood of the contact line, we then examine the stability of small-amplitude disturbances with spanwise variation, using long-wavelength asymptotics and numerical simulations to describe the growth-rate/wavenumber relationship. In addition to revealing physical mechanisms and new scaling properties, our analysis shows how initial conditions and transient dynamics have a long-lived influence on late-time flow structures, spreading rates and contact-line stability.

Toward a description of contact line motion at higher capillary numbers

The surface of a liquid near a moving contact line is highly curved owing to diverging viscous forces. Thus, microscopic physics must be invoked at the contact line and matched to the hydrodynamic solution farther away. This matching has already been done for a variety of models, but always assuming the limit of vanishing speed. This excludes phenomena of the greatest current interest, in particular the stability of contact lines. Here we extend perturbation theory to arbitrary order and compute finite speed corrections to existing results. We also investigate the impact of different contact line models on the large-scale shape of the interface.

Contact Line Stability and “Undercompressive Shocks” in Driven Thin Film Flow

We present new experimental results for films driven by a thermal gradient with an opposing gravitational force. When the gravitational effect becomes non-negligible, the advancing front produces a very large capillary ridge which shows a remarkable tendency to remain stable. This phenomenon can be explained by new mathematical results for a lubrication model of the experiment. The advancing front evolves into an ``undercompressive'' capillary shock structure which is stable to contact line perturbations, unlike typical capillary ridges in driven film flows.

Stability of contact line accompanied by solidification

The cooling rate in actual roll casting systems is markedly decreased by contact resistance between the chilled roll and melt (or solidified shell). In this study, focusing on the dynamic behavior of a contact line, the mechanism generating the contact resistance is experimentally investigated using liquid paraffin as a melt and flat plates as chilled surfaces. The experimental results obtained show that the smoothness of the solidified shell is closely related to the stability of the contact line. The range of immersion velocities of the plate, and stable contact lines appear only at middle immersion velocities. The range of immersion velocity in which stable contact lines appear becomes narrower with increasing undercooling degree of the plate. The unstable contact line appearing at high immersion velocities results from the dynamic nonwetting condition at the contact line. The unstable contact line at low immersion velocities is closely related to the formation of a solidified shell in the vicinity of the contact line and to the interface temperature upon contact between the melt and the chilled surface

Stability of Contact Line Accompanied by Solidification.

The cooling rate in actual roll casting systems is markedly decreased by contact resistance between the chilled roll and melt (or solidified shell). In this study, focusing on the dynamic behavior of a contact line, the mechanism generating the contact resistance is experimentally investigated using liquid paraffin as a melt and flat plates as chilled surfaces. The experimental results obtained show that the smoothness of the solidified shell is closely related to the stability of the contact line. The range of immersion velocities of the plate, and stable contact lines appear only at middle immersion velocities. The range of immersion velocity in which stable contact lines appear becomes narrower with increasing undercooling degree of the plate. The unstable contact line appearing at high immersion velocities results from the dynamic nonwetting condition at the contact line. The unstable contact line at low immersion velocities is closely related to the formation of a solidified shell in the vicinity of the contact line and to the interface temperature upon contact between the melt and the chilled surface

Contact line stability at edges: Comments on Gibbs’s inequalities

In his discussion of contact line equilibrium for a system comprising two liquids and a solid, Gibbs [Scientific Papers (Dover, New York, 1961), Vol. 1, p. 326] used an argument that resulted in two inequalities he claimed to be applicable when the three-phase contact line coincides with an edge on the solid surface. A simple counterexample is given that shows Gibbs’s inequalities lack universal applicability. A serious objection to Gibbs’s argument is noted and his discussion is altered to remove the objectionable feature. This leads to modified inequalities, which surprisingly are known and have been attributed to Gibbs by recent authors.

Experimental Study of Evaporation in the Contact Line Region of a Thin Film of Hexane

The transport processes in the contact line region (junction of evaporating thin liquid film, vapor, and substrate) of stationary steady-state evaporating thin films of hexane with various bulk compositions were studied experimentally. The substrate temperature distribution and liquid film thickness profile were measured, analyzed, and compared with previous results on other systems. The results demonstrate that small changes in the bulk composition significantly alter the characteristics of the transport processes in the contact line region. The curvature gradient at the liquid-vapor interface is a strong function of evaporation rate and composition. Concentration and temperature gradients give interfacial shear stresses and flow patterns that enhance contact line stability.

Comments on the stability of solid/liquid/fluid contact lines

Solid/liquid/gas contact lines are encountered in such phenomena as flotation, detergency, adhesion, and oil recovery. Gibb's method of constrained equilibrium states is applied to the problem of contact line stability. Two situations are considered: a somewhat general configuration not subjected to external fields and a specific configuration in the gravity field. The latter configuration is the axisymmetric dry patch whose stability has already been rigorously studied by Huh and Taylor and Michael. In the discussion, it is always assumed that the solid surface is ideal in that it is smooth, homogeneous, and in a constant state of strain independent of the presence of the other phases. Furthermore, the solid is mutually insoluble with the liquid and gas phases. (18 refs.)