Related papers: Comments on the compositional boundary condition f…
So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems…
In this work, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model consists of a Cahn-Hilliard equation, a Navier-Stokes equation and…
A major challenge for molecular modeling consists in optimizing the unlike interaction potentials. In many cases, combination rules are generally suboptimal when accurate predictions of properties like the mixture vapor pressure are needed.…
The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, including curvature effects, within a unified, energetically…
We investigate a possibility to regularize the hydrodynamic contact line singularity in the configuration of partial wetting (liquid wedge on a solid substrate) via evaporation-condensation, when an inert gas is present in the atmosphere…
Van der Waals interactions are ubiquitous and they play an important role for the stability of materials. Current understanding of this type of coupling is based on linear response theory, while optical nonlinearities are rarely considered…
We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
Phase field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived…
We account for the presence of surface charges towards describing variations in the dynamic contact angle of an advancing liquid-gas meniscus. Starting from the thin-film based formalism, we present closed-form analytical expressions…
We developed a sharp interface level-set approach for two-phase immiscible flow with moving contact lines. The Cox-Voinov model is used to describe the moving contact line. A piecewise linear interface method is used to construct the signed…
In this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous convective Cahn-Hilliard system,…
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of…
A difficulty in the classical hydrodynamic analysis of moving contact-line problems, associated with the no-slip wall boundary condition resulting in an unbalanced divergence of the viscous stresses, is reexamined with a smoothed,…
Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature…
A moving contact line occurs at the intersection of an interface formed between two immiscible liquids and a solid. According to viscous theory, the flow is entirely governed by just two parameters, the viscosity ratio, $\lambda$, and the…
Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated . Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are…
A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation…
Droplets form a cornerstone of the spatiotemporal organization of biomolecules in cells. These droplets are controlled using physical processes like chemical reactions and imposed gradients, which are costly to simulate using traditional…
We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response. We achieve this by rewriting the interaction energy expression exclusively in terms of…