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Soft lubricated contacts exhibit complex interfacial behaviours governed by the coupled effects of multiscale surface roughness and non-linear fluid-solid interactions. Accurately capturing this interplay across thin-film flows is…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact…
New diffuse interface and sharp interface models for soluble and insoluble surfactants fulfilling energy inequalities are introduced. We discuss their relation with the help of asymptotic analysis and present an existence result for a…
We study the mixing in the presence of convective flow in a porous medium. Convection is characterized by the formation of vortices and stagnation points, where the fluid interface is stretched and compressed enhancing mixing. We analyze…
In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any…
We study the free boundary in the supercooled Stefan problem, a classical model for the solidification of water below its freezing temperature. In contrast with the melting problem, physical experiments and heuristics indicate that the…
We use a hybrid method of lattice Boltzmann and finite differences to simulate flat and curved interfaces between the nematic and isotropic phases of a liquid crystal described by the Landau-de Gennes theory. For the flat interface, we…
The design of polycrystalline alloys hinges on a predictive understanding of the interaction between the diffusing solutes and the motion of the constituent crystalline interfaces. Existing frameworks ignore the dynamic multiplicity of and…
In modeling phase transitions, it is useful to be able to connect diffuse interface descriptions of the dynamics with corresponding limiting sharp interface motions. In the case of the deep quench obstacle problem (DQOP) and surface…
We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…
We consider a transmission problem consisting of a semilinear parabolic equation in a general non-smooth setting with emphasis on rough interfaces which bear a fractal-like geometry and nonlinear dynamic (possibly, nonlocal)\ boundary…
While equilibrium interfaces display universal large-scale statistics, interfaces in phase-separated active and driven systems are predicted to belong to distinct non-equilibrium universality classes. Yet, such behavior has proven difficult…
The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random…
Starting from a phase-field description of the isothermal solidification of a dilute binary alloy, we establish a model where capillary waves of the solidification front interact with the diffusive concentration field of the solute. The…
A simple theoretical approach is used to investigate active colloids at the free interface and near repulsive substrates. We employ dynamical density functional theory to determine the steady-state density profiles in an effective…
In this paper, we study a diffuse interface model for two-phase immiscible flows coupled by Navier-Stokes equations and mass-conserving Allen-Cahn equations. The contact line (the intersection of the fluid-fluid interface with the solid…
Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to…
We study both diffuse and sharp liquid-vapor interfaces. The equilibrium equation of fluids is derived by using the principle of virtual work in a domain including the interfaces. For diffuse interfaces, the surface tension coefficient…
We find stationary thin-brane geometries that are dual to far-from-equilibrium steady states of two-dimensional holographic interfaces. The flow of heat at the boundary agrees with the result of CFT and the known energy-transport…
A variational model for describing the morphology of two-phase continua by allowing for the interplay between coherent and incoherent interfaces is introduced. Coherent interfaces are characterized by the microscopical arrangement of atoms…