Related papers: Sharp interface model for solid-state dewetting pr…
The hydrodynamic phase field model is applied to the problem of film spreading on a solid surface. The disjoining potential, responsible for modification of the fluid properties near a three-phase contact line, is computed from the…
True contact between randomly rough solids consists of myriad individual micro-junctions. While their total area controls the adhesive friction force of the interface, other macroscopic features, including viscoelastic friction, wear,…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
This paper presents an existence result for the anisotropic Cahn--Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account an anisotropic energy. The model allows for the degeneracy of…
The understanding of the spreading of liquids on solid surfaces is an important challenge for contemporary physics. Today, the motion of the contact line formed at the intersection of two immiscible fluids and a solid is still subject to…
Accurate estimation of surface wettability for various degrees of hydrophobicity becomes increasingly important in the molecular design of membrane. In this paper, we develop simple yet physically realistic model for estimating contact…
Contact angle hysteresis and generation of dynamics angle are two fundamental phenomena about the contact angle deviation from the equilibrium state. Roughness on the solid surface, disjoining pressure in the thin film, and liquid-solid…
Solid contacts involving soft materials are important in mechanical engineering or biomechanics. Experimentally, such contacts have been shown to shrink significantly under shear, an effect which is usually explained using adhesion models.…
We consider two stacked ultra-thin layers of different liquids on a solid substrate. Using long-wave theory, we derive coupled evolution equations for the free liquid-liquid and liquid-gas interfaces. Linear and non-linear analyses show…
In this work, we aim to develop energy-stable parametric finite element approximations for a sharp-interface model with strong surface energy anisotropy, which is derived from the first variation of an energy functional composed of…
Mathematical model that allows for direct tracking of the homoepitaxial crystal growth out of the window etched in the solid, pre-deposited layer on the substrate is described. The growth is governed by the normal (to the crystal-vapor…
We present a theoretical study of wetting phenomena and interactions between liquid-vapor interfaces based on the density functional theory. The focus is mostly on the impact of long-range van der Waals interactions both within the fluid…
In the classic theory of solid adhesion, surface energy drives deformation to increase contact area while bulk elasticity opposes it. Recently, solid surface stress has been shown also to play an important role in opposing deformation of…
This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described…
In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting,…
The spreading of liquid drops on soft substrates is extremely slow, owing to strong viscoelastic dissipation inside the solid. A detailed understanding of the spreading dynamics has remained elusive, partly owing to the difficulty in…
While isotropic in-plane swelling problems for thin elastic sheets have been studied extensively in recent years, many shape-programmable materials, including nematic solids and 3D-printed structures, are anisotropic, as are most industrial…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
The three-phase contact line of a droplet on a smooth surface can be characterized by the Young-Dupr\'e equation. It relates the interfacial energies with the macroscopic contact angle $\theta_e$. On the mesoscale, wettability is modeled by…
A novel phase field material point method is introduced for robust simulation of dynamic fracture in elastic media considering the most general case of anisotropic surface energy. Anisotropy is explicitly introduced through a properly…