Related papers: Characteristic Angles in the Wetting of an Angular…
We consider a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss mean curvature flow scaled with a term that depends on a quantity…
The wetting of solid surfaces by fluids is a problem of great practical importance that has been extensively studied over the years. Most often, the experimental work has involved measurements of the contact angle made by a liquid on the…
We consider binary liquid mixtures near their critical consolute points and exposed to geometrically flat but chemically structured substrates. The chemical contrast between the various substrate structures amounts to opposite local…
We study singularities and geometric properties of surfaces given by the singular loci of normal congruence of frontals with pure-frontal singular points. These surfaces consist of the normal ruled surface and focal surfaces of the initial…
We consider the smooth inverse mean curvature flow of strictly convex hypersurfaces with boundary embedded in $\mathbb{R}^{n+1},$ which are perpendicular to the unit sphere from the inside. We prove that the flow hypersurfaces converge to…
We classify the topological types of surfaces in the 3-dimensional unit sphere that contain both a great and a small circle through each point. In particular, these surfaces are homeomorphic to one of five normal forms and are either the…
Rivulets and droplets are naturally appearing shapes when small amounts of liquid are deposited on a partially wettable substrate. Here we study, by means of numerical simulations, the dewetting dynamics of a ring-rivulet on substrates with…
Liquids in oil-bearing porous media assume complex shapes that depend on the reservoir characteristics and the wetting properties of the liquid. The wide variation in the geometry of rock formations makes it difficult to accurately predict…
We study the geometric flow of a planar curve driven by its curvature and the normal derivative of its capacity potential. Under a convexity condition that is natural to our problem, we establish long term existence and large time…
The wetting of a charged wedge-like wall by an electrolyte solution is investigated by means of classical density functional theory. As in other studies on wedge wetting, this geometry is considered as the most simple deviation from a…
We present the theory of liquid bridges between two axisymmetric solids, sphere and plane, with prescribed contact angles in a general setup, when the solids are non-touching, touching or intersecting, We give a detailed derivation of…
When a viscous liquid hits a pool of liquid of same nature, the impact region is hollowed by the shock. Its bottom becomes extremely sharp if increasing the impact velocity, and we report that the curvature at that place increases…
The simplest patterns of qualitative changes on the configurations of lines of principal curvature} around umbilic points on surfaces whose immersions into $\mathbb R^3$ depend smoothly on a real parameter (codimension one umbilic…
Particle diffusion in a two dimensional curved surface embedded in $R_3$ is considered. In addition to the usual diffusion flow, we find a new flow with an explicit curvature dependence. New diffusion equation is obtained in $\epsilon$…
Manifestations of orbital angular momentum induced effects in the diffraction of a radially polarized vector beam by an off-axis tilted aperture are studied both experimentally and theoretically. Experiments were carried out to extract the…
A lattice model is used to study repulsive active particles at a planar surface. A rejection-free Kinetic Monte Carlo method is employed to characterize the wetting behaviour. The model predicts a mobility induced phase separation of active…
We show that curvatures in general ambient flow profiles can align shape-asymmetric active particles, revealing a previously overlooked competition with externally applied aligning fields. Focusing on the ubiquitous case of channel flows,…
We report on the shape taken by the interface of a liquid bath when hit by a smooth oblique steady jet. When the angle between the jet and the bath decreases below $50^\circ$, a cavity is formed in front of the jet. In the inertial regime…
We classify complete biharmonic surfaces with parallel mean curvature vector field and non-negative Gaussian curvature in complex space forms.
We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we…