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We study theoretically the self-propulsion dynamics of a small droplet on general curved surfaces by a variational approach. A new reduced model is derived based on careful computations for the capillary energy and the viscous dissipation…

Exact solutions are reported for a stream of asymmetric bubbles steadily moving in a Hele-Shaw channel. From the periodicity along the streamwise direction, the flow region is reduced to a rectangular unit cell containing one bubble, which…

Coarsening of two-phase systems is crucial for the stability of dense particle packings such as alloys, foams, emulsions or supersaturated solutions. Mean field theories predict an asymptotic scaling state with a broad particle size…

Let $(M,g_0)$ be a closed Riemannian manifold of dimension $n \geq 25$ with positive Yamabe invariant $Y(M,g_0)>0$ and positive fourth-order invariant $Y_4(M,g_0)>0$. We show that, arbitrarily $C^1$-close to $g_0$, there exists a Riemannian…

We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based…

The classical Blake threshold indicates the onset of quasistatic evolution leading to cavitation for gas bubbles in liquids. When the mean pressure in the liquid is reduced to a value below the vapor pressure, the Blake analysis identifies…

Theoretical studies of nearly spherical vesicles and microemulsion droplets, that present typical examples for thermally-excited systems that are subject to constraints, are reviewed. We consider the shape fluctuations of such systems…

We present a parametric study of the unsteady phenomena associated with the flow of elongated gas bubbles travelling through liquid-filled square capillaries under high Weber number conditions. These conditions consistently induce the…

In this paper, we will derive a small energy regularity theorem for the mean curvature flow of arbitrary dimension and codimension. It says that if the parabolic integral of $|A|^2$ around a point in space-time is small, then the mean…

We study the global existence and stability of surface diffusion flow (the normal velocity is given by the Laplacian of the mean curvature) of smooth boundaries of subsets of the $n$--dimensional flat torus. More precisely, we show that if…

A steady-state convection-diffusion problem with a small diffusion of order $\mathcal{O}(\varepsilon)$ is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations.The physical origin of both phenomena has remained somewhat obscure.…

We consider the free boundary problem for a 3-dimensional, incompressible, irrotational liquid drop of nearly spherical shape with capillarity. We study the problem from the beginning, extending some classical results from the flat case…

We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion…

The Local and Loop I superbubbles are the closest and best investigated supernova (SN) generated bubbles and serve as test laboratories for observations and theories of the interstellar medium. Since the morphology and dynamical evolution…

We study random bubble lattices which can be produced by processes such as first order phase transitions, and derive characteristics that are important for understanding the percolation of distinct varieties of bubbles. The results are…

We consider an anisotropic curvature flow $V= A(\mathbf{n})H + B(\mathbf{n})$ in a band domain $\Omega :=[-1,1]\times R$, where $\mathbf{n}$, $V$ and $H$ denote the unit normal vector, normal velocity and curvature, respectively, of a…

During his experiments W. D. Ristenpart made a very remarkable discovery. If two oppositely charged droplets of fluid are close enough, at first they attract each other and touch eventually. Surprisingly after that the droplets are repelled…

We create a highly controlled lab environment-accessible to both global and local monitoring-to analyse turbulent boiling flows and in particular their shear stress in a statistically stationary state. Namely, by precisely monitoring the…