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We present a macroscopic theory of capillary condensation in slits formed by parallel walls of unequal length. Using the concept of an edge contact angle, we identify four distinct condensation states and derive Kelvin-like relations for…
The matching conditions at the interface between two non-mixed fluids at rest are obtained directly using the equation of movement of the whole media. This is a non-usual point of view in hydrodynamics courses and our aim is to fix ideas…
Vertical thermal convection is a non-equilibrium system in which both buoyancy and shear forces play a role in driving the convective flow. Beyond the onset of convection, the driven dissipative system exhibits chaotic dynamics and…
Two cylinders rotating next to each other generate a large hydrodynamic force if the intermediate space is filled with a viscous fluid. Herein, we explore the case where the cylinders are separated by two layers of viscous immiscible…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to…
Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
Capillary rise occurs when a thin tube contacts a liquid, which rises against gravity due to the capillary force. This phenomenon is present in a wide range of everyday and industrial settings and provides the means to measure the physical…
The statistical physics and dynamics of double supported bilayers are studied theoretically. The main goal in designing double supported lipid bilayers is to obtain model systems of biomembranes: the upper bilayer is meant to be almost…
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…
We study the behavior of a three-dimensional dynamical system with respect to some set $S$ given in 3-dimensional euclidian space. Geometrically such a system arises from the normalized Ricci flow on some class of generalized Wallach spaces…
These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario derived from the solution…
We present a systematic study of capillary filling for a binary fluid by using mesoscopic a lattice Boltzmann model describing a diffusive interface moving at a given contact angle with respect to the walls. We compare the numerical results…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…
The present work revisits the problem of modeling diffusion above a stagnant liquid interface in a capillary tube geometry. In this revisitation we elucidate a misconception found in the classical model proposed by Bird et. al. Furthermore,…
We analyze the dynamics of liquid filling in a thin, slightly inflated rectangular channel driven by capillary forces. We show that although the amount of liquid $m$ in the channel increases in time following the classical Lucas-Washburn…
Using numerical simulations, we examine a simple model of two or more coupled one-dimensional channels of driven particles with repulsive interactions in the presence of quenched disorder. We find that this model exhibits a remarkably rich…
A wetting liquid is driven through a thin gap due to surface tension and when the gap boundaries are elastic, the liquid deforms the gap as it rises. But when the fluid boundaries are also permeable (or poroelastic), the liquid can permeate…
When modeling of tumor-driven angiogenesis, a major source of analytical and computational complexity is the strong coupling between the kinetic parameters of the relevant stochastic branching-and-growth of the capillary network, and the…
Aqueous capillary liquid bridges are ubiquitous in nature and in technological processes. Here, we comparatively investigate capillary bridges formed between three distinct types of surfaces: (i) hydrophilic glass, (ii) hydrophobic…