Related papers: Lack of contact in a lubricated system
The 120-year old so-called Painleve paradox involves the loss of determinism in models of planar rigid bodies in point contact with a rigid surface, subject to Coulomb-like dry friction. The phenomenon occurs due to coupling between normal…
This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and…
A huge number of technological and biological systems involves the lubricated contact between rough surfaces of soft solids in relative accelerated motion. Examples include dynamical rubber seals and the human joints. In this study we…
We consider an adhesive contact between a thin soft layer on a rigid substrate and a rigid cylindrical indenter ("line contact") with account of the surface tension of the layer. First, it is shown that the boundary condition for the…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
The problem of partially hinged and partially free rectangular plate that aims to represent a suspension bridge subject to some external forces (for example the wind) is considered in order to model and simulate the unstable end behavior.…
We study the surface transport properties of stationary localized configurations of relativistic fluids to the first two non-trivial orders in a derivative expansion. By demanding that these finite lumps of relativistic fluid are described…
We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy…
Molecular dynamics (MD) simulations have been carried out to investigate the slip of fluid in the lid driven cavity flow where the no-slip boundary condition causes unphysical stress divergence. The MD results not only show the existence of…
Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible…
Lubricated surfaces have shown promise in numerous applications where impinging foreign droplets must be removed easily; however, before they can be widely adopted, the problem of lubricant depletion, which eventually leads to decreased…
We prove a global existence result for weak solutions to a one-dimensional free boundary problem with flux boundary conditions describing swelling along a halfline. Additionally, we show that solutions are not only unique but also depend…
In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics. An off-lattice modelling approach is considered…
When a droplet spreads on a solid substrate, it is unclear what are the correct boundary conditions to impose at the moving contact line. The classical no-slip condition is generally acknowledged to lead to a non-integrable singularity at…
In any number of space variables, we study the Cauchy problem related to the thin-film equation in the simplest case of a linearly degenerate mobility. This equation, derived from a lubrication approximation, also models the surface tension…
Wetting flows are controlled by the contact line motion. We derive an equation that describes the slow time evolution of the triple solid-liquid-fluid contact line for an arbitrary distribution of defects on a solid surface. The capillary…
The purpose of this note is to study the existence of a nontrivial solution for an elliptic system which comes from a newly introduced mathematical problem so called Field-Road model. Specifically, it consists of coupled equations set in…
The motion of an elastic solid inside of an incompressible viscous fluid is ubiquitous in nature. Mathematically, such motion is described by a PDE system that couples the parabolic and hyperbolic phases, the latter inducing a loss of…
The problem of determining equilibrium configurations of the free surface of a conducting liquid is considered with allowance for a finite interelectrode distance. The analogy is established between this electrostatic problem and that of…
In this paper, we study an interaction problem between an elastic plate and a compressible viscous fluid located between the rigid bottom $z=0$ and the plate. First, by utilizing the vertical fluid dissipation, we show that $\ln\eta(t) \in…