Related papers: Density-constrained Chemotaxis and Hele-Shaw flow
We consider a continuum mechanical model of cell invasion through thin membranes. The model consists of a transmission problem for cell volume fraction complemented with continuity of stresses and mass flux across the surfaces of the…
The diffuse interface model of Cahn-Hilliard-van der Waals is often used to study various aspects of multi-phase flows such as droplets coalescence and contact line dynamics. The original model of Cahn-Hilliard-van der Waals uses an…
We investigate the dynamics of relaxation, by surface tension, of a family of curved interfaces between an inviscid and viscous fluids in a Hele-Shaw cell. At t=0 the interface is assumed to be of the form |y|=A x^m, where A>0, m \geq 0,…
This paper studies a chemotaxis system where cells move in response to a chemical signal within a confined habitat. The model includes external source terms that combine local and nonlocal growth with dampening effects. The main focus is on…
We investigate the flow of two immiscible, viscous fluids in a rotating Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining…
In this paper we examine boundary effects in a fractional chemotactic equation derived from a kinetic transport model describing cell movement in response to chemical gradients (chemotaxis). Specifically, we analyze reflecting boundary…
We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the…
This paper is concerned with a parabolic-elliptic chemotaxis model with density-suppressed motility and general logistic source in an $n$-dimensional smooth bounded domain with Neumann boundary conditions. Under the minimal conditions for…
We report on the modeling of the dynamics of confined lipid membranes. We derive a thin film model in the lubrication limit which describes an inextensible liquid membrane with bending rigidity confined between two adhesive walls. The…
Chemotaxis is a fundamental mechanism of cells and organisms, which is responsible for attracting microbes to food, embryonic cells into developing tissues, or immune cells to infection sites. Mathematically chemotaxis is described by the…
The interplay of chemotaxis and diffusion of nutrients or signaling chemicals in bacterial suspensions can produce a variety of structures with locally high concentrations of cells, including phyllotactic patterns, filaments, and…
A new general class of exact solutions is presented for the time evolution of a bubble of arbitrary initial shape in a Hele-Shaw cell when surface tension effects are neglected. These solutions are obtained by conformal mapping the viscous…
We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…
This work concerns with a class of chemotaxis models in which external sources, comprising nonlocal and gradient-dependent damping reactions, influence the motion of a cell density attracted by a chemical signal. The mechanism of the two…
When a fluid surface adheres to a substrate, the location of the contact line adjusts in order to minimize the overall energy. This adhesion balance implies boundary conditions which depend on the characteristic surface deformation…
In this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODE, while the…
A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the nonlinear stage of the…
Using a hydrodynamic lattice-gas model, we study interface growth in a binary fluid with various concentrations of surfactant. We find that the interface is smoothed by small concentrations of surfactant, while microemulsion droplets form…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
In this review article, we discuss recent studies on drops and bubbles in Hele-Shaw cells, focusing on how scaling laws exhibit crossovers from the three-dimensional counterparts and focusing on topics in which viscosity plays an important…