Related papers: Linear models for thin plates of polymer gels
Torques on interfaces can be described by a divergence-free tensor which is fully encoded in the geometry. This tensor consists of two terms, one originating in the couple of the stress, the other capturing an intrinsic contribution due to…
This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic diffusion equation defined on a domain $D$ such that…
The transport of deformable particles through porous media underlies a wealth of applications ranging from filtration to oil recovery to the transport and spreading of biological agents. Using direct numerical simulations, we analyze the…
Gels are used to design bilayered structures with high residual stresses. The swelling of a thin layer on a compliant substrate leads to compressive stresses. The post-buckling of this layer is investigated experimentally; the wavelengths…
The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable.…
In this paper we derive consistent shallow water equations for thin films of power law fluids down an incline. These models account for the streamwise diffusion of momentum which is important to describe accurately the full dynamic of the…
Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of…
We introduce a microscopically realistic model of a physical gel and use computer simulations to study its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a…
We propose a model for thermo-elastic beams, consistent with the theory of linear three-dimensional thermo-elasticity and deduced by a suitable version of the Principle of Virtual Powers. Dimensional reduction is achieved by postulating…
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the…
Consider the three-dimensional flow of a viscous Newtonian fluid upon an abitrarily curved substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a model of the dynamics of the film, the…
In this thesis the formation and properties of a polymer gel on and at a surface are investigated. The gel under investigation is defined as a three-dimensional network of "phantom" macromolecules that form permanent links with one another…
We review continuum elastic models for the transmission of both external forces and internal active cellular forces in biopolymer gels, and relate them to recent experiments. Rather than being exhaustive, we focus on continuum elastic…
Ion-conducting glasses and polymer systems show several characteristic peculiarities in their composition-dependent diffusion properties and in their dynamic response. First we give a brief review of the current understanding of the ion…
This work presents a mathematical model for the optimal control of thin-film flows over a flexible topography influenced by an external force. Our thin-film model allows for the rupture of films as well as the coalescence of bubbles. The…
A mathematical model is derived for the dynamics of a cylinder, or wheel, rolling over a thin viscous film. The model combines the Reynolds lubrication equation for the fluid with an equation of motion for the wheel. Two asymptotic limits…
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant…
We discuss a 1D variational problem modeling an elastic sheet on water, lifted at one end. Its terms include the membrane and bending energy of the sheet as well as terms due to gravity and surface tension. By studying a suitable…
Following our first report (A. Groisman and V. Steinberg, $\sl Nature$ $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between…
'A basic and basically unsolved problem in fluid dynamics is to determine the evolution of rising bubbles and falling drops of one miscible liquid in another' [1]. Here, we address this important literature gap and present the first theory…