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We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
Stably stratified layers are thought to develop at the top of the liquid metallic cores of many terrestrial planets. We consider the case where the thermal gradient is stable but the compositional gradient is unstable, a situation…
A linear analysis of thermal diffusion and Maxwell equations is applied to study the thermomagnetic instability in a type-II superconducting slab. It is shown that the instability can lead to formation of spatially nonuniform distributions…
We investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the…
The linear hydrodynamic stability of proto-neutron stars (PNSs) is considered taking into account dissipative processes such as neutrino transport and viscosity. We obtain the general instability criteria which differ essentially from the…
The first stages of finger formation in a Hele-Shaw cell with lifting plates are investigated by means of linear stability analysis. The equation of motion for the pressure field (growth law) results to be that of the directional…
Many environmental, energy, and industrial processes involve the flow of polymer solutions in three-dimensional (3D) porous media where fluid is confined to navigate through complex pore space geometries. As polymers are transported through…
It is shown that step moving to meet solution flow can be unstable against lateral perturbations. The instability of long-wavelength perturbations occurs at values of the solution flow intensity less than some critical value depending on…
Viscous fingering patterns form in confined geometries at the interface between two fluids as the lower-viscosity fluid displaces the one with higher viscosity. Previous studies have examined the most unstable wavelength of the patterns…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
When a liquid viscous bridge between two parallel substrates is stretched by accelerating one substrate, its interface recedes in the radial direction. In some cases the interface becomes unstable. Such instability leads to the emergence of…
Simple observations of evaporating solutions reveal a complex hierarchy of spatio-temporal instabilities. We analyze one such instability suggested by the qualitative observations of Du and Stone and find that it is driven by a novel…
A new element is proposed to play a role in the evolution of extrasolar planetary systems: the tidal (or elliptical) instability. It comes from a parametric resonance and takes place in any rotating fluid whose streamlines are (even…
We perform a laboratory-scale experiment of submarine avalanches on a rough inclined plane. A sediment layer is prepared and thereafter tilted up to an angle lower than the spontaneous avalanche angle. The sediment is scrapped until an…
A thin water film on a cleaved mica substrate undergoes a first order phase transition between two values of film thickness. By inducing a finite evaporation rate of the water, the interface between the two phases develops a fingering…
Sand ripples are commonly observed in both nature and industry. For example, they are found on riverbeds and in oil pipelines that transport sand. In both natural and industrial cases, ripples increase friction between the bed and fluid and…
Failure and fault slip in crystalline rocks is associated with dilation. When pore fluids are present and drainage is insufficient, dilation leads to pore pressure drops, which in turn lead to strengthening of the material. We conducted…
In a binary fluid mixture, the concentration gradient of a heavier molecular solute leads to a diffusive flux of solvent and solute to achieve thermodynamic equilibrium. If the solute concentration decreases with height, the system is…
Understanding the dynamics of staircases in salt fingering convection presents a long-standing theoretical challenge to fluid dynamicists. Although there has been significant progress, particularly through numerical simulations, there are a…
We present a theory of the interfacial stability of two immiscible electrolytes under the coupled action of pressure gradients and electric fields in a Hele-Shaw cell or porous medium. Mathematically, our theory describes a phenomenon of…