Related papers: Nonlinear Rupture of Thin Liquid Films on Solid Su…
The reactive-infiltration instability, which develops when a porous matrix is dissolved by a flowing fluid, contains two important length scales. Here we outline a linear stability analysis that simultaneously incorporates both scales. We…
The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…
We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett. 94, 054501 (2005)] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. Numerically solving the…
Recent experimental observations have demonstrated interesting instability phenomenon during thermal drawing of microstructured glass/polymer fibers, and these observations motivate us to examine surface-tension-driven instabilities in…
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…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
This work presents a study of the interfacial dynamics of thin viscoelastic films subjected to the gravitational force and substrate interactions induced by the disjoining pressure, in two spatial dimensions. The governing equation is…
We develop a self-consistent theory of temporal fluctuations of a speckle pattern resulting from the multiple scattering of a coherent wave in a weakly nonlinear disordered medium. The speckle pattern is shown to become unstable if the…
Practical applications of nanocrystalline metallic thin films are often limited by instabilities. In addition to grain growth, the thin film itself can become unstable and collapse into islands through solid-state dewetting. Selective…
The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here we highlight the…
We present a theoretical study of wetting phenomena and interactions between liquid-vapor interfaces based on the density functional theory. The focus is mostly on the impact of long-range van der Waals interactions both within the fluid…
In capillary-driven fluid dynamics, simple departures from equilibrium offer the chance to quantitatively model the resulting relaxations. These dynamics in turn provide insight on both practical and fundamental aspects of thin-film…
We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric…
We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability of such flow, it is hard to treat the Navier--Stokes…
We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…
We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…
We consider the stochastic thin-film equation with linear deterministic and stochastic It\^o perturbations. The existence of nonnegative weak martingale solutions on the semi-axis is established, and their asymptotic behavior as $t \to…
This fluid dynamics video demonstrates an experiment on superfast thinning of a freestanding thin aqueous film. The production of such films is of fundamental interest for interfacial sciences and the applications in nanoscience. The stable…
The spontaneous formation of droplets via dewetting of a thin fluid film from a solid substrate allows for materials nanostructuring, under appropriate experimental control. While thermal fluctuations are expected to play a role in this…
In this paper, the nonlinear (orbital) stability of static 180^\circ N\'eel walls in ferromagnetic films, under the reduced wave-type dynamics for the in-plane magnetization proposed by Capella, Melcher and Otto [CMO07], is established. It…