Related papers: Shear viscosity: velocity gradient as a constraint…
We perform a linear stability analysis of extended domains in phase-separating fluids of equal viscosity, in two dimensions. Using the coupled Cahn-Hilliard and Stokes equations, we derive analytically the stability eigenvalues for long…
We consider a kinetic model, which describes the sedimentation of rod-like particles in dilute suspensions under the influence of gravity. This model has recently been derived by Helzel and Tzavaras in \cite{HT2015}. Here we restrict our…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. It is proved that no small-amplitude waves are supported by a horizontal shear flow whose free surface is still…
We study the relation between flow structure and fluid deformation in steady two-dimensional random flows. Beyond the linear (shear flow) and exponential (chaotic flow) elongation paradigms, we find a broad spectrum of stretching behaviors,…
The expected universality of small-scale properties of turbulent flows implies isotropic properties of the velocity gradient tensor in the very large Reynolds number limit. Using direct numerical simulations, we determine the tensors formed…
Molecular dynamics (MD) and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate…
Unlike crystalline solids, liquids lack long-range order, resulting in diffusive shear fluctuations rather than propagating waves. Simulations predict that liquids exhibit a $k$-gap in wave-vector space, where solid-like transverse waves…
Using the Lagrangian transport analysis for the turbulence momentum, the Reynolds stress gradient can be expressed as a function of the local momentum flux and force terms. From this perspective of an observer moving at the local mean…
We investigate the single-point probability density function of the velocity in three-dimensional stationary and decaying homogeneous isotropic turbulence. To this end we apply the statistical framework of the Lundgren-Monin-Novikov…
Turbulent shear flows driven by a combination of a pressure gradient and buoyancy forcing are investigated using direct numerical simulations. Specifically, we consider the setup of a differentially heated vertical channel subject to a…
A curve shortening equation related to the evolution of grain boundaries is presented. This equation is derived from the grain boundary energy by applying the maximum dissipation principle. Gradient estimates and large time asymptotic…
The ubiquitous appearance of regions of localized deformation (shear bands) in different kinds of disordered materials under shear is studied in the context of a mesoscopic model of plasticity. The model may or may not include relaxational…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is performed to study the conditions for stability of a suspension of solid particles immersed in a viscous gas. The dissipation in such…
We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy…
Discrete mechanics makes it possible to formulate any problem of fluid mechanics or fluid-structure interaction in velocity and potentials of acceleration; the equation system consists of a single vector equation and potentials updates. The…
The traditional approach in the study of hydrodynamic stability of stratified fluids includes the stick boundary conditions between layers. However, this rule may be violated in polymer systems and as a consequence various instabilities may…
The dynamic behavior of the slip length in a fluid flow confined between atomically smooth surfaces is investigated using molecular dynamics simulations. At weak wall-fluid interactions, the slip length increases nonlinearly with the shear…
The linear instability of Faraday waves in Hele-Shaw cells is investigated with consideration of the viscosity of fluids after gap-averaging the governing equations due to the damping from two lateral walls and the dynamic behavior of…
We examine a simple mechanism for the spatio-temporal evolution of transient, slow slip. We consider the problem of slip on a fault that lies within an elastic continuum and whose strength is proportional to sliding rate. This rate…
The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity $V(y)$ declines strongly with distance $y$ from the moving wall, independent of the shear rate…