Related papers: Continuum Nanofluidics
The fluid-gravity correspondence documents a precise mathematical map between a class of dynamical spacetime solutions of the Einstein field equations of gravity and the dynamics of its corresponding dual fluid flows governed by the…
Recent advances have allowed to tackle exact path-space probabilistic representations of macroscopic advection-diffusion models involving advection nonlinearities by step forward approaches in terms of continuous branching stochastic…
We propose a geometrical approach to the mechanics of continuous media equipped with inner structures and give the basic (mass conservation, Navier-Stokes and energy conservation) equations of their motion.
The Navier-Stokes-Fourier system is a well established model for describing the motion of viscous compressible heat-conducting fluids. We study the existence of time-periodic weak solutions and improve the known result in the following…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
So far transport properties of nanoscale contacts have been mostly studied within the static scattering approach. The electron dynamics and the transient behavior of current flow, however, remain poorly understood. We present a numerical…
The statistical nature of discrete fluid molecules with random thermal motion so far has not been considered in mainstream fluid mechanics based on Navier-Stokes equations, wherein fluids have been treated as a continuum breaking into many…
Lubrication theory makes use of the assumptions of a long and thin fluid domain and a small scaled Reynolds number to formulate a linearized approximation to the Navier-Stokes equations. Extended lubrication theory aims to improve the model…
A freely falling stream of weakly cohesive granular particles is modeled and analysed with help of event driven simulations and continuum hydrodynamics. The former show a breakup of the stream into droplets, whose size is measured as a…
We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: Global existence and critical values of the adiabatic constant;…
This paper is concerned with steady, fully developed motion of a Navier-Stokes fluid with shear-dependent viscosity in a curved pipe under a given axial pressure gradient. We establish existence and uniqueness results, derive appropriate…
The motion of the electrolyte, comprising of solute ions and solvent molecules, is a frequently-occurring natural phenomenon. The motion of the electrolyte leads to the flows of ions and solvent molecules, known as electrochemical flows. In…
Discrete mechanics is presented as an alternative to the equations of fluid mechanics, in particular to the Navier-Stokes equation. The derivation of the discrete equation of motion is built from the intuitions of Galileo, the principles of…
Despite the nonlinear nature of wall turbulence, there is evidence that the energy-injection mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise…
We consider incompressible flows between two transversely vibrating solid walls and construct an asymptotic expansion of solutions of the Navier-Stokes equations in the limit when both the amplitude of vibrations and the thickness of the…
Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a…
We analyze the creeping flow generated by a spherical particle moving through a viscous fluid with nematic directional order, in which momentum diffusivity is anisotropic and which opposes resistance to bending. Specifically, we provide…
A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…
A simple analytical model for a turbulent flow is proposed, which considers the flow as a collection of localized spatial structures that are composed of elementary "cells" in which the state of the particles (atoms or molecules) is…