Related papers: Scaling Navier-Stokes Equation in Nanotubes
The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one…
Mechanical effects that span multiple physical scales -- such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions -- play a critical role in real fluid systems. The spin angular…
By rewriting the Navier-Stokes equation in terms of differential forms we give a formulation which is abstracted and reproduced in a finite dimensional setting. We give two examples of these finite models and, in the latter case, prove some…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
We show that molecular dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations…
Hydrodynamics at the macroscopic scale, composed of a vast ensemble of microscopic particles, is described by the Navier-Stokes equation. However, at the mesoscopic scale, bridging the microscopic and macroscopic domains, fluctuations…
We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions we show that the average in the thin direction of a strong…
Heuristic derivations of the Navier-Stokes equations are unable to reveal the applicability limits of these equations. In this paper we rederive the Navier-Stokes equations from kinetic theory, using a method that affords a step by step…
We consider the three-dimensional incompressible Navier--Stokes equations in a curved thin domain with Navier's slip boundary conditions. The curved thin domain is defined as a region between two closed surfaces which are very close to each…
We introduce a coupled Cahn-Hilliard Navier-Stokes model that governs the two-phase dynamics of a system that consists of a fluid and a solid phase and prove its thermodynamic consistency. Moreover, we present an associated fully-discrete…
A remarkable feature of fluid dynamics is its relationship with classical dynamics and statistical mechanics. This has motivated in the past mathematical investigations concerning, in a special way, the "derivation" based on kinetic theory,…
In Navier-Stokes turbulence, energy and helicity injected at large scales are subject to a joint direct cascade, with both quantities exhibiting a spectral scaling $\propto k^{-5/3}$. We demonstrate via direct numerical simulations that the…
We investigate the dynamics of pressure driven transient flows of incompressible Newtonian fluids through circular microtubes having thin elastic walls under the long-wavelength and small deformation assumptions, which are valid for many…
The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of…
We investigate the high viscosity limit (also called inertial limit) of the barotropic compressible Navier-Stokes equations supplemented with initial data which are perturbations of a stable constant solution. In the case of constant…
We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid such as water, surrounded by the gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapour…
Systems of spherical particles moving in Stokes flow are studied for a different particle internal structure and boundaries, including the Navier-slip model. It is shown that their hydrodynamic interactions are well described by treating…
When speaking of unsolved problems in physics, this is surprising at first glance to discuss the case of fluid mechanics. However, there are many deep open questions that come with the theory of fluid mechanics. In this paper, we discuss…
Molecular dynamics simulations are used to study the behavior of closely-fitting spherical and ellipsoidal particles moving through a fluid-filled cylinder at nanometer scales. The particle, the cylinder wall and the fluid solvent are all…
This paper presents a rigorous derivation of an effective model for fluid flow through a thin elastic porous membrane separating two fluid bulk domains. The microscopic setting involves a periodically structured porous membrane composed of…