Related papers: Scaling Navier-Stokes Equation in Nanotubes
Recent advance in nanotechnology has led to rapid advances in nanofluidics, which has been established as a reliable means for a wide variety of applications, including molecular separation, detection, crystallization and biosynthesis.…
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes…
Flow of viscous fluids are not usually discussed in detail in general and basic courses of physics. This is due in part to the fact that the Navier-Stokes equation has analytical solution only for a few restricted cases, while more…
We derive and analyze a new diffuse interface model for incompressible, viscous fluid mixtures with bulk-surface interaction. Our system consists of a Navier--Stokes--Cahn--Hilliard model in the bulk that is coupled to a surface…
Molecular dynamics simulations have been performed on pure liquid water, aqueous solutions of sodium chloride, and polymer solutions exposed to a strong external electric field with the goal to gain molecular insight into the structural…
Systems of hydrodynamic type equations derived from the Navier-Stokes equations and the boundary layer equations are considered. A transformation of the Crocco type reducing the equation order for the longitudinal velocity component is…
In this paper, based on a theoretical model [1], it has been shown experimentally that the initial stage of development of a nanosecond breakdown in liquids is associated with the appearance of discontinuities in the liquid (cavitation)…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant…
In the laminar mode interactions among molecules generate friction between layers of water that slide with respect to each other. This friction triggers the shear stress, which is traditionally presumed to be linearly proportional to the…
This paper concerns the instability and stability of the trivial steady states of the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a slab domain in dimension two. The main results show that the stability…
Open problems in fluid dynamics, such as the existence of finite-time singularities (blowup), explanation of intermittency in developed turbulence, etc., are related to multi-scale structure and symmetries of underlying equations of motion.…
We propose a kinetic framework for single-component non-ideal isothermal flows. Starting from a kinetic model for a non-ideal fluid, we show that under conventional scaling the Navier-Stokes equations with a non-ideal equation of state are…
We study the effect of volumetric constraints on the structure and electronic transport properties of distilled water in a nanopore with embedded electrodes. Combining classical molecular dynamics simulations with quantum scattering theory,…
A carbon nanotube is an ideal object for understanding the atomic scale aspects of interface interaction and friction. Using molecular statics and dynamics methods different types of motion of nanotubes on a graphite surface are…
A robust control scheme is derived and tested for the Navier-Stokes equations for two-dimensional multiphase flow of a thin film underneath an inclined solid surface. Control is exerted via the use of an electrode parallel to the substrate,…
We survey results of recent activity towards studying controllability and accessibility issues for equations of dynamics of incompressible fluids controlled by low-dimensional or, degenerate, forcing. New results concerning controllability…
For the gas near a solid planar wall, we propose a scaling formula for the mean free path of a molecule as a function of the distance from the wall, under the assumption of a uniform distribution of the incident directions of the molecular…
The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at…
Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or, in an evolving flow, becomes infinite at any point within a finite time). Such singularities can…