Kinetic theory of sound propagation in gaseous mixtures. I. Two‐fluid 5‐moment, 13‐moment, and Navier‐Stokes Theories

1974 ◽  
Vol 55 (4) ◽  
pp. 775-782 ◽  
Author(s):  
Francis J. McCormack ◽  
David E. Craven
Keyword(s):  
Kinetic Theory ◽  
Sound Propagation ◽  
Navier Stokes ◽  
Gaseous Mixtures ◽  
Two Fluid

ON THE EXISTENCE AND UNIQUENESS OF TWO‐FLUID CHANNEL FLOWS

2005 ◽  
Vol 9 (1) ◽  
pp. 67-78 ◽  
Author(s):  
J. Socolowsky
Keyword(s):  
Stokes Equations ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Density Ratios ◽  
Steady State Solutions ◽  
Two Fluid

iscous two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations. In this paper the solvability of the related stationary problems is discussed and computational results are presented. Furthermore, it is shown that depending on the flow parameters like viscosity or density ratios and on the fluxes there can happen nonexistence of steady‐state solutions. For other parameter sets the solution is even unique. Dvieju, tekančiu kanale, klampiu skysčiu srauto uždavinys iškyla taikant ivairias skirtingu rušiu paviršiu padengimo technologijas. Atitinkamas matematinis modelis išreiškiamas dvimačiu kraštiniu uždaviniu su laisvu paviršiumi Navje-Stokso lygtims. Straipsnyje nagrinejamas santykinai stacionaraus uždavinio išsprendžiamumas ir pateikiami skaičiavimo rezultatai. Be to parodoma, kad priklausomai nuo sroves parametru kaip ir nuo klampumo ir tankio santykio stacionarus sprendiniai gali neegzistuoti. Su kitais parametrais egzistuoja tiksliai vienas sprendinys.

Energy balances for axisymmetric gravity currents in homogeneous and linearly stratified ambients

2008 ◽  
Vol 616 ◽  
pp. 303-326 ◽  
Author(s):  
MARIUS UNGARISH ◽  
HERBERT E. HUPPERT
Keyword(s):  
High Reynolds Number ◽  
Gravity Current ◽  
Water Model ◽  
Navier Stokes ◽  
Shallow Water Model ◽  
Fluid System ◽  
Dense Fluid ◽  
High Reynolds ◽  
Energy Balances ◽  
Two Fluid

We analyse the exchange of energy for an axisymmetric gravity current, released instantaneously from a lock, propagating over a horizontal boundary at high Reynolds number. The study is relevant to flow in either a wedge or a full circular geometry. Attention is focused on effects due to a linear stratification in the ambient. The investigation uses both a one-layer shallow-water model and Navier–Stokes finite-difference simulations. There is fair agreement between these two approaches for the energy changes of the dense fluid (the current). The stratification enhances the accumulation of potential energy in the ambient and reduces the energy decay (dissipation) of the two-fluid system. The total energy of the axisymmetric current decays considerably faster with distance of propagation than for the two-dimensional counterpart.

Numerical Navier-Stokes Solutions from Gas Kinetic Theory

1994 ◽  
Vol 114 (1) ◽  
pp. 9-17 ◽  
Author(s):  
Kun Xu ◽  
Kevin H. Prendergast
Keyword(s):  
Kinetic Theory ◽  
Navier Stokes ◽  
Gas Kinetic Theory

Nanofluidic transport and formation of nano-emulsions

2008 ◽  
Vol 2 (1) ◽  
Author(s):  
P.A. Chando ◽  
S.S. Ray ◽  
A.L. Yarin
Keyword(s):  
Stokes Equations ◽  
Theoretical Calculations ◽  
Ccd Camera ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Fluid Layers ◽  
Pressure Driven Flow ◽  
Two Fluid

The focus of this research is to study fluidic transport through carbon nanotubes. The nanotubes studied were formed by electrospinning Polycaplrolactone (PCL) nanofibers and then using them as channel templates in colyacrylamide blocks which were carbonized. A pressure driven flow is initiated through the nanochannels and the rate of emulsion formation is recorded with a CCD camera. Theoretical calculations are conducted for nanochannels because in many experiments, the nanochannels studied have two-phase flows, which make direct application of Poiseuille law impossible. The model used for the calculations is a slit with two fluid layers in between. In particular, in many experiments, decane-air system is of interest. The calculations are carried out using the Navier-Stokes equations. The results of the model are used to evaluate experimental volumetric flow rates and find the distribution of air and decane in the nanochannels.

Two-Fluid Flow Between Rotating Annular Disks

1976 ◽  
Vol 98 (2) ◽  
pp. 214-222 ◽  
Author(s):  
J. E. Zweig ◽  
H. J. Sneck
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Small Clearance ◽  
Annular Disks ◽  
Two Fluid

The general hydrodynamic behavior at small clearance Reynolds numbers of two fluids of different density and viscosity occupying the finite annular space between a rotating and stationary disk is explored using a simplified version of the Navier-Stokes equations which retains only the centrifugal force portion of the inertia terms. A criterion for selecting the annular flow fields that are compatible with physical reservoirs is established and then used to determine the conditions under which two-fluid flows in the annulus might be expected for specific fluid combinations.

Generalized Boltzmann kinetic theory for EMMS-based two-fluid model

2016 ◽  
Vol 156 ◽  
pp. 44-55 ◽  
Author(s):  
Bidan Zhao ◽  
Shuyue Li ◽  
Junwu Wang
Keyword(s):  
Kinetic Theory ◽  
Fluid Model ◽  
Two Fluid Model ◽  
Two Fluid

A NEW LATTICE GAS MODEL FOR 1-D SOUND PROPAGATION

1993 ◽  
Vol 01 (04) ◽  
pp. 423-454 ◽  
Author(s):  
YASUSHI SUDO ◽  
VICTOR W. SPARROW
Keyword(s):  
Truncation Error ◽  
Lattice Gas ◽  
Sound Propagation ◽  
Lattice Gas Model ◽  
Wave Number ◽  
General Boundary Condition ◽  
Impedance Boundary ◽  
Fluid Media ◽  
Two Fluid ◽  
The Continuum

A new lattice gas model for sound propagation in one space dimension is proposed. This model has zero truncation error, and the group velocity is independent of wave number as is required from the continuum limit. Conventional finite difference approaches do not have these properties in general. Boundary condition treatments, applicable to the lattice gas formulation, are also given. Both the boundary between two fluid media and an impedance boundary are considered.

scholarly journals Illusions of Elastic Collisions in the Sciences:

2020 ◽  
Vol 5 (1) ◽  
pp. 87-90
Author(s):  
Kent W. Mayhew
Keyword(s):  
Statistical Theory ◽  
Kinetic Theory ◽  
Stokes Equations ◽  
Inelastic Collisions ◽  
Navier Stokes ◽  
Lagrangian Mechanics ◽  
Navier Stokes Equations ◽  
Elastic Collisions

Employing elastic collisions rather than the reality of inelastic collisions simplifies much of the theoretical sciences. The consequences of such simplification is completely ignored/unrealized by the majority, hence must be addressed. At the crux of the problem is arguably the illusion of elastic collisions in kinetic theory, but this extends to other realms of physics including statistical theory, Lagrangian mechanics and the Navier-Stokes equations.

From Kinetic Theory to Navier–Stokes Hydrodynamics

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Kinetic Theory ◽  
Knudsen Number ◽  
Asymptotic Expansions ◽  
Large Scale ◽  
Local Equilibrium ◽  
Navier Stokes ◽  
Fluid Equations ◽  
Scale Limit

This Chapter illustrates the derivation of the macroscopic fluid equations, starting from Boltzmann’s kinetic theory. Two routes are presented, the heuristic derivation based on the enslaving of fast modes to slow ones, and the Hilbert–Chapman–Enskog procedure, based on low-Knudsen number asymptotic expansions. The former is handier but mathematically less rigorous than the latter. Either ways, the assumption of weak departure from local equilibrium proves crucial in recovering hydrodynamics as a large-scale limit of kinetic theory.

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