scholarly journals Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension

2020 ◽  
Vol 236 (2) ◽  
pp. 967-1087 ◽  
Author(s):  
Julian Fischer ◽  
Sebastian Hensel
Keyword(s):  
Surface Tension ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Strong Uniqueness ◽  
Navier Stokes Equation ◽  
Two Fluids

Convection in Pulsed Laser Formed Melts

1980 ◽  
Vol 1 ◽  
Author(s):  
G. E. Possin ◽  
H. G. Parks ◽  
S. W. Chiang
Keyword(s):  
Surface Tension ◽  
Approximate Solution ◽  
Mass Transport ◽  
Stokes Equation ◽  
Pulsed Laser ◽  
Metal Films ◽  
Navier Stokes ◽  
Mixing Times ◽  
Navier Stokes Equation ◽  
Theoretical Considerations

ABSTRACTIn this paper we treat surface tension driven convection effects in pulsed laser formed melts. Mass transport is determined from an approximate solution of the Navier Stokes equation. It is shown that for small laser spot diameters the characteristic mixing times are on the order of 100's of ns. The dependence of the convection mechanism on material and laser parameters is discussed and extended to thin metal films on Si. Experimental results substantiating the theoretical considerations are presented.

An Actively Controlled Micromixer

1999 ◽  
Author(s):  
Marion Volpert ◽  
Carl D. Meinhart ◽  
Igor Mezic ◽  
Mohammed Dahleh
Keyword(s):  
Stokes Equation ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Navier Stokes ◽  
Mixing Efficiency ◽  
Navier Stokes Equation ◽  
Two Fluids ◽  
Flow Through ◽  
Flow Configurations ◽  
Active Mixing

Abstract An active mixing strategy has been developed to enhance mixing of two fluids through a microchannel. Mixing is enhanced when the flow through the main channel of the mixer is perturbed by three sets of secondary flow channels. Numerical solutions of the flow through the mixer are calculated by simulating the full Navier-Stokes equation, the Stokes equation, and a simple analytical model based upon the superposition of elementary velocity profiles. The analytical model agrees qualitatively with Navier-Stokes and Stokes solutions for Reynolds numbers, Re = 5. A mixing coefficient is developed to quantitatively evaluate mixing efficiency for various flow configurations. The results indicate enhanced mixing for two possible flow configurations.

Three-Dimensional Calculation of Bubble Growth and Drop Ejection in a Bubble Jet Printer

1992 ◽  
Vol 114 (4) ◽  
pp. 638-641 ◽  
Author(s):  
A. Asai
Keyword(s):  
Experimental Data ◽  
Surface Tension ◽  
Stokes Equation ◽  
Bubble Growth ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Bubble Behavior ◽  
Navier Stokes Equation ◽  
Bubble Pressure ◽  
First Time

The three-dimensional Navier-Stokes equation for the motion of ink both inside and outside the nozzle of a bubble jet printer is numerically solved, for the first time, to predict the bubble behavior and the drop ejection. The results of calculation for three types of ink agreed well with experimental data. The effect of initial bubble pressure, viscosity and surface tension on the volume and the velocity of the drop is numerically investigated. The three-dimensional calculation is very useful to the design of bubble jet printers because it saves a lot of time and cost to make and evaluate prototypes.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

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