What is the meaning of :- porous media???

Think of a sponge

what is sponge ??? am not an english native speaker-SORRY!

http://www.creativeglazes.com/tiles/tools/sponge-1.jpg

http://photos1.blogger.com/img/99/1034/640/sponge%20bob.jpg

http://www.mc.maricopa.edu/~gilcrease/jpg/sponge10.jpg

A porous medium is something that allows fluid to flow through it. Media is the plural of medium.

Perfect, do you think gas-liquid is a porous media, what about three-phase such as gas-liquid-oil then!!!!

no, porous media is usually a solid that allows fluid (gas or liquid) to pass 'through' or 'between' it.

Think of water (or oil) seeping through a bed of sand. Or air flowing through a filter.

This is what I want Jim, thank you.

The question now is: how can one develop a mathematical model?

Can we think of the two-phase flow model, two-fluid model, which suffer from too many mathematical problems as we know???? Or what about considering the relative velocity between the two phases to consider a mixture model, forget about the ill-posedness for the meantime.

Any ideas then!!!!!!

Depends on the details of course.

Often with the flow of a fluid in sand (small pores), you can model the flow using Darcy's law, which is essentially

velocity = - (k/rho) grad p. (1)

k is the permeability, which in the stuff I worked with was determined experimentally. Rho is the fluid density of course, and p is the pressure.

This essentially replaces the momentum equations. For incompressible, take the divergence of eq. (1) and you have a continuity statement,

div (v) = - div {(k/rho) [grap p]} = 0 (2)

Looks a lot like a LaPlace equation, doesn't it? The equation gets a bit more complex if you consider compressible flows and/or unsteady flows.

I haven't tried to weave this into an established CFD code - it always seemed to be easier to just code it up. The boundary conditions are usually on the normal component of velocity. So you use eq. (1) to get a pressure gradient on the boundary from those boundary conditions.

For situations where the Darcy assumptions don't work, take a look at a two-phase formulation of the NS equations and set one phase velocity to zero. That might (?) work in a commercial CFD code with a two-phase capability.

Good luck!

could u please described that what u mean two-phase formulation of the NS equations and set one phase velocity to zero. That might (?) work in a commercial CFD code with a two-phase capability.

It'll be hard to write that out on this web site.

You might want to look at Bird, Stewart, and Lightfoot, "Transport Phenomena", a classic chemical engineering text (been around for more than 50 years but periodically updated). Look at the chapters outlined in the right-hand column of table 1.