Fluid dynamics for the sepiolite

Question

I would like to know some about the physics of an interesting material, the sepiolite. I mean the material from the Wikipedia article Sepiolite where are explained the general and identification characteristics in the right column, and its applications. The motivation of this question is that I'm interested about the more important physical facts that one can to show for this material (the industry provides the sepiolite in several forms, for example as small stones/granules or as dust), for which if I'm right are arising new applications in the industry due to its high porosity.

Question. In the past I've studied, as student, the Euler equations in fluid dynamics and I know basics about Navier-Stokes equations. I would like to kow what should be a simple model for how sepiolite absorbs a liquid, and that liquid does not flow out of this material again. Many thanks.

I'm asking for a simple model of how do it the sepiolite (about why this is an absorbent), I don't know if it is required to use the equations of fluid dynamics in your explanation. If it is in the literature feel free to refer the literature, answering my question as a reference request and I try to search and read it from the literature.

Answer 1

Interesting question. According to wiki Sepiolite has porous nature, so it keeps liquid inside similarly like dish-wash sponge. Water has many "tiny obstacles" and resistance inside, so you need to apply pressure gradient, to induce a flow.

In porous materials liquid flow is descibed by a Darcy's law :

$$ Q=-{\frac {kA}{\mu }} \,\nabla p $$

Where $Q$ is volumetric flow rate, $k$ - permeability of porous medium, $\mu$ - fluid viscosity, $A$ - cross-sectional area of porous medium and finally $\nabla p$ is pressure gradient inside porous material. This law may be derived from ordinal Navier–Stokes equations. You can check this derivation elsewere - there are plenty of them.

So when you puff at pipe made by this porous material, you induce pressure gradient and thus tobacco tar begins to flow into material. Hypothetically if you would reverse pressure gradient - would start to swell into that pipe - tar would start to go back into pipe fireplace.