Fluid flow through porous and nanoporous media within the prisme of extended thermodynamics: emphasis on the notion of permeability

Abstract

The study of fluid flows through porous and nanoporous media is important in many natural and industrial situations. One relevant parameter is the permeability of the porous material. An original approach is proposed within the prism of Extended Irreversible Thermodynamics. More specifically, the system fluid-solid matrix is modelled by a two-component mixture and the permeability is obtained after calculating the seepage velocity and comparison with Darcy's law. An explicit analytical expression of the permeability coefficient is proposed and discussed. The analysis is restricted to one-dimensional situations and incompressible fluids. The validity of the model is checked by calculating the flow rate through cylindrical nano pores: comparison with experimental data shows a good agreement.

Universal relation between the density and the viscosity of dispersions of nanoparticles and stabilized emulsions

“…If, furthermore, the densities of the nanoparticles and the fluid are close to one another, i.e. 𝜌 ≈ 𝜌 ≈ 𝜌, Einstein's equation for the viscosity of dispersion is found back a Reported value for alkalinated water in [32] The values for ℓ need some comments. For Al2O3 -water nanofluids, nano-ultrasonics [45] and molecular dynamics [62] studies show that bulk values for the water density and viscosity are measured at a distance around 1 nm from the Al2O3 surface.…”

“…For later purposes, we find it more convenient to work with the fluid mass flux, 𝑱 . As 𝑱 + 𝑱 = 0, the mass flux evolution can be written as [29][30][31][32] 𝜏𝜕 𝑱 + 𝑱 = −𝜌𝐷∇𝑐 + ℓ ∇ 𝑱 = 𝜌𝐷∇c + ℓ ∇ 𝑱 ,…”

On the chemical potential of nanoparticle dispersion

“…The symbol 𝜒 can be found by considering that in the case of equilibrium diffusion, Eq. ( 36) should reduce to Fick's law, 𝑱 = −𝜌𝐷∇(1 − c), with 𝐷 the self-diffusion coefficient [8,29]. In this case, the chemical potential gradient can be defined as…”

“…We start with discussing the standard form for the free energy of mixing. As the density plays a role in not only porous flow but is also accounted for in some studies dealing with thermodynamics of dispersions [4,[29][30][31][32], we propose a development for the free energy of mixing that takes into account density differences between the nanoparticles and the fluid or matrix. Subsequently, we apply the principles of our model in order to propose the free energy of dispersion.…”

Numerical Investigation on Heat-Transfer and Hydromechanical Performance inside Contaminant-Insensitive Sublimators under a Vacuum Environment for Spacecraft Applications

“…When water flows in the porous substrate, the Reynolds number is less than 10 and it is laminar flow. Therefore, the relationship between velocity and pressure and viscous force is expressed by darcy's law, where the permeability identified by κ is a function of the porosity and the pore size [51,52].…”