scholarly journals The breakdown of Darcy's law in a soft porous material

Soft Matter ◽  
2020 ◽  
Vol 16 (4) ◽  
pp. 939-944 ◽  
Author(s):  
Marco Edoardo Rosti ◽  
Satyajit Pramanik ◽  
Luca Brandt ◽  
Dhrubaditya Mitra
Keyword(s):  
Shear Modulus ◽  
Porous Material ◽  
Linear Function ◽  
Pressure Difference ◽  
Darcy’S Law ◽  
Universal Function ◽  
Darcy's Law ◽  
Poroelastic Material

We show that the flux through a poroelastic material is a super-linear function of the pressure-difference. The permeability is a universal function of the ratio of the pressure-difference over the shear modulus, proportional to the cube of porosity.

scholarly journals Variational principles of liquid–porous material interactions with applications to approximate solutions and finite-element modelling

2021 ◽  
Vol 477 (2248) ◽  
Author(s):  
Jing Tang Xing ◽  
Hongling Qin
Keyword(s):  
Finite Element ◽  
Porous Material ◽  
Variational Principles ◽  
Darcy’S Law ◽  
Approximate Solutions ◽  
Coupling Factor ◽  
Darcy's Law ◽  
Frequency Separation ◽  
Force Frequency ◽  
Local Resonance

For liquid–porous material interactions (LPMI), three variational principles are developed in Biot's theory of porous materials in association with Darcy's Law. First one takes solid acceleration, and fluid velocity, acceleration, pressure with time derivative as five variables, while second and third, respectively, have three and two variables when Darcy's Law used as variational constraint reducing variables. These principles provide a means to derive approximate solutions and finite-element (FE) models for LPMI. Each LPMI element includes fluid and solid together with it being no longer necessary to distinguish fluid domain from solid. Examples illustrate applications to establish FE model for numerical solutions of LPMI. Solution of a one-dimensional problem reveals that LPMI behaves a coupled-frequency separation measured by a defined-coupling factor. Dynamic response explores coupled-dynamic absorber mechanism in LPMI system, from which it is found that the external force at fluid does not contribute to fluid response but fully absorbed by solid local resonance if the force frequency equals the solid natural frequency; while in the reverse case when the force frequency equals the fluid one, the force at solid does not produce the solid response but fully absorbed by fluid local resonance. New findings with defined LPMI coupling factor provide guidelines for designing LPMI system with expected dynamic behaviour meeting engineering requirements.

scholarly journals An extension of Darcy’s law incorporating dynamic length scales

2019 ◽  
Vol 129 ◽  
pp. 70-79 ◽  
Author(s):  
Yuhang Wang ◽  
Saman A. Aryana ◽  
Myron B. Allen
Keyword(s):  
Darcy’S Law ◽  
Darcy's Law ◽  
Length Scales ◽  
Dynamic Length

scholarly journals The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

2001 ◽  
Vol 19 (4) ◽  
pp. 177-188
Author(s):  
B Eitzinger ◽  
G Ederer
Keyword(s):  
Pressure Drop ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Constitutive Equations ◽  
Darcy’S Law ◽  
Stationary Flow ◽  
Darcy's Law ◽  
Nonlinear Behaviour ◽  
Cigarette Paper ◽  
Drop Flow

AbstractThis study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.

scholarly journals Simulation of Water Filtration in Porous Zone Based on Darcy's Law

2013 ◽  
Vol 36 ◽  
pp. 163-168
Author(s):  
Mohammed Amine Kendouci ◽  
Benali Kharroubi ◽  
Rachid Khelfaoui ◽  
Ali Bendida ◽  
Brahim Dennai ◽  
...  
Keyword(s):  
Darcy’S Law ◽  
Darcy's Law ◽  
Water Filtration ◽  
Porous Zone
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