Derivation of the Conventional and a Generalized Form of Darcy’s Law from the Langevin Equation

2021 ◽  
Author(s):  
Dag Chun Standnes
Keyword(s):  
Langevin Equation ◽  
Darcy’S Law ◽  
Darcy's Law

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

Error of Darcy's law for serpentine flow fields: Dimensional analysis

2019 ◽  
Vol 412 ◽  
pp. 391-397 ◽  
Author(s):  
Xuyang Zhang ◽  
Xu Zhang ◽  
Hidetaka Taira ◽  
Hongtan Liu
Keyword(s):  
Dimensional Analysis ◽  
Darcy’S Law ◽  
Flow Fields ◽  
Darcy's Law
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