Term information
The Brinkman equation is a "derrivation of Darcy's Law". "Darcy's Law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments[1] on the flow of water through beds of sand. It also forms the scientific basis of fluid permeability used in the earth sciences." ""the Brinkman term ... is used to account for transitional flow between boundaries (introduced by Brinkman in 1947), \beta \nabla^{2}q +q =-K \nabla , where is an effective viscosity term. This correction term accounts for flow through medium where the grains of the media are porous themselves, but is difficult to use, and is typically neglected." source: http://en.wikipedia.org/wiki/Darcy%27s_law
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <mrow> <mrow> <mi>β</mi> <mo>⁢</mo> <msup> <mo>∇</mo> <mn>2</mn> </msup> <mo>⁢</mo> <mi>q</mi> </mrow> <mo>+</mo> <mi>q</mi> </mrow> <mo>=</mo> <mrow> <mo>-</mo> <mrow> <mi>K</mi> <mo>⁢</mo> <mo>∇</mo> </mrow> </mrow> </mrow> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <mi>β</mi> <msup> <mo>∇</mo> <mn>2</mn> </msup> <mi>q</mi> <mo>+</mo> <mi>q</mi> <mo>=</mo> <mo>-</mo> <mi>K</mi> <mo>∇</mo> </mrow> <annotation encoding="SnuggleTeX">\[ \beta \nabla^{2}q +q =-K \nabla \]</annotation> </semantics> </math>