Hele-Shaw Flows: Historical Overview
Hele-Shaw Flows: Historical Overview
Hele-Shaw Flows: Historical Overview
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Darcy’s Low<br />
• 1855 experimental works by Darcy.<br />
• Mathematically proved in 1940 (M. King Hubbert),<br />
1972 (J. Bear), 1978 (Ernan McMullin).<br />
• Averaging across random structures we get<br />
where k is permeability.<br />
V = − k<br />
µ ∇p,<br />
• Compare with the <strong>Hele</strong>-<strong>Shaw</strong> equation:<br />
V = − h2<br />
12µ ∇p.<br />
BIRS, Canada, July 2007 – p. 57
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