Minimization of viscous fluid fingering: a variational scheme for optimal flow rates

Conventional viscous fingering flow in radial Hele-Shaw cells employs a constant injection rate, resulting in the emergence of branched interfacial shapes. The search for mechanisms to prevent the development of these bifurcated morphologies is relevant to a number of areas in science and technology...

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Bibliographic Details
Published in:Physical review letters 2012-10, Vol.109 (14), p.144502-144502, Article 144502
Main Authors: Dias, Eduardo O, Alvarez-Lacalle, Enrique, Carvalho, Márcio S, Miranda, José A
Format: Article
Language:English
Subjects:
Cells
chemistry
Cèl·lules
Enginyeria mecànica
Física
Àrees temàtiques de la UPC
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Summary:Conventional viscous fingering flow in radial Hele-Shaw cells employs a constant injection rate, resulting in the emergence of branched interfacial shapes. The search for mechanisms to prevent the development of these bifurcated morphologies is relevant to a number of areas in science and technology. A challenging problem is how best to choose the pumping rate in order to restrain the growth of interfacial amplitudes. We use an analytical variational scheme to look for the precise functional form of such an optimal flow rate. We find it increases linearly with time in a specific manner so that interface disturbances are minimized. Experiments and nonlinear numerical simulations support the effectiveness of this particularly simple, but nontrivial, pattern controlling process.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.109.144502