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Viscous fingering with chemical reaction: effect of in-situ production of surfactants

Published online by Cambridge University Press:  30 April 2003

JUAN FERNANDEZ
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106, USA
G. M. HOMSY
Affiliation:
Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106, USA

Abstract

Viscous fingering experiments are performed in a radial Hele-Shaw cell for a liquid–liquid system in the presence of a well-characterized interfacial reaction capable of changing the surface tension on the time scale of the experiments. The reaction is a neutralization of a fatty acid by an alkaline material to form a surfactant, which exhibits first-order kinetics for the surface tension as a function of time. The experiments are carried out for capillary numbers, $Ca$, high enough for the fingering to always be in the fractal regime, and for a wide range of Damköhler numbers, $Da$. The fingers are typically wider in the presence of the chemical reaction than the non-reactive case. We observe two different-behaviours of the reactive fingering patterns. For intermediate values of $Da, 0.5 < Da < 4$, the fractal dimension $d_{f}$ is higher than the classical value measured for the non-reactive fingering patterns and reaches a maximum of about 1.9. For both small ($Da < 0.5$) and high $Da (Da > 4)$, the reactive fingering patterns are similar to the fingers with no reaction: the fractal dimension is found to be the same for both systems. These effects are consistent with the hypothesis that Marangoni stresses are present and produce wider fingers.

Type
Research Article
Copyright
© 2003 Cambridge University Press

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