Flory approximant for the fractal dimension of radial viscous finger pattern: transients and asymptotic behaviour

Buragohain, C. ; Bandhu, R. S. ; Bhattacharjee, Jayanta K. ; Chowdhury, Debashish (1995) Flory approximant for the fractal dimension of radial viscous finger pattern: transients and asymptotic behaviour Physical Review E, 51 (1). pp. 407-410. ISSN 1063-651X

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Official URL: http://link.aps.org/doi/10.1103/PhysRevE.51.407

Related URL: http://dx.doi.org/10.1103/PhysRevE.51.407

Abstract

We present a "Flory-type" mean-field theory to calculate the fractal dimension D of the radial viscous finger pattern formed by the less viscous fluid in a Hele-Shaw cell. We predict (a) the relation between the interfacial tension s between the two fluids and the onset of the asymptotic behavior and (b) the variation of the effective fractal dimension with time in the transient regime for a fixed σ.

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