Evidence for a universal saturation profile for radial viscous fingers

Complex fingering patterns develop when a low viscosity fluid is injected from a point source into the narrow space between two parallel plates initially saturated with a more viscous, immiscible fluid. We combine historical and new experiments with (a) a constant injection rate; (b) a constant sour...

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Bibliographic Details
Published in:Scientific reports 2019-05, Vol.9 (1), p.7780-7780, Article 7780
Main Authors: Beeson-Jones, Tim H., Woods, Andrew W.
Format: Article
Language:English
Subjects:
639/766/189
704/242
Fractals
Humanities and Social Sciences
Injection
multidisciplinary
Saturation
Science
Science (multidisciplinary)
Viscosity
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Summary:Complex fingering patterns develop when a low viscosity fluid is injected from a point source into the narrow space between two parallel plates initially saturated with a more viscous, immiscible fluid. We combine historical and new experiments with (a) a constant injection rate; (b) a constant source pressure; and (c) a linearly increasing injection rate, together with numerical simulations based on a model of diffusion limited aggregation (DLA), to show that for viscosity ratios in the range 300–10,000, (i) the finger pattern has a fractal dimension of approximately 1.7 and (ii) the azimuthally-averaged fraction of the area occupied by the fingers, S ( r , t ), is organised into three regions: an inner region of fixed radius, r  
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-019-43728-z