Fractal dimension of non-Newtonian Hele-Shaw flow subject to Saffman-Taylor instability

We introduce a discrete numerical method based on the diffusion-limited aggregation (DLA) approach to simulate two-fluid Hele-Shaw flow subject to the Saffman-Taylor interfacial instability, in the case where the displaced fluid is non-Newtonian. Focusing on fluids for which the most relevant non-Ne...

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Bibliographic Details
Published inPhysical review. E Vol. 110; no. 6-2; p. 065107
Main Authors Adriazola, J, Gu, B, Cummings, L J, Kondic, L
Format Journal Article
LanguageEnglish
Published United States 01.12.2024
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Summary:We introduce a discrete numerical method based on the diffusion-limited aggregation (DLA) approach to simulate two-fluid Hele-Shaw flow subject to the Saffman-Taylor interfacial instability, in the case where the displaced fluid is non-Newtonian. Focusing on fluids for which the most relevant non-Newtonian aspect of the thin-gap flow is shear thinning, we introduce a history-dependent aspect into the algorithm, modeling shear-rate-dependent fluid viscosity. The main finding is that the morphology of the emerging patterns, characterized by the fractal dimension, is modified in a nontrivial manner by the shear-thinning nature of the displaced fluid. In particular, we consistently find that shear thinning leads to the formation of patterns characterized by a smaller fractal dimension, compared to the corresponding Newtonian fluid.
ISSN:2470-0053
DOI:10.1103/PhysRevE.110.065107