On the fractal dimension of non-Newtonian Hele-Shaw flow subject to Saffman-Taylor instability
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917834197565440 |
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| author | Adriazola, J. Gu, B. Cummings, L. Kondic, L. |
| author_facet | Adriazola, J. Gu, B. Cummings, L. Kondic, L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the fractal dimension of non-Newtonian Hele-Shaw flow subject to Saffman-Taylor instability Adriazola, J. Gu, B. Cummings, L. Kondic, L. Fluid Dynamics Soft Condensed Matter Computational Physics 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. |
| title | On the fractal dimension of non-Newtonian Hele-Shaw flow subject to Saffman-Taylor instability |
| topic | Fluid Dynamics Soft Condensed Matter Computational Physics |
| url | https://arxiv.org/abs/2407.06476 |