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arXiv · 2311.12518

Homogeneous incompressible Bingham viscoplastic as a limit of bi-viscosity fluids

Wassim Aboussi·Fayssal Benkhaldoun·Ahmed Aberqi·Abdallah Bradji·Jaouad Bennouna
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Abstract

In this paper, the existence of a weak solution for homogeneous incompressible Bingham fluid is investigated. The rheology of such a fluid is defined by a yield stress $\tau_y$ and a discontinuous stress-strain law. This non-Newtonian fluid behaves like a solid at low stresses and like a non-linear fluid above the yield stress. In this work we propose to build a weak solution for Navier stokes Bingham equations using a bi-viscosity fluid as an approximation, in particular, we proved that the bi-viscosity tensor converges weakly to the Bingham tensor.

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Wassim Aboussi, Fayssal Benkhaldoun, Ahmed Aberqi, Abdallah Bradji, Jaouad Bennouna. 2023-11-21. Homogeneous incompressible Bingham viscoplastic as a limit of bi-viscosity fluids. https://doi.org/10.1007/s41808-023-00221-z

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