The key highlights and insights from the content are:
The content analyzes the flow of a thin layer of electrically conducting fluid, such as saltwater or liquid mercury, between two closely spaced parallel plates in a Hele-Shaw geometry. An external uniform magnetic field is applied normal to the plates, and electrical current is driven between conducting probes immersed in the fluid layer.
The authors first elucidate the physical mechanism by which the Lorentz force, arising from the interaction of the electrical current and magnetic field, can induce fluid flow and circulation. This overcomes the inherent limitation of zero circulation in pressure-driven Hele-Shaw flows.
The authors present mathematical solutions for the fluid flow in a class of canonical multiply-connected geometries, using the framework of the prime function developed by Crowdy (2020). In doubly-connected geometries, the solutions can be written explicitly as series and are thus exact.
For more general geometries where exact solutions are not possible, the authors demonstrate how recently developed fast numerical methods based on series solutions can be used to accurately determine the flow field.
The authors validate their theoretical results by comparing to a new experiment involving two conducting cylinders in a Hele-Shaw cell, showing good agreement between the theoretical predictions and the observed flow patterns.
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by Kyle McKee klokken arxiv.org 04-09-2024
https://arxiv.org/pdf/2404.04840.pdfDypere Spørsmål