Analytical solutions of compacting flow past a sphere

Rudge, John F. (2014) Analytical solutions of compacting flow past a sphere. Journal of Fluid Mechanics, 746. pp. 466-497. ISSN 0022-1120, ESSN: 1469-7645 DOI https://doi.org/10.1017/jfm.2014.109

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Abstract

A series of analytical solutions are presented for viscous compacting flow past a rigid impermeable sphere. The sphere is surrounded by a two-phase medium consisting of a viscously deformable solid matrix skeleton through which a low-viscosity liquid melt can percolate. The flow of the two-phase medium is described by McKenzie’s compaction equations, which combine Darcy flow of the liquid melt with Stokes flow of the solid matrix. The analytical solutions are found using an extension of the Papkovich–Neuber technique for Stokes flow. Solutions are presented for the three components of linear flow past a sphere: translation, rotation and straining flow. Faxén laws for the force, torque and stresslet on a rigid sphere in an arbitrary compacting flow are derived. The analytical solutions provide instantaneous solutions to the compaction equations in a uniform medium, but can also be used to numerically calculate an approximate evolution of the porosity over time whilst the porosity variations remain small. These solutions will be useful for interpreting the results of deformation experiments on partially molten rocks.

Item Type:	Article
Uncontrolled Keywords:	2014AREP; IA68;
Subjects:	02 - Geodynamics, Geophysics and Tectonics 05 - Petrology - Igneous, Metamorphic and Volcanic Studies
Divisions:	02 - Geodynamics, Geophysics and Tectonics 05 - Petrology - Igneous, Metamorphic and Volcanic Studies 08 - Green Open Access
Journal or Publication Title:	Journal of Fluid Mechanics
Volume:	746
Page Range:	pp. 466-497
Identification Number:	https://doi.org/10.1017/jfm.2014.109
Depositing User:	Sarah Humbert
Date Deposited:	19 Sep 2014 16:19
Last Modified:	02 Nov 2014 00:46
URI:	http://eprints.esc.cam.ac.uk/id/eprint/3125

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