Well-posedness and ill-posedness of single-phase models for suspensions

Barker, T., Gray, J. M. N. T., Schaeffer, D. and Shearer, M. 2023. Well-posedness and ill-posedness of single-phase models for suspensions. Journal of Fluid Mechanics 954 , A17. 10.1017/jfm.2022.1004

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Abstract

Classical theories for suspensions have been formulated by starting from the Navier–Stokes equations describing pure liquid flow and then introducing additional dependencies to account for the presence of suspended particles. These models are often accurate for low particle concentrations but have lacked a convincing description of the frictional interactions of particles, which are important at larger solid volume fractions. The μ(J),Φ(J) rheology, which draws a direct analogy between suspension flow and dry granular flow, is a recent theory that addresses this issue, but is shown here to be dynamically ill-posed for large solid volume fractions. An alternative well-posed theory is introduced that includes additional dependence on the particle-phase dilation and compression. The new theory, denoted vCIDR, is tested numerically to show grid convergence for problems in which the μ(J),Φ(J) rheology instead suffers from catastrophic blow-up. A further well-posed extension provides a framework for handling the transition between viscous and inertial flows.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Cambridge University Press
ISSN:	0022-1120
Date of First Compliant Deposit:	6 December 2022
Date of Acceptance:	23 November 2022
Last Modified:	05 Jun 2023 12:00
URI:	https://orca.cardiff.ac.uk/id/eprint/154681

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