Yield limit analysis of particle motion in a yield-stress fluid

Emad Chaparian, Ian A. Frigaard

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


A theoretical and numerical study of yield-stress fluid creeping flow about a particle is presented. Yield-stress fluids can hold rigid particles statically buoyant if the yield stress is large enough. In addressing sedimentation of rigid particles in viscoplastic fluids, we should know this critical 'yield number' beyond which there is no motion. As we get close to this limit, the role of viscosity becomes negligible in comparison to the plastic contribution in the leading order, since we are approaching the zero-shear-rate limit. Admissible stress fields in this limit can be found by using the characteristics of the governing equations of perfect plasticity (i.e.The sliplines). This approach yields a lower bound of the critical plastic drag force or equivalently the critical yield number. Admissible velocity fields also can be postulated to calculate the upper bound. This analysis methodology is examined for three families of particle shapes (ellipse, rectangle and diamond) over a wide range of aspect ratios. Numerical experiments of either resistance or mobility problems in a viscoplastic fluid validate the predictions of slipline theory and reveal interesting aspects of the flow in the yield limit (e.g. viscoplastic boundary layers). We also investigate in detail the cases of high and low aspect ratio of the particles.

Original languageEnglish
Pages (from-to)311-351
Number of pages41
JournalJournal of Fluid Mechanics
Early online date24 Apr 2017
Publication statusPublished - 25 May 2017


  • non-Newtonian flows
  • particle/fluid flow
  • plastic materials


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