Stabilities in plane Poiseuille flow of Herschel–Bulkley fluid

R. Liu*, Zijing Ding, K. X. Hu

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)


Linear stability in plane Poiseuille flow of a yield-stress shear-thinning fluid is considered. The rheological behavior of the fluid is described by the Herschel–Bulkley model. The effect of shear-thinning on the stability is investigated using the energy method and the nonmodal stability theory. The result of the energy method shows that with the increase of shear thinning, the critical energy Reynolds number decreases for both the streamwise and spanwise disturbances. For the nonmodal stability, we focus on the response to initial conditions by examining the energy growth function G(t). For a Herschel–Bulkley fluid, it is found that there can be a rather large transient growth even though the linear operator of the plan Poiseuille flow has no unstable eigenvalue. The results show that the shear thinning plays an important role in determining the energy growth rate and the structure of the disturbance with optimal transient growth.

Original languageEnglish
Pages (from-to)132-144
Number of pages13
JournalJournal of Non-Newtonian Fluid Mechanics
Early online date11 Dec 2017
Publication statusPublished - 1 Jan 2018


  • Herschel–Bulkley fluid
  • Nonmodal stability
  • Plan Poiseuille flow


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