화학공학소재연구정보센터
홈 로그인 로그아웃 연락처 사이트맵
Korea-Australia Rheology Journal, Vol.31, No.4, 211-228, November, 2019
DOI10.1007/s13367-019-0022-5  Export Citation
Stability of flows with the BMP model in the yield stress limit
Ian Frigaard†, and Alondra Renteria1
  • Departments of Mathematics and Mechanical Engineering, University of British Columbia, Vancouver V6T 1Z2, Canada
  • 1Department of Mechanical Engineering, University of British Columbia, Vancouver V6T 1Z4, Canada
E-mail:
Common features of complex fluids include yield stress, thixotropy and elasticity. A comprehensive constitutive model attempts to effectively predict flow responses dominated by such characteristics. Nevertheless, when constructing a constitutive model that deals with yield stress fluids one must try to preserve the fundamental characteristics of a yield stress. This paper explores the static and energy stability of a classic viscoplastic model when elasticity or thixotropy are introduced. We exemplify this analysis using the Bautista-Manero-Puig (BMP) model in the yield stress limit. This model has the advantages of a small number of parameters, a physically intuitive kinetic equation, and it has been widely used to represent fluids with time-dependent rheology. We analyze stability of the BMP model for different limiting cases. Viscoplastic flows (VP), where we remove the elasticity and thixotropy behaviour, are shown to respond qualitatively in an analogous way to a simple yield stress fluid, e.g. Bingham, Casson. Thixo-visco-plastic flows (TVP), identified by having an elastic time scale much faster than the thixotropic and viscous timescales, preserve the notion of static and energy stability but with bounds now dependent on the stress and no longer with finite time decay. Finally, elasto-visco-plastic flows (EVP), where the thixotropic evolution is faster than the elastic, have a static stability limit perturbed linearly by the Weissenberg number. Numerically solved examples of each of flow regime are given for stopping and starting flow, based on the plane Poiseuille flow.
Keywords:viscoelastoplasticity;thixotropy;yield stress fluids;energy stability;BMP model
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