Abstract
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. Vis-coplastic 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 Poi-seuille flow.
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Acknowledgments
This paper has been written to commemorate the 30th anniversary of the Korean Society of Rheology in 2019. We wish the KSR many more years of successful scientific endeavor and are grateful to them for providing the impetus to look into the BMP model, itself 20 years old in 2019. The research has been carried out at the University of British Columbia, supported by Natural Sciences and Engineering Research Council of Canada via their Discovery Grants programme (Grant No. RGPIN-2015-06398). The authors also express their gratitude to the Mexican National Council for Science and Technology (SENER-CONACYT) for financial support (AR).
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This paper is based on an invited lecture presented by the corresponding author at the 30th Anniversary Symposium of the Korean Society of Rheology (The 18th International Symposium on Applied Rheology (ISAR)), held on May 21-24, 2019, Seoul.
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Frigaard, I., Renteria, A. Stability of flows with the BMP model in the yield stress limit. Korea-Aust. Rheol. J. 31, 211–228 (2019). https://doi.org/10.1007/s13367-019-0022-5
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DOI: https://doi.org/10.1007/s13367-019-0022-5