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    This chapter has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ali, A. Saba, S. Asghar, S. and Khan, D. N. 2017. Transport Phenomenon in a Third-Grade Fluid Over an Oscillating Surface. Journal of Applied Mechanics and Technical Physics, Vol. 58, Issue. 6, p. 990.

    Hu, Xianpeng and Lin, Fanghua 2016. Global Solutions of Two-Dimensional Incompressible Viscoelastic Flows with Discontinuous Initial Data. Communications on Pure and Applied Mathematics, Vol. 69, Issue. 2, p. 372.

    Hu, Xianpeng Lin, Fang-Hua and Liu, Chun 2016. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. p. 1.

  • Print publication year: 2012
  • Online publication date: November 2012

4 - Remarks on complex fluid models


Abstract We review recent global existence and uniqueness results of solutions for models of complex fluids in ℝd. We describe results concerning the Oldroyd-B and related models.


Complex fluids are ubiquitous in nature and manifest a rather large number of different behaviours. There is no single accepted general model for all these, and the presence of a large array of complicated models is an indication of the difficulties encountered at a fundamental level. In this article I will describe some of the mathematical issues. A complex fluid is a mixture between a solvent, which is treated as a normal fluid, and particulate matter in it. The particles are sufficiently many and sufficiently small compared to the characteristic scales of the motions of the solvent, so that one may hope for a description that does not have to resolve the fluid mechanical problem of flow past the particles. The particles themselves are treated in a simplified manner as objects m ∈ M, where M is a finite-degrees-of-freedom configuration space accounting for the salient features of the particles. For instance M can be a subset of ℝN or a more complicated metric space. Models have been devised to deal with microscopic elastic thread-like objects such as polymers (Doi & Edwards, 1998, Öttinger, 1996). The complicated hydrodynamic interactions are simplified using the separation of scales, replacing the many degrees of freedom due to them by a few representative ones.

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