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Rheology of Complex Fluids pp 67–84Cite as

Mechanics of Liquid Mixtures

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Abstract

A brief introduction is provided for modeling the response of mixtures under the assumption that the constituents can be modeled as a continuum and that the constituents co-occupy the region of the mixture in a homogenized sense. The constituents of the mixture can undergo chemical reactions and there can be interconversion between the constituents. Balance laws are provided for the constituents of the mixture that allow for the chemical reactions as well as the numerous other interaction mechanisms between the constituents. After developing the general framework, the theory will be used to develop a model for the flow of a mixture of fluids.

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Notes

  1. 1.

    The word “atop” is inappropriate but provides some basis for understanding the co-occupancy of the constituents. Each of the particles simultaneously co-exist at the same point in the mixture. Of course, there are serious physical problems with such an assumption, but this is far less worrisome from a philosophical stand point of existence than the notion of a “point”, an entity with no dimension! We seem to have no problem whatsoever with coming to grips with this unfathomable concept. Since each particle belonging to a constituent has no dimension allowing them to co-occupy should not lead to any unsurmountable difficulty.

  2. 2.

    Unless a summation symbol is explicitly used, repeated indices do not mean summation over that index.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Texas A&M University, College Station, Texas, 77845, USA

    Kumbakonam Ramamani Rajagopal

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  1. Kumbakonam Ramamani Rajagopal
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Correspondence to Kumbakonam Ramamani Rajagopal .

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Editors and Affiliations

  1. Indian Institute of Technology Madras, Chennai, 600036, India

    J. Murali Krishnan

  2. Dept. Chemical Engineering, Indian Institute of Technology, I.I.T. P.O., Chennai, 600 036, India

    Abhijit P. Deshpande

  3. Dept. Physics, Indian Institute of Technology, Sardar Patel Rd., Chennai, 600036, India

    P. B. Sunil Kumar

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Rajagopal, K.R. (2010). Mechanics of Liquid Mixtures. In: Krishnan, J., Deshpande, A., Kumar, P. (eds) Rheology of Complex Fluids. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6494-6_3

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  • DOI: https://doi.org/10.1007/978-1-4419-6494-6_3

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