Abstract
Nonlinear hydrodynamic equations for non-Newtonian fluids are discussed. We start from the recently derived hydrodynamic-like nonlinear description of a slowly relaxing orientational order parameter tensor. The reversible quadratic nonlinearities in this tensor’s dynamics are material dependent due to the generalized nonlinear flow alignment effect that comes in addition to the material independent corotational convected derivative. In the entropy production these terms are balanced by linear and nonlinear orientational-elastic contributions to the stress tensor. These can be used to get a nonlinear dynamic equation for the stress tensor (sometimes called constitutive equation) in terms of a power series in the variables. A comparison with existing phenomenological models is given. In particular we discuss how these ad-hoc models fit into the hydrodynamic description and where the various non-Newtonian contributions are coming from. We also discuss the connection to the hydrodynamic-like description of non-Newtonian effects that employs a relaxing strain tensor.
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Pleiner, H., Liu, M., Brand, H.R. (2005). Non-Newtonian Constitutive Equations Using the Orientational Order Parameter. In: Calderer, MC.T., Terentjev, E.M. (eds) Modeling of Soft Matter. The IMA Volumes in Mathematics and its Applications, vol 141. Springer, New York, NY. https://doi.org/10.1007/0-387-32153-5_4
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DOI: https://doi.org/10.1007/0-387-32153-5_4
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