Abstract
In the microstructure approach, a relevant model for the microstructure is postulated, and the consequences are then explored at the macrostructural level, with appropriate averages being taken to smear out the details of the microstructures. The advantage of this is that the resulting constitutive equation is expected to be relevant to the material concerned; and if a particular phenomenon is not well modelled, the microstructural model can be revisited and the relevant physics put in place. This iterative model-building process is always to be preferred over the continuum approach. In this chapter, we will concentrate on the constitutive modelling of dilute polymer solutions.
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References
P. Langevin (1872–1940) introduced the stochastic DE (7.20) in 1908, and showed that the particle obeys the same diffusion equation as described by Einstein (1905).
A.D. Fokker derived the diffusion equation for a Brownian particle in velocity space in 1914. The general case was considered by M. Planck (1858–1947) in 1917.
The general solution to the random walk problem in one dimension was obtained by M. von Smoluchowski in 1906.
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© 2002 Springer-Verlag Berlin Heidelberg
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Phan-Thien, N. (2002). Polymer Solutions. In: Understanding Viscoelasticity. Advanced Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10704-1_7
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DOI: https://doi.org/10.1007/978-3-662-10704-1_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07779-1
Online ISBN: 978-3-662-10704-1
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