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MS 1 MINISYMPOSIUM: ADVANCED IMAGING FOR INDUSTRIAL APPLICATION Read chapter Read first chapter

2016 | Supplement | Chapter

Fiber Suspension Flows: Simulations and Existence Results

Author : Uldis Strautins

Published in: Progress in Industrial Mathematics at ECMI 2014

Publisher: Springer International Publishing

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Abstract

Main result of this article is demonstrating the weak global in time well posedness result for the equations governing fiber suspension flows for sufficiently small initial data under mild assumptions about the nonlinear equation for fiber orientation dynamics and the constitutive law, thus extending the previous local in time results. The required estimate of growth of the H 2 norm is granted if the L ∞ norm of fiber orientation state variables remains bounded. This is the case for fiber orientation tensors.

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previous chapter Electro-Manipulation of Droplets for Microfluidic Applications
next chapter Global Existence of Weak Solutions to an Angiogenesis Model
Literature
1.
Chung, D.H., Kwon, T.H: Fiber orientation in the processing of polymer composites. Korea-Aust. Rheol. J. 14, 175–188 (2002)
2.
Galdi, G.P., Reddy, D.B.: Well-posedness of the problem of fiber suspension flows. J. Non-Newtonian Fluid Mech. 83, 205–230 (1999)CrossRefMATH
3.
Guillope, C., Saut, J.C.: Existence results for the flow of viscoelastic fluids with a differential constitutive law. Nonlinear Anal. Theory Methods Appl. 15, 849–869 (1990)MathSciNetCrossRefMATH
4.
Munganga, J.M.W.: Existence and stability of solutions for steady flows of fiber suspension flows. J. Math. Fluid Mech. 15, 197–214 (2013)MathSciNetCrossRefMATH
5.
Munganga, J.M.W., Reddy, D.B.: Local and global existence of solutions to the equations for fibre suspension flows. Math. Models Methods Appl. Sci. 12, 1177–1203 (2002)MathSciNetCrossRefMATH
6.
Strautins, U.: Flow-driven orientation dynamics in two classes of fibre suspensions. Ph.D. thesis, TU Kaiserslautern (2008)
Metadata
Title
Fiber Suspension Flows: Simulations and Existence Results
Author
Uldis Strautins
Copyright Year
2016
Book
Progress in Industrial Mathematics at ECMI 2014

Print ISBN: 978-3-319-23412-0

Electronic ISBN: 978-3-319-23413-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-23413-7_150

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