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The extensional flow of a thin sheet of incompressible, transversely isotropic fluid

Published online by Cambridge University Press:  01 June 2008

J. EDWARD F. GREEN  and
AVNER FRIEDMAN
J. EDWARD F. GREEN
Affiliation:
Mathematical Biosciences Institute, The Ohio State University, Columbus, Ohio, 43210USA email: [email protected], [email protected]
AVNER FRIEDMAN
Affiliation:
Mathematical Biosciences Institute, The Ohio State University, Columbus, Ohio, 43210USA email: [email protected], [email protected]
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Abstract

Motivated by the aim of modelling the mechanical behaviour of biological gels (such as collagen gels) which have a fibrous microstructure, we consider the extensional flow of a thin two-dimensional film of incompressible, transversely isotropic viscous fluid. Neglecting inertia, and the effects of gravity and surface tension, leading-order equations are derived from a perturbation expansion of the full flow problem in powers of the (small) inverse aspect ratio. The existence and uniqueness of the solution of the reduced system of equations for small times is then proven. Special cases, in which the solution may be determined explicitly, are considered and we discuss the physical interpretation of the results.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 19 , Issue 3 , June 2008 , pp. 225 - 257
Copyright
Copyright © Cambridge University Press 2008

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