Enabling microscopic simulators to perform system-level analysis of viscoelastic flows

State-of-the-art methods for simulating viscoelastic flows couple the conservation equations for mass and momentum with a model from kinetic theory that describes the microstructural state of the polymer. Introduction of appropriate numerical discretization and boundary conditions for these equations leads to a hybrid simulation for studying the dynamic behavior of polymeric liquids in complex geometries. This approach represents a rare example of a successful multiscale solution of a physical problem, as it allows investigation of arbitrary models of kinetic theory. The simulations, however, are not amenable to standard numerical techniques for system-level stability, bifurcation, and control analysis as this requires closed form equations. These simulation either use stochastic descriptions for the polymer microstructure that cannot be reduced to closed form, or involve equations for the evolution of a distribution of polymer conformations, which can only be written in closed form by invoking mathematical closure approximations that can have a significant qualitative impact on the predictive ability of these simulations. The focus of this thesis was to develop a novel numerical method that can enable hybrid simulations to perform system-level analysis of polymeric flows. This numerical approach has been applied directly to kinetic theory models and hybrid simulations to obtain stationary states and associated bifurcations and stability information. The method is general in its applicability in that it treats kinetic theory models and hybrid simulations as black boxes that are then used to obtain system-level information without any modification. The methods developed here are illustrated in a variety of problems.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Chemical Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Anwar, Zubair

Advisor dc:contributor.advisor

• Robert C. Armstrong.

• Chemical Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/42943

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/42943