Nematic liquids in weak capillary Poiseuille flow: structure scaling laws and effective conductivity implications
Authors
Zhou, Hong
Forest, M. G.
Subjects
Liquid crystal (nematic) polymers
asymptotic expansions
paratial differential equations
capillary
Poiseuille flow
conductivity
asymptotic expansions
paratial differential equations
capillary
Poiseuille flow
conductivity
Advisors
Date of Issue
2007
Date
Publisher
Language
Abstract
We study the scaling properties of heterogeneities in nematic (liquid crystal) polymers that are generated by pressure-driven, capillary Poiseuille flow. These studies complement our earlier drag-driven structure simulations and analyses. We use the mesoscopic Doi-Marrucci-Greco model, which incorporates excluded-volume interactions of the rod-like particle ensemble, distortional elasticity of the dispersion, and hydrodynamic feedback through orientation dependent viscoelestic stresses. The geometry likewise introduces anchoring conditions on the nano-rods which touch the solid boundaries. We first derive flow-orientation steady-state structures for three different anchoring conditions, by asymptotic analysis in the limit of weak pressure gradient. These closed-form expressions yield scaling laws, which predict how lengthscales of distortions in the flow and orientational distributions vary with strength of the excluded volume potential, molecule geometry, and distortional elasticity constants. Next, the asymptotic structures are verified by direct numerical simulations, which provide a high level benchmark on the numerical code and algorithm. Finally, we calculate the effective (thermal or electrical) conductivity tensor of the composite films, and determine scaling behavior of the effective property enhancements generated by capillary Poiseuille flow.
Type
Article
Description
The article of record as published may be located at http://www.math.ualberta.ca/ijnamb/contents.htm
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
International Journal of Numerical Analysis and Modeling / Volume 4, Issue 41337, pp. 460-477
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.