Hybrid models for perfect complex fluids with multipolar interactions

Cesare Tronci

doi:10.3934/jgm.2012.4.333

Article Contents

2012, Volume 4, Issue 3: 333-363. Doi: 10.3934/jgm.2012.4.333

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Hybrid models for perfect complex fluids with multipolar interactions

Cesare Tronci^1,

1.
Department of Mathematics, University of Surrey, Guildford GU2 7XH

Received: October 31, 2010

Revised: September 30, 2011

Published: August 2012

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Abstract

Multipolar order in complex fluids is described by statistical correlations. This paper presents a novel dynamical approach, which accounts for microscopic effects on the order parameter space. Indeed, the order parameter field is replaced by a statistical distribution function that is carried by the fluid flow. Inspired by Doi's model of colloidal suspensions, the present theory is derived from a hybrid moment closure for Yang-Mills Vlasov plasmas. This hybrid formulation is constructed under the assumption that inertial effects dominate over dissipative phenomena (perfect complex fluids), so that the total energy is conserved and the Hamiltonian approach is adopted. After presenting the basic geometric properties of the theory, the effect of Yang-Mills fields is considered and a direct application is presented to magnetized fluids with quadrupolar order (spin nematic phases). Hybrid models are also formulated for complex fluids with symmetry breaking. For the special case of liquid crystals, the moment method can be applied to the hybrid formulation to study to the dynamics of cubatic phases.

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Mathematics Subject Classification: 70Hxx, 82Cxx, 76Axx.

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