A kinetic theory approach to ordered fluids

Abstract: Boltzmann derived the kinetic equation for monatomic gases in 1872. It took 85 years before Curtiss developed the extension to polyatomic gases, enlarging the phase space with Euler angles to describe the orientations of the molecules. What is the right kinetic equation for molecules with other kinds of internal ordering, such as the rodlike molecules constituting liquid crystals? This talk presents a framework that aims to address exactly this question.

The internal structure of a molecule is described by a point on an order parameter manifold, a concept introduced by Capriz in continuum mechanics in 1989. With this manifold, a group action describing how rotations change ordering, and the intermolecular potential, we derive a general BBGKY hierarchy and a Vlasov—Boltzmann kinetic equation that governs the evolution the one-particle density function.

We prove that in certain situations the system thermalises to a Maxwellian distribution, simulate the resulting novel kinetic equation for liquid crystals with direct simulation Monte Carlo, and discuss taking hydrodynamic closures to derive novel models at the level of continuum mechanics.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)