Poisson-bracket formulation of the dynamics of fluids of deformable particles

TL;DR

This paper develops a continuum fluid model for deformable particles using Poisson brackets, capturing shape deformations and nematic alignment, with applications to biological tissues and tissue rheology.

Contribution

It introduces a novel Poisson-bracket-based derivation of continuum equations for deformable particle fluids, including shape and alignment fields, applied to biological tissue modeling.

Findings

Derived continuum equations for deformable particle fluids.

Captured coupling between cell shape and flow in tissues.

Provided a framework for tissue rheology modeling.

Abstract

Using the Poisson bracket method, we derive continuum equations for a fluid of deformable particles in two dimensions. Particle shape is quantified in terms of two continuum fields: an anisotropy density field that captures the deformations of individual particles from regular shapes and a shape tensor density field that quantifies both particle elongation and nematic alignment of elongated shapes. We explicitly consider the example of a dense biological tissue as described by the Vertex model energy, where cell shape has been proposed as a structural order parameter for a liquid-solid transition. The hydrodynamic model of biological tissue proposed here captures the coupling of cell shape to flow, and provides a starting point for modeling the rheology of dense tissue.