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

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.

arXiv comment8 pages, 1 figure

References in corpus (9)

• A density-independent glass transition in biological tissues
• Motility-driven glass and jamming transitions in biological tissues
• Energy barriers govern glassy dynamics in tissues
• Discrete rearranging disordered patterns, part I: Robust statistical tools in two or three dimensions
• From cells to tissue: A continuum model of epithelial mechanics
• Active dynamics of tissue shear flow
• The role of deformability in determining the structural and mechanical properties of bubbles and emulsions
• Poisson-Bracket Approach to the Dynamics of Nematic Liquid Crystals. The Role of Spin Angular Momentum
• Confluent and non-confluent phases in a model of cell tissue

Cited by in corpus (6)

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• Intercellular Friction and Motility Drive Orientational Order in Cell Monolayers
• Coarse-graining the vertex model and its response to shear
• Soliton approximation in continuum models of leader-follower behavior
• Channel flows of deformable nematics
• A Mechanistic Model of the Organization of Cell Shapes in Epithelial Tissues