Onsager's variational principle in active soft matter

Abstract

Onsager's variational principle (OVP) was originally proposed by Lars Onsager in 1931 [L. Onsager, $Phys.Rev.$, 1931, $37$, 405]. This fundamental principle provides a very powerful tool for formulating thermodynamically consistent models. It can also be employed to find approximate solutions, especially in the study of soft matter dynamics. In this work, OVP is extended and applied to the dynamic modeling of active soft matter such as suspensions of bacteria and aggregates of animal cells. We first extend the general formulation of OVP to active matter dynamics where active forces are included as external non-conservative forces. We then use OVP to analyze the directional motion of individual active units: a molecular motor walking on a stiff biofilament and a toy two-sphere microswimmer. Next, we use OVP to formulate a diffuse-interface model for an active polar droplet on a solid substrate. In addition to the generalized hydrodynamic equations for active polar fluids in the bulk region, we have also derived thermodynamically consistent boundary conditions. Finally, we consider the dynamics of a thin active polar droplet under the lubrication approximation. We use OVP to derive a generalized thin film equation and then employ OVP as an approximation tool to find the spreading laws for the thin active polar droplet. By incorporating the activity of biological systems into OVP, we develop a general approach to construct thermodynamically consistent models for better understanding the emergent behaviors of individual animal cells and cell aggregates or tissues.

References in corpus (37)

• Novel type of phase transition in a system of self-driven particles
• Statistical physics of social dynamics
• Traffic and Related Self-Driven Many-Particle Systems
• Active Particles in Complex and Crowded Environments
• The hydrodynamics of swimming microorganisms
• The large deviation approach to statistical mechanics
• Motility-Induced Phase Separation
• Physics of Microswimmers - Single Particle Motion and Collective Behavior
• Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles
• A variational approach to the moving contact line hydrodynamics
• Physics of adherent cells
• Scalar ${\varphi }^4$ field theory for active-particle phase separation
• Tuned, driven, and active soft matter
• Spontaneous symmetry breaking in active droplets provides a generic route to motility
• Theories of Binary Fluid Mixtures: From Phase-Separation Kinetics to Active Emulsions
• Data-driven quantitative modeling of bacterial active nematics
• Ring to Mountain Transition in Deposition Pattern of Drying
• A minimal physical model captures the shapes of crawling cells
• Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid
• Activated escape of a self-propelled particle from a metastable state
• Nonequilibrium Statistical Mechanics of Self-propelled Hard Rods
• A Drop of Active Matter
• Instabilities and waves in thin films of living fluids
• Vapor-Induced Motion of Liquid Droplets on an Inert Substrate
• Active dynamics of tissue shear flow
• Dynamics of Viscoelastic Filaments Based on Onsager Principle
• Viscoelastic response of contractile filament bundles
• Dynamics of active nematic defects on the surface of a sphere
• Thin-Film Modelling of Resting and Moving Active Droplets
• Tractionless Self-Propulsion of Active Drops
• Note on the hydrodynamic description of thin nematic films: strong anchoring model
• Application of Onsager Machlup integral in solving dynamic equations in non-equilibrium systems
• How many ways a cell can move: the modes of self-propulsion of an active drop
• Defect removal by solvent vapor annealing in thin films of lamellar diblock copolymers
• Thin film models for active gels
• Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid
• Post-Tanner stages of droplet spreading: the energy balance approach revisited

Cited by in corpus (11)

• Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation
• Perspective: How to overcome dynamical density functional theory
• Time-correlation functions for odd Langevin systems
• Synchronization in cilia carpets and the Kuramoto model with local coupling: breakup of global synchronization in the presence of noise
• Variational methods and deep Ritz method for active elastic solids
• Onsager's variational principle for nonreciprocal systems with odd elasticity
• Most probable path of an active Brownian particle
• Symmetry-breaking, motion and bistability of active drops through polarization-surface coupling
• Spontaneous Bending of Hydra Tissue Fragments Driven by Supracellular Actomyosin Bundles
• Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes
• Variational approximation method for the long-range force transmission in biopolymer gels