Dynamics of filaments and membranes in a viscous fluid

Abstract

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for calculating internal stresses and forces, and we derive the full nonlinear equations of motion. In the case of membranes, we pay particular attention to the formulation of the equations of hydrodynamics on a curved, deforming surface. The formalism is illustrated by two simple case studies: (1) the twirling instability of straight elastic rod rotating in a viscous fluid, and (2) the pearling and buckling instabilities of a tubular liposome or polymersome.

26 pages, 12 figures, to be published in Reviews of Modern Physics

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• Models for twistable elastic polymers in Brownian dynamics, and their implementation for LAMMPS
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• Slip Morphology of Elastic Strips on Frictional Rigid Substrates
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• Morphodynamics of Active Nematic Fluid Surfaces
• Well-posedness of Hydrodynamics on the Moving Elastic Surface
• Geometry and dynamics of lipid membranes: The Scriven--Love number
• Membrane stress tensor in the presence of lipid density and composition inhomogeneities
• Mixing and de-mixing of model microswimmers in bi-motility mixtures
• Twist dynamics and buckling instability of ring DNA: Effect of groove asymmetry and anisotropic bending
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• Slender body theories for rotating filaments
• Undulation Amplitude of a Fluid Membrane Surrounded by Near-Critical Binary Fluid Mixtures
• Dynamics of passive and active membrane tubes
• Chaos and irreversibility of a flexible filament in periodically-driven Stokes flow
• Spontaneous knotting of a flexible fiber in chaotic flows
• Catenaries in viscous fluid
• Shear stresses in fluid and solid membranes with bending elasticity
• High-throughput measurement of elastic moduli of microfibers by rope coiling
• Fluid transport by active elastic membranes
• Spinor representation of surfaces and complex stresses on membranes and interfaces
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• Tunable dynamics of flexible magnetic microcrosses: synchronous rotation, breathing and out-of-plane arm overtaking
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• Undulatory swimming in suspensions and networks of flexible filaments
• Dynamics of pearling instability in polymersomes: the role of shear membraneviscosity and spontaneous curvature
• At the end of a moving string