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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
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Dynamics of passive and active membrane tubes.

Sami C Al-Izzi1, Pierre Sens2, Matthew S Turner3

  • 1School of Physics & EMBL-Australia node in Single Molecule Science, University of New South Wales, Sydney, Australia and Department of Mathematics, University of Warwick, Coventry CV4 7AL, UK and Institut Curie, PSL Research University, CNRS, Physical Chemistry Curie, F-75005, Paris, France and Sorbonne Université, CNRS, UMR 168, F-75005, Paris, France.

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Summary

This study models fluid membrane tube relaxation dynamics, considering viscosity contrasts and surface tension. It predicts relaxation rates for various perturbations and analyzes thermal and active fluctuations.

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Area of Science:

  • Soft Matter Physics
  • Biophysics
  • Fluid Dynamics

Background:

  • Fluid membrane tubes are crucial in biological systems.
  • Understanding their dynamics, including relaxation and fluctuations, is key to comprehending cellular processes.
  • Existing models often simplify membrane properties and external forces.

Purpose of the Study:

  • To derive and analyze the dynamical equations for fluid membrane tube relaxation under small deformations.
  • To investigate the influence of solvent viscosity contrast and membrane incompressibility on relaxation rates.
  • To incorporate and characterize both passive thermal and active non-equilibrium fluctuations.

Main Methods:

  • Utilizing Onsager's variational formulation to derive dynamical equations.
  • Computing relaxation rates for axis-symmetric and azimuthal (m-modes) perturbations.
  • Employing asymptotic arguments for long and short wavelength analysis.
  • Incorporating stochastic terms for thermal and active forces.

Main Results:

  • Derived dynamical equations for fluid membrane tube relaxation with viscosity contrast.
  • Computed relaxation rates, confirming known results and predicting new ones for higher-order modes.
  • Derived expressions for fluctuation amplitudes, effective temperature of active fluctuations, and power spectral density.
  • Analyzed long and short wavelength behaviors of different modes.

Conclusions:

  • The study provides a comprehensive theoretical framework for active fluid membranes.
  • New predictions for m-mode relaxation rates offer avenues for experimental validation.
  • Characterization of thermal and active fluctuations provides insights into membrane properties and active noise.