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Many-particle mobility and diffusion tensors for objects in viscous sheets.

Yulia Sokolov1, Haim Diamant1

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Researchers developed a mobility tensor for cylindrical objects in viscous sheets, ensuring positive energy dissipation. This tool aids simulations of biomembranes and liquid films.

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Area of Science:

  • Fluid dynamics
  • Soft matter physics
  • Biophysics

Background:

  • Understanding hydrodynamic interactions is crucial for modeling complex fluids.
  • Existing mobility tensors often focus on spherical particles, limiting applications for non-spherical objects.
  • Cylindrical objects are prevalent in biological systems and material science.

Purpose of the Study:

  • To derive a mobility tensor applicable to multiple cylindrical objects in a viscous sheet.
  • To ensure the derived tensor guarantees a positive dissipation rate for all configurations.
  • To provide a tool for Brownian dynamics simulations involving hydrodynamic interactions.

Main Methods:

  • Derivation of a mobility tensor for cylindrical inclusions in a 2D viscous fluid.
  • Mathematical analysis to prove the positive-definite property of the tensor.
  • Testing the tensor's performance using a ring of radially driven particles.

Main Results:

  • A novel mobility tensor for many-body systems of cylindrical objects in a viscous sheet was successfully derived.
  • The tensor guarantees a positive dissipation rate, analogous to the Rotne-Prager-Yamakawa tensor for spheres.
  • The positive-definite property was demonstrated across various particle densities in simulation tests.

Conclusions:

  • The derived mobility tensor offers a robust method for simulating hydrodynamic interactions of cylindrical objects.
  • This advancement is applicable to systems like proteins in biomembranes and inclusions in liquid films.
  • The tensor facilitates more accurate Brownian dynamics simulations in relevant soft matter and biophysical contexts.