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Dynamics of force dipoles in curved fluid membranes

Sarthak Bagaria1 and Rickmoy Samanta2,*

  • 1Quantitative Strategies, Goldman Sachs, London EC4A 4AU, United Kingdom
  • 2Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India

  • *rickmoysamanta@gmail.com
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Phys. Rev. Fluids 7, 093101 – Published 9 September, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.093101

Abstract

We construct a model to explore the hydrodynamic interactions of active inclusions in curved biological membranes. The curved membrane is modeled as a two-dimensional layer of highly viscous fluid, surrounded by external solvents of different viscosities. The active inclusions are modeled as point force dipoles. The point dipole limit is taken along a geodesic of the curved geometry, incorporating the change in orientation of the forces due to curvature. We demonstrate this explicitly for the case of a spherical membrane, leading to an analytic solution for the flow generated by a single inclusion. We further show that the flow field features an additional defect of negative index, arising from the membrane topology, which is not present in the planar version of the model. We finally explore the hydrodynamic interactions of a pair of inclusions in regimes of low and high curvature, as well as situations where the external fluid outside the membrane is confined. Our study suggests aggregation of dipoles in curved biological membranes of both low and high curvatures, under strong confinement. However, very high curvatures tend to destroy dipole aggregation, even under strong confinement.

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Phys. Rev. Fluids 7, 093101– Published 9 September, 2022
  • Received 22 November 2021
  • Accepted 15 August 2022
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