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Slender body theory for ultrathin plates in two-dimensional viscous flow

Giulia Salussolia*,†

Catherine Kamal‡

  • School of Engineering, Faculty of Science, Engineering and Technology, Universidad Mayor, Santiago 7500994, Chile

  • *Contact author: giulia.salussolia@umayor.cl
  • †Also at Multidisciplinary Center for Physics, Vicerrectoría de Investigación, Universidad Mayor, Santiago 8580745, Chile.
  • ‡Contact author: c.kamal@ucl.ac.uk
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Phys. Rev. Fluids 10, 054301 – Published 7 May, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.054301

Abstract

The numerical modeling of ultrathin platelike particles in viscous flow is challenging because it requires an accurate representation of the particles' ultrathin edge. However, in many flow conditions, the effect of the edges on the flow and rheology is negligible. This paper presents a slender body theory for active or passive platelike particles in two-dimensional viscous flow. The theory simplifies the treatment of the particle geometry for the fluid-structure interaction, particularly by excluding the edge effects. The slender body theory is derived from the boundary integral formulation of the incompressible Stokes equations, which recasts the equations as an integral equation over the boundary of the particle's cross-section. By expanding the integral equation to leading order via a matched asymptotic expansion in the particle slenderness, a simplified nonlocal line integral across the central line of the particle is obtained. This integral relates the flow velocity and the hydrodynamic traction and does not depend on nontrivial edge effects. The results are validated for passive and active cases of ultrathin two-dimensional particles for which analytical results are known. The validations confirm the capability of the two-dimensional slender body theory to accurately describe the flow and rheology of passive and active ultrathin platelike particles under many flow conditions.

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Phys. Rev. Fluids 10, 054301– Published 7 May, 2025
  • Received 18 November 2024
  • Accepted 31 March 2025
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