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Hydrodynamic slip significantly alters chaotic advection and scattering of small particles

Jason K. Kabarowski and Aditya S. Khair*

  • Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

  • *akhair@andrew.cmu.edu
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Phys. Rev. Fluids 7, 084504 – Published 31 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.084504

Abstract

The motion of small spherical particles in unsteady fluid flow can be predicted using the Boussinesq-Basset-Oseen equation, which is an integrodifferential equation balancing the particle inertia with the unsteady hydrodynamic force on a particle. For rigid spherical particles on whose surface the no-slip condition is obeyed, the Basset history force has been shown to significantly alter the statistical behavior of ensembles of particles in unsteady flows [Daitche and Tél, Phys. Rev. Lett. 107, 244501 (2011)]. Here, we determine the effect of hydrodynamic slip at the surface of the particle on the statistical behavior of an ensemble of spherical particles in a two-dimensional von Kármán flow in the wake of a cylinder. We compute the dynamics of a large quantity of spherical particles (on the order of a million) in this flow, and therefrom calculate escape rates, invariant manifold locations, and the uncertainty dimension of scattering trajectories for two cases: no-slip spheres and perfectly slipping spheres. We compare individual particle trajectories, locations of invariant manifolds, and residence time distributions for the two cases. We find that the presence of slip on a particle can lead to significant differences in escape rates, more initial positions that lead to vortex trapping at long times, and a greater uncertainty in scattering predictions. Thus, our paper shows that hydrodynamic slip significantly affects particle trajectories in unsteady flows.

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Outline

Information

Phys. Rev. Fluids 7, 084504– Published 31 August, 2022
  • Received 26 January 2022
  • Accepted 9 August 2022
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