Journal of Nonlinear Science

, Volume 28, Issue 4, pp 1379–1396 | Cite as

Hydrodynamic Capture and Release of Passively Driven Particles by Active Particles Under Hele-Shaw Flows

  • Grant Mishler
  • Alan Cheng Hou Tsang
  • On Shun Pak


The transport of active and passive particles plays central roles in diverse biological phenomena and engineering applications. In this paper, we present a theoretical investigation of a system consisting of an active particle and a passive particle in a confined micro-fluidic flow. The introduction of an external flow is found to induce the capture of the passive particle by the active particle via long-range hydrodynamic interactions among the particles. This hydrodynamic capture mechanism relies on an attracting stable equilibrium configuration formed by the particles, which occurs when the external flow intensity exceeds a certain threshold. We evaluate this threshold by studying the stability of the equilibrium configurations analytically and numerically. Furthermore, we study the dynamics of typical capture and non-capture events and characterize the basins of attraction of the equilibrium configurations. Our findings reveal a critical dependence of the hydrodynamic capture mechanism on the external flow intensity. Through adjusting the external flow intensity across the stability threshold, we demonstrate that the active particle can capture and release the passive particle in a controllable manner. Such a capture-and-release mechanism is desirable for biomedical applications such as the capture and release of therapeutic payloads by synthetic micro-swimmers in targeted drug delivery.


Microswimmer Hydrodynamic interaction Confinement 

Mathematics Subject Classification

76Z10 76D99 



Grant Mishler acknowledges financial support through a Hayes Research Fellowship. Alan Cheng Hou Tsang thanks the Croucher Foundation for a Postdoctoral Fellowship. On Shun Pak acknowledges support from the Packard Junior Faculty Fellowship.

Supplementary material


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Grant Mishler
    • 1
  • Alan Cheng Hou Tsang
    • 2
  • On Shun Pak
    • 1
  1. 1.Department of Mechanical EngineeringSanta Clara UniversitySanta ClaraUSA
  2. 2.Department of BioengineeringStanford UniversityStanfordUSA

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