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The long-time dynamics of two hydrodynamically-coupled swimming cells
Sébastien Michelin1, Eric Lauga
1Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA. smichelin@ucsd.edu
Bulletin of Mathematical Biology
|December 17, 2009
Summary
Hydrodynamic interactions between swimming microorganisms, like spermatozoa, in dilute suspensions lead to collective behaviors. Even with confined trajectories, these cells either attract or repel each other over long times.
Area of Science:
- * Biophysics
- * Fluid Dynamics
- * Microorganism Locomotion
Background:
- * Swimming microorganisms exhibit collective locomotion in dense suspensions.
- * Analyzing dilute suspensions is challenging due to complex fluid-mediated interactions.
- * Spatially confined trajectories offer a tractable analytical approach.
Purpose of the Study:
- * To analytically derive the long-time kinematics of relative locomotion for two swimming cells with circular trajectories.
- * To investigate the role of hydrodynamic interactions in dilute suspensions with confined cell motion.
- * To identify emergent collective behaviors in microswimmer pairs.
Main Methods:
- * Multiple-scale analysis of fluid-mediated interactions.
- * Derivation of a reduced two-dimensional dynamical system for cell pair behavior.
- * Mathematical analysis of equilibrium points and long-time dynamics.
- * Numerical computations to validate analytical findings.
Main Results:
- * A clear separation of timescales between intrinsic swimming and hydrodynamic interaction.
- * Identification of unstable equilibrium and rotational equilibrium points.
- * Demonstration of two possible long-time behaviors: attraction or repulsion between cells.
- * Confirmation of these behaviors through numerical simulations.
Conclusions:
- * Hydrodynamic interactions drive novel cell-cell locomotion modes even in dilute, confined systems.
- * The long-time behavior of microswimmer pairs is limited to attraction or repulsion.
- * Analytical and numerical methods reveal fundamental principles of microswimmer collective dynamics.
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