Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 108, Issue 26, Pages 10391-10395Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1107046108
Keywords
biofluid dynamics; low Reynolds number; flagella
Categories
Funding
- National Science Foundation [NSF DMR-0803153]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [0804944] Funding Source: National Science Foundation
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Fluid mixing in active suspensions of microorganisms is important to ecological phenomena and presents a fascinating stochastic process. We investigate the mixing produced by swimming unicellular algal cells (Chlamydomonas) in quasi-two-dimensional liquid films by simultaneously tracking the motion of the cells and that of microscopic passive tracer particles advected by the fluid. The reduced spatial dimension of the system leads to long-range flows and a surprisingly strong dependence of tracer transport on the concentration of swimmers, which is explored over a wide range. The mean square displacements are well described by a stochastic Langevin model, which is used to parameterize the mixing. The effective diffusion coefficient D grows rapidly with the swimmer concentration F as D similar to Phi(3/2), as a result of the increasing frequency of tracer-swimmer interactions and the long-range hydrodynamic disturbances created by the swimmers. Conditional sampling of the tracer data based on the instantaneous swimmer position shows that the rapid growth of the diffusivity enhancement with concentration must be due to particle interactions with multiple swimmers simultaneously. Finally, the anomalous probability distributions of tracer displacements become Gaussian at high concentration, but manifest strong power-law tails at low concentration, while the tracer displacements always grow diffusively in time.
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