Abstract
We present the first direct measurement of the orbits of microscale passive tracers in the unsteady flow created by an oscillating microsphere. Using a time-shared optical trap to position tracers in several concentric arcs around a driven central sphere, we find that the tracers exhibit elliptical Lissajous figures whose orientation and aspect ratio are in quantitative agreement with a scaling law that arises from a low-frequency expansion of the underlying unsteady Stokes equations. The implications of these results for the understanding of metachronal waves in ciliated microorganisms are discussed.
Highlights
In his landmark 1851 paper on viscous fluids [1], George Gabriel Stokes developed the theoretical framework for understanding the competition between inertial and viscous forces, but he considered several physical situations in which that competition is simple to analyze
Even nearest-neighbor somatic cells have a significant phase shift. This is in contrast to the situation in Chlamydomonas, the unicellular relative of Volvox whose size is comparable to Volvox somatic cell and whose two 10–12 μm flagella are mounted just a few microns apart and beat at ∼ 50 Hz; the phase shift between the flagella is rather small
The regime of sizes and frequencies explored is such that Brownian motion makes only a modest contribution to the tracer dynamics, with an effective Péclet number generally exceeding unity
Summary
In his landmark 1851 paper on viscous fluids [1], George Gabriel Stokes developed the theoretical framework for understanding the competition between inertial and viscous forces, but he considered several physical situations in which that competition is simple to analyze These include his celebrated problems I and II—viscous fluid in the half space adjacent to a no-slip wall that is impulsively started into motion or oscillated from side to side at some frequency ω—as well as the case of a sphere oscillated back and forth. In the context of the dynamics of tracer particles in flows generated by the beating flagella of alga [15,16,17,18] that unsteadiness has been identified as a potentially significant feature of biophysical flows
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