#### Abstract

To clarify the rate at which particles similar in size to the smallest eddies in a turbulent fluid encounter one another via turbulent shear, 3-D video motion analysis was used to make direct measurements of relative velocities between closely spaced, near-neutrally buoyant, 700-μm mean diameter, polystyrene latex spheres suspended in an oscillating-grid turbulence tank. Smallest eddy size, termed the Kolmogorov scale, *λ*, was estimated as (*ν*^{3}/ε)^{0.25} where *ν* is fluid viscosity and ε is the dissipation rate of turbulent kinetic energy. For runs made in water, the effective particle diameter examined was ≈ 3–6 times larger than *λ*. To measure relative velocities for particles just smaller than the Kolmogorov scale, the viscosity of the suspending fluid was increased ≈ 25 times by the addition of Methocel, a commercially available, methyl cellulose synthetic gum used for fluid thickening. For runs made in Methocel, effective sphere diameter was ≈ 0.2–0.5 times the Kolmogorov scale. Turbulent kinetic energy dissipation rate was estimated by traversing the measuring volume of a laser-Doppler velocimeter fiberoptic probe through the fluid at speeds high relative to the fluctuating fluid velocities in the tank. Resulting time series were used in analogy with instantaneous spatial series to calculate root-mean-square fluctuating velocities and integral length scales of turbulence, which in turn served as input for calculation of ε. By examining the relationship between Reynolds number based on relative velocity between particles and particle separation distance relative to *λ*, two competing hypotheses were tested. The first, that turbulent eddying motions control relative velocity between closely spaced particles, was accepted for particles both slightly larger and slightly smaller than the Kolmogorov scale (0.05 < *p* < 0.10). The second, that viscous forces control relative velocity between particles, was strongly rejected in both cases (*p* = 0.004). The finding contradicts earlier assumptions and assertions that viscosity dominates small-scale particle interactions for sizes near the Kolmogorov scale, and it indicates that relative velocities between particles are greater than previously thought. Relative to biological mechanisms of particle encounter, turbulence therefore plays a role greater than is presently assumed in effecting encounter among particles and also between particles and organisms.

#### Recommended Citation

Hill, P. S., A. R. Nowell, and P. A. Jumars.
1992.
"Encounter rate by turbulent shear of particles similar in diameter to the Kolmogorov scale."
*Journal of Marine Research*
50,
(4).
https://elischolar.library.yale.edu/journal_of_marine_research/2049