Small-scale turbulence — Which factors influence the Kolmogorov micro-eddy (smallest eddy) size in a stirred bioreactor?

Introduction:
The Kolmogorov length scale characterizes the smallest eddies in turbulent flow where viscous dissipation dominates. In bioprocessing, matching or exceeding cell size by these eddies can influence shear sensitivity. The question asks which variables govern this micro-scale.

Given Data / Assumptions:

• Turbulent regime or near-transitional with appreciable energy dissipation.
• Newtonian approximation for concept; non-Newtonian effects change effective viscosity.
• Homogeneous temperature and composition.

Concept / Approach:
Kolmogorov length scale eta scales approximately with (nu^3/epsilon)^(1/4), where nu is kinematic viscosity and epsilon is the local energy dissipation rate. Thus, increasing power input (via higher speed or certain impellers) shrinks eta, while higher viscosity enlarges it. Impeller geometry and size map into epsilon distribution throughout the tank.

Step-by-Step Solution:
Relate stirrer speed and impeller choice to power number and P/V, which set epsilon.Recognize that nu explicitly enters Kolmogorov scaling, so liquid properties matter.Conclude that speed, fluid properties, and impeller design jointly determine micro-eddy size.

Verification / Alternative check:
Use correlations for P = Np * rho * N^3 * D^5 and estimate epsilon ≈ P/(rho * V). Insert nu and epsilon into eta ≈ (nu^3/epsilon)^(1/4) to see trends consistent with the qualitative answer.

Why Other Options Are Wrong:

• (a), (b), (c) each omit other influential factors; all act together.
• (e) Tank volume alone does not set eta; local dissipation and viscosity are decisive.

Common Pitfalls:
Assuming a single global eta when dissipation is nonuniform; ignoring non-Newtonian viscosity in cell culture broths; over-relying on average P/V without considering impeller zone hotspots.

Final Answer:
All of these