Mixing Reynolds Number in STRs — With liquid density and viscosity constant, how does the impeller Reynolds number depend on the impeller diameter (Dtank fixed)?

Introduction:
The impeller Reynolds number in a stirred-tank reactor (STR) classifies the mixing regime and strongly influences power draw, mass transfer, and blending. Knowing the correct geometric dependence is essential for scale-up and for comparing vessels with different impeller sizes.

Given Data / Assumptions:

• Reynolds number for mixing is defined as Re = rho * N * D^2 / mu.
• Liquid density rho and viscosity mu are constant.
• Impeller speed N and diameter D are variables of interest.

Concept / Approach:

By definition, Re depends linearly on the rotational speed N and on the square of the impeller diameter D. Holding rho and mu constant, any change in D affects Re through the D^2 term. This quadratic dependence underlies why even modest changes in impeller size can move a system from laminar to transitional or turbulent mixing regimes at a fixed speed.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional analysis confirms the result. Practical observations show that doubling D at fixed N increases Re fourfold, often shifting the flow regime measurably.

Why Other Options Are Wrong:

A suggests linear scaling; B suggests square-root scaling; D suggests cubic scaling; E ignores the explicit D^2 dependence in the definition.

Common Pitfalls:

Confusing the D^2 dependence in Re with the D^5 dependence in impeller power correlations; they arise from different relationships.

Final Answer:

It varies with the square of the impeller diameter (Re ∝ D^2).