Specific surface shape factor (spherical particles): which expression is constant for spheres and equals 6?

Introduction / Context:
Shape factors relate measurable geometry (surface area A, volume V, and characteristic diameter D) to capture how particle shape affects transport and reaction. For spheres, certain ratios become constants, simplifying correlations in drying, reaction kinetics, and mass transfer.

Given Data / Assumptions:

• Spherical particle with diameter D.
• Surface area A = π D^2 and volume V = π D^3 / 6.
• Define a "shape factor" that is constant for spheres.

Concept / Approach:
Compute A/V for a sphere: A/V = (π D^2) / (π D^3 / 6) = 6 / D. Multiplying by D gives (A * D) / V = 6, a constant independent of size for perfect spheres. Many correlations use AD/V as a dimensionless indicator of compactness, equalling 6 for spheres and differing for non-spherical shapes.

Step-by-Step Solution:
Start with sphere geometry.Derive A/V = 6/D.Multiply both sides by D: AD/V = 6 (constant).Therefore, AD/V is the desired expression.

Verification / Alternative check:
Check units: A (L^2) * D (L) / V (L^3) → dimensionless, appropriate for a shape factor.

Why Other Options Are Wrong:
A/V alone equals 6/D, which varies with particle size; D/V and other permutations are not constant and lack standard physical meaning as shape constants.

Common Pitfalls:
Confusing specific surface (A/V or A/mass) with shape factors; the former depends on size, the latter on geometry.

Final Answer:
AD/V