Sedimentation Theory for Soil Particles – Lower Size Limit for Stokes’ Law Validity Stokes’ law is used in sedimentation analysis of fine soils. It does not hold good if the particle size becomes smaller than approximately which value (due to Brownian motion and non-laminar micro-effects)?

Introduction / Context:
Hydrometer and pipette analyses rely on Stokes’ law to relate particle size to settling velocity. However, Stokes’ law has bounds of applicability. At extremely small sizes, random thermal motion and non-ideal effects distort the laminar settling assumptions, invalidating direct use of the formula.

Given Data / Assumptions:

• Lamina flow with Reynolds number < 1 is assumed for Stokes’ law.
• Particles are assumed rigid, smooth, and spherical, without mutual interference.
• Fluid properties are constant and temperature effects are controlled.

Concept / Approach:

Stokes’ law gives terminal settling velocity v = (g * (G_s − 1) * d^2) / (18 * ν) for a single, isolated sphere in laminar flow. The relationship fails at both extremes: (i) at larger sizes (higher Reynolds number) where turbulence and form drag increase; and (ii) at very tiny sizes (~sub-micron to a few tenths of micron) where Brownian motion dominates. In classical soil mechanics, a widely cited lower size threshold is about 0.0002 mm (0.2 micrometre). Below this, Stokes’ sedimentation assumptions break down.

Step-by-Step Solution:

Verification / Alternative check:

Laboratory observations show erratic settling for colloidal-sized particles; dispersion chemistry becomes more significant than gravity settling predictions.

Why Other Options Are Wrong:

0.2 mm and 0.02 mm are much larger (where Stokes may fail due to turbulence, but the question asks about smaller than a limit). 0.002 mm is still too large for the Brownian-motion-driven lower limit.

Common Pitfalls:

Confusing upper and lower validity limits; ignoring flocculation that invalidates the single-particle assumption.

Final Answer:

0.0002 mm