Particle settling and micro-scale motion: In which particle size range is Brownian motion most prominent, significantly affecting sedimentation behavior in fluids?

Difficulty: Easy

Correct Answer: 0.01 to 0.10 microns

Explanation:


Introduction / Context:
Brownian motion is the random thermal movement of small particles suspended in a fluid. It becomes important when designing colloid separation processes, ultrafiltration, and nanoparticle characterization, where gravity settling is minimal.


Given Data / Assumptions:

  • Isothermal conditions; fluid at rest on average.
  • Particles are rigid spheres for conceptual discussion.
  • Continuum assumptions begin to break down at extremely small scales.


Concept / Approach:
As particle diameter decreases, the gravitational settling velocity (Stokes regime) decreases with d^2, while thermal agitation remains significant. In the submicron range (tens of nanometers to about 0.1 micron), Brownian diffusion dominates, countering sedimentation and leading to stable suspensions absent aggregation.


Step-by-Step Solution:

Use Stokes settling: Vs ∝ d^2; for very small d, Vs → very small.Brownian diffusivity from Stokes–Einstein: D ∝ 1/d; smaller particles diffuse more rapidly.Compare effects: At 0.01–0.10 μm, Brownian diffusion overwhelms gravity settling.


Verification / Alternative check:
Colloid science texts define colloids roughly 1 nm to 1 μm, with strongest Brownian effects below ~0.1 μm, consistent with the given range.


Why Other Options Are Wrong:

  • 2–3 μm and larger ranges: Gravity settling predominates; Brownian motion is negligible for most practical fluids.
  • 100–1000 μm and 200–300 μm: Granular settling fully dominates; Brownian motion is irrelevant.


Common Pitfalls:
Assuming turbidity stability at micrometer scales without considering flocculation; interparticle forces and surfactants also affect suspension stability.


Final Answer:
0.01 to 0.10 microns

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