Particle settling and micro-scale motion: In which particle size range is Brownian motion most prominent, significantly affecting sedimentation behavior in fluids?
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A2 to 3 microns
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B0.01 to 0.10 microns
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C200 to 300 microns
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D100 to 1000 microns
Answer
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