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GATE 2021 CH – Question 14

Fluid Mechanics and Mechanical Operations · Settling, centrifuges, cyclones, thickening, filtration, agitation and mixing · 1 mark · Multiple choice

A batch settling experiment is performed in a long column using a dilute dispersion containing equal number of particles of type A and type B in water (density $1000\ \mathrm{kg\,m^{-3}}$) at room temperature. Type A are spherical particles of diameter $30\ \mu\mathrm m$ and density $1100\ \mathrm{kg\,m^{-3}}$. Type B are spherical particles of diameter $10\ \mu\mathrm m$ and density $1900\ \mathrm{kg\,m^{-3}}$. Assuming that Stokes’ law is valid throughout the duration of the experiment, the settled bed would

  1. consist of a homogeneous mixture of type A and type B particles
  2. consist of type B particles only
  3. be completely segregated with type B particles on top of type A particles
  4. be completely segregated with type A particles on top of type B particles

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Correct answer: (A) consist of a homogeneous mixture of type A and type B particles

Explanation

Under Stokes settling, $v_t=g(\rho_p-\rho_f)d^2/(18\mu)$. The fluid and gravity are common, so compare $(\rho_p-\rho_f)d^2$.

For A this is $100(30)^2=90000$; for B it is $900(10)^2=90000$, using the same micrometre units. Their terminal velocities are identical despite their different sizes and densities.

Neither type systematically overtakes the other, so the initially mixed dilute dispersion settles without segregation. **Answer: A.**