Question

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 kg m^–3) at room temperature.

Type A are spherical particles of diameter 30 μm and density 1100 kg m^–3.
Type B are spherical particles of diameter 10 μm and density 1900 kg m^–3.
Assuming that Stokes’ law is valid throughout the duration of the experiment, the settled bed would

• A. consist of a homogeneous mixture of type A and type B particles
• B. consist of type B particles only
• C. be completely segregated with type B particles on top of type A particles
• D. be completely segregated with type A particles on top of type B particles

Hint:

If settling velocities match, particles settle together — no segregation occurs.

Answer 1

The Correct Option is A

Stokes' settling velocity for small particles is given by:
\[ v = \frac{g(\rho_p - \rho_f)d^2}{18\mu} \] where \(d\) is particle diameter and \(\rho_p\) is particle density.
Type A: \(d = 30\mu m\), \(\rho_p = 1100 \, kg/m^3\)
Type B: \(d = 10\mu m\), \(\rho_p = 1900 \, kg/m^3\)
Settling velocity depends on both diameter squared and density difference.
Even though type B has higher density, type A has 9 times larger diameter effect because velocity ∝ \(d^2\).
Checking the magnitudes:
\[ v_A \propto (1100 - 1000)(30)^2 \] \[ v_B \propto (1900 - 1000)(10)^2 \] \[ v_A \propto 100 \times 900 = 90000 \] \[ v_B \propto 900 \times 100 = 90000 \] Thus: \[ v_A \approx v_B \] Both particle types settle at nearly the same velocity, resulting in no segregation.
Therefore, the settled bed will contain a homogeneous mixture of both types of particles.