Question

Differential settling methods utilize the difference in ______

• A. densities
• B. terminal velocities
• C. viscosities
• D. particle sizes

Hint:

To successfully separate two materials of densities \( \rho_A \) and \( \rho_B \) based on density alone, the fluid density \( \rho_f \) must be chosen such that it lies between \( \rho_A \) and \( \rho_B \).
This is known as sink-and-float separation.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the fundamental physical principle exploited in differential settling methods.
This is part of solid-liquid separation and classification in mechanical operations.

Step 2: Key Formula or Approach:
Differential settling is a classification technique used to separate particles based on how they behave when settling through a fluid.
The governing separation metric is the terminal settling velocity of the particles.

Step 3: Detailed Explanation:

• Mechanism of Separation: When a mixture of particles with varying sizes and densities is introduced into a fluid column, each particle reaches its unique terminal settling velocity.
Terminal velocity depends on both particle size and density, as shown by Stokes' Law:
\[ u_t = \frac{g \cdot d_p^2 \cdot (\rho_p - \rho_f)}{18 \cdot \mu} \]

• Why not just Density or Size? If we only used density, two particles of different sizes might still settle together if their combination of size and density resulted in the same settling velocity (equal-settling particles).
The separation process specifically separates particles because their net terminal velocities are different.
By controlling the upward velocity of the fluid, we can carry slower-settling particles out the top while allowing faster-settling particles to sink.
Therefore, the differential settling method ultimately utilizes differences in terminal velocities.


Step 4: Final Answer:
Differential settling methods utilize the difference in terminal velocities of particles.