Equal-settling particles in a classifier: two particles are called “equal settling” when they have the same what (in the same fluid and field of force)?

Introduction:
Separators and classifiers often sort particles by their settling behavior rather than by diameter alone. The term “equal-settling” formalizes this idea: particles that fall at the same rate behave similarly in the separator even if their sizes or densities differ.

Given Data / Assumptions:

• Same continuous fluid and same gravitational (or centrifugal) field.
• Particles may differ in size, density, and shape.

Concept / Approach:
Terminal settling velocity depends on particle size, density difference, fluid viscosity, and drag regime. Two particles are equal-settling if their terminal velocities match under identical fluid and field conditions. This is the basis of “equal-settling ratios” used in sizing classifiers and hydrocyclones for mixed-density ores.

Step-by-Step Solution:
Define v_t as the terminal settling velocity.Equal-settling condition: v_t1 = v_t2 in the same fluid and field.This does not require equal diameter or equal density; combinations can compensate.Thus, classification behavior groups such particles together.

Verification / Alternative check:
In Stokes or Newton regimes, explicit v_t expressions show that a smaller but denser particle may equal-settle with a larger but lighter particle when v_t values coincide.

Why Other Options Are Wrong:

• Size or specific gravity alone does not guarantee equal settling.
• “None of these” is incorrect because the precise definition is given in option (c).
• Sphericity influences drag but is not the defining equality.

Common Pitfalls:
Assuming screens and classifiers separate on the same metric. Screens sort by size; classifiers respond to settling velocity.

Final Answer:
Terminal settling velocities in the same fluid and field of force