Aerosol filtration by diffusion: under otherwise identical conditions, the collection efficiency due to Brownian diffusion increases with which changes?

Introduction:
Depth and fibrous filters collect very small particles by Brownian diffusion. The random motion of submicron particles enhances their probability of contacting and being captured by filter fibers. Understanding how particle size and face velocity influence diffusion capture helps optimize air and vent filtration in bioprocess settings.

Given Data / Assumptions:

• Diffusion dominates for small particles (typically < 0.3 μm).
• Air velocity affects residence time and the Péclet number.
• Other mechanisms (inertial impaction, interception) may dominate for larger particles.

Concept / Approach:
Smaller particles exhibit larger Brownian motion (higher diffusivity), increasing their zig-zag path and contact with fibers. Lower air velocity increases residence time in the filter matrix, giving more opportunity for diffusive contact. Therefore, diffusion collection efficiency rises as particle size decreases and as air velocity decreases.

Step-by-Step Solution:
Relate diffusivity to particle size: smaller size → higher diffusivity.Relate residence time to velocity: lower velocity → longer contact time.Combine effects: both changes increase capture probability.

Verification / Alternative check:
Filtration models show diffusion efficiency terms inversely related to flow velocity and directly related to particle diffusivity, matching the qualitative trends.

Why Other Options Are Wrong:

• Increasing particle size or velocity: Both reduce diffusion capture.
• Single-choice (a) or (b) alone: Each is true but incomplete; both together is the most correct.

Common Pitfalls:
Assuming one mechanism dominates at all sizes; actual total efficiency is the sum of diffusion, interception, and impaction contributions.

Final Answer:
both (a) and (b)