Interception mechanism in filtration — The interception efficiency can be expressed as which dimensionless ratio? (Here, dp is the particle diameter and Dc is the cylindrical collector/collection diameter.)

Introduction:
In granular and fibrous filtration theory, one of the key capture mechanisms is interception. Interception occurs when a particle follows a streamline that passes close enough to a collector (e.g., a cylinder or fiber) so that the particle touches and adheres to it simply due to its finite size. This question asks for the classical, dimensionless expression used to characterize interception in terms of particle and collector diameters.

Given Data / Assumptions:

• dp: particle (or microbial) diameter.
• Dc: diameter of a cylindrical collector/fiber in the filter bed.
• Low-inertia particles that track streamlines (interception, not impaction).
• Steady laminar flow around the collector (conceptual model).

Concept / Approach:
The interception parameter is typically written as NR = dp/Dc. Because both dp and Dc are lengths, the ratio is dimensionless. Interception efficiency scales with this size ratio and with the number of collectors encountered. When reported as a percent, the same ratio may be multiplied by 100, but the raw efficiency parameter is the dimensionless fraction dp/Dc.

Step-by-Step Solution:
Define the geometric criterion for interception: closest approach distance must be less than or equal to dp/2.Normalize with respect to the collector scale Dc, leading to a dimensionless group.Identify the standard form used in filtration models: NR = dp/Dc.

Verification / Alternative check:
Many semi-empirical models for overall single-collector efficiency (eta) include an interception term that is an increasing function of NR = dp/Dc, consistent with greater capture of larger particles relative to the collector size.

Why Other Options Are Wrong:

• dp × Dc and dp × Dc / 100 are dimensional (length^2), not suitable as dimensionless efficiency measures.
• (dp/Dc) × 100 expresses a percent; while sometimes used for reporting, the efficiency parameter itself is dp/Dc.
• Dc/dp is the inverse ratio and does not directly represent interception efficiency.

Common Pitfalls:
Confusing interception with inertial impaction (which depends on Stokes number); forgetting to use dimensionless groups when comparing different filter media.

Final Answer:
dp/Dc