Filter medium resistance: in practical filtration, what constitutes the resistance attributed to the “filter medium”?

Introduction / Context:
In Darcy-type filtration models, total hydraulic resistance comprises the filter medium resistance and the cake resistance. Correctly attributing medium resistance is important for start-up behavior, cloth selection, and cleaning schedule since it affects the initial filtrate flux before appreciable cake has formed.

Given Data / Assumptions:

• The medium is usually a fabric (cloth) or porous plate supporting the cake.
• Over time, particles embed within the pores of the cloth/septum.
• We consider steady, repeated cycles typical of industrial practice.

Concept / Approach:
The “filter medium resistance” is not just the virgin cloth resistance; it quickly includes the resistance of particles that lodge in the medium pores and remain after discharge. Thus, effective medium resistance equals the resistance of the cloth plus the embedded solids, forming a composite baseline independent of the removable cake layer.

Step-by-Step Solution:
Define R_total = R_medium + R_cake.Recognize R_medium = R_cloth + R_embedded (persistent fouling layer).Conclude that option describing both cloth and embedded particles is correct.

Verification / Alternative check:
Filter cycle data show that initial clean-bed flux declines over successive cycles unless cloth is backwashed or replaced, indicating accumulation of embedded resistance.

Why Other Options Are Wrong:
Cloth alone omits embedded fines, underestimating resistance.Embedded particles alone ignore the baseline cloth resistance.“None of these” contradicts standard filtration practice.

Common Pitfalls:
Assuming medium resistance is constant; in reality, it drifts upward with fouling and must be managed via cleaning protocols.

Final Answer:
filter cloth and the embedded particle collectively.