Filtration fundamentals: which statement best describes how cake resistance behaves during constant-pressure filtration of a slurry?

Introduction / Context:
In constant-pressure filtration, solids deposit on the medium to form a cake. The hydraulic resistance of that cake governs the filtrate rate as operation proceeds. Understanding how cake resistance evolves is crucial for cycle-time estimates and equipment sizing.

Given Data / Assumptions:

• Operation at constant pressure drop.
• Cake builds up with time as solids collect on the medium.
• Cake may be compressible (common in many slurries), making resistance pressure-dependent.

Concept / Approach:
At the very start, cake resistance is minimal; flow is governed by the medium resistance. As cake thickness grows, total resistance rises, reducing filtrate rate. For compressible cakes, specific cake resistance increases with pressure. Thus, cake resistance is not “important in the beginning,” it does not “decrease with time,” and it is not strictly “independent of pressure drop.”

Step-by-Step Solution:
Early stage: R_cake ≈ 0; filtrate rate high, dominated by medium resistance.Growth: R_cake increases with deposited mass/area and often with pressure (compressibility).Conclusion: all three listed statements are incorrect; select “none of these.”

Verification / Alternative check:
Darcy-based models show filtrate volume rising with t^0.5 under constant pressure for incompressible cakes; any compressibility increases resistance faster, confirming growing importance of cake resistance over time.

Why Other Options Are Wrong:
“Important in the beginning”: false; cake scarcely exists at start.“Decreased with time”: the opposite occurs as cake accumulates.“Independent of pressure drop”: compressible cakes show clear dependence on ΔP.

Common Pitfalls:
Conflating medium resistance with cake resistance; medium dominates initially, cake dominates later.

Final Answer:
none of these.