Constant-pressure cake filtration behavior: how does the filtrate flow rate change with time during a run, assuming increasing cake thickness?

Introduction / Context:
In constant-pressure filtration of a cake-forming slurry, the pressure drop is held constant while cake thickness grows. This increases resistance over time.

Concept / Approach:
Darcy’s law: filtrate flux J = ΔP / (μ (Rm + Rc)). As the cake builds, Rc increases with time, so J decreases. Thus the instantaneous flow rate declines monotonically during the run.

Step-by-Step Solution:
Hold ΔP constant.Rc(t) ↑ as cake thickens.Therefore J(t) ∝ 1/(Rm + Rc(t)) ↓ with time.

Common Pitfalls:
Confusing initial surge (wetting/priming) with sustained behavior; after the initial transient, the trend is decreasing due to added resistance.

Final Answer:
It continuously decreases.