Plate-and-frame filtration concept: in constant-pressure operation, how does cake resistance change with filtration time?

Introduction / Context:
This question checks understanding of how cake resistance evolves in a plate-and-frame filter and distinguishes between constant-pressure and constant-rate modes. Knowing which operating variable is held fixed is the key to predicting how the other variables and the cake resistance behave during a cycle.

Given Data / Assumptions:

• Equipment: plate-and-frame filter (batch cake filtration).
• Operation mode: constant-pressure filtration (ΔP is held constant).
• Incompressible-to-moderately-compressible cake behavior typical of many slurries.

Concept / Approach:
Under constant-pressure filtration, Darcy’s law for laminar flow through a growing cake gives dV/dt = ΔP / (μ*(Rm + αCV/A)), where symbols have their usual meaning. As filtrate volume V increases, cake thickness grows and the term αCV/A increases, so the overall resistance rises steadily. Consequently, the filtrate rate falls with time even though the applied pressure is fixed.

Step-by-Step Solution:
Recognize mode: constant pressure → ΔP fixed by pump/vacuum.Cake builds with time → cake resistance Rc increases.Since ΔP is fixed, increasing Rc lowers the instantaneous filtration rate with time.Therefore, the statement “cake resistance increases steadily with time” applies to constant-pressure filtration, not constant-rate.

Verification / Alternative check:
In constant-rate operation, the rate is held fixed and the required pressure rises over time to overcome the growing cake resistance. That is the complementary scenario and contrasts with the present case.

Why Other Options Are Wrong:
Rate: incorrect—at constant-rate operation the pressure changes, not the held variable.Both / Neither: incorrect because the described behavior aligns specifically with constant-pressure filtration.

Common Pitfalls:
Confusing constant-pressure with constant-rate tests; forgetting that cake thickness and hence resistance increase as volume accumulates, regardless of mode.

Final Answer:
pressure