During constant-pressure filtration of a slurry, how does the filtration rate vary with time as the cake builds on the medium?

Introduction / Context:
Filtration performance depends on the driving force and the resistance of both the filter medium and the deposited cake. Under constant pressure, the cake thickness increases over time, changing the overall resistance.

Given Data / Assumptions:

• Pressure drop is fixed (constant-pressure mode).
• Cake is incompressible to moderately compressible.

Concept / Approach:
Darcy’s law for filtration: rate ∝ ΔP / (μ (R_m + R_cake)). As filtration proceeds, R_cake increases with cake mass/height; therefore, at constant ΔP, the volumetric filtration rate decreases with time.

Step-by-Step Solution:
Write: dV/dt = ΔP / (μ (R_m + α V/A)).As V increases, R_cake rises linearly for incompressible cakes.Hence, dV/dt decreases with time.

Verification / Alternative check:
Filtration plots (V^2 vs t for constant-pressure) are linear for incompressible cakes, reflecting decreasing instantaneous rate.

Why Other Options Are Wrong:
Constant rate: occurs at constant-flux or constant-rate operation, not constant pressure.Increasing rate: contradicts rising resistance.

Common Pitfalls:
Confusing constant-pressure and constant-rate control strategies.

Final Answer:
Rate of filtration decreases with time