Filtration mode identification: the operation in which inlet pressure is progressively increased to maintain throughput as cake builds up is termed

Introduction / Context:
As a filter cake grows, its resistance rises, causing the filtrate rate to fall if driving pressure is held constant. Operators can choose different operating modes depending on product goals: maintain pressure (and accept declining rate) or maintain rate (and raise pressure). Correctly naming these modes is essential when specifying filter presses, rotary vacuum filters with boosters, or pressure nutsche systems.

Given Data / Assumptions:

• Single-phase liquid through a compressible or incompressible cake.
• Operation seeks to keep filtrate flow approximately steady despite rising cake resistance.
• Pressure can be manipulated by the process (e.g., pump ramping).

Concept / Approach:
By Darcy's law, Q = ΔP / (μ * R_total) * A. If R_total increases with time due to cake buildup, keeping Q constant requires ΔP to increase correspondingly. This is called constant-rate filtration. Conversely, holding ΔP constant and allowing Q to decline is constant-pressure filtration.

Step-by-Step Solution:
Recognize the operational goal: maintain throughput as cake resistance rises.Infer the manipulated variable: increase inlet pressure over time.Name the mode: constant-rate filtration.

Verification / Alternative check:
Filter press cycles sometimes employ stepped pressure profiles to approximate constant rate early in the cycle, verifying the link between increasing pressure and rate stabilization.

Why Other Options Are Wrong:
“Varying pressure” is descriptive but not the standard mode name; the recognized term is “constant rate.”“Varying rate” and “constant pressure” describe the alternative mode where pressure is fixed and the rate declines.

Common Pitfalls:
Confusing “constant rate” with “constant velocity” of the cake front in dewatering beds; ensure you refer to filtrate volumetric flow rate.

Final Answer:
constant rate