Constant-pressure cake filtration behavior: how does the filtrate flow rate change with time during a run, assuming increasing cake thickness?
Chemical Engineering
Mechanical Operations
Difficulty: Easy
Choose an option
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AIt continuously increases.
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BIt continuously decreases.
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CIt remains constant throughout.
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DIt may increase or decrease; depends only on pressure.
Answer
Correct Answer: It continuously decreases.
Explanation
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.