For cake filtration, the instantaneous filtrate rate is directly proportional to which parameters and inversely proportional to which resistance/viscosity terms?

Introduction / Context:
Filtration equations show how flow depends on driving force, medium/cake resistances, fluid viscosity, and area. Understanding proportionalities aids in debottlenecking and scale-up.

Concept / Approach:
For a given pressure drop, superficial flux is proportional to area and inversely proportional to total hydraulic resistance and viscosity. Hence, higher S increases throughput, while higher R or μ reduces it.

Step-by-Step Solution:
Identify variables: S, R, μ under constant ΔP.Rate ∝ S and ∝ 1/R and ∝ 1/μ.Therefore, all listed statements are correct.

Final Answer:
All of the above