Rotary drum vacuum filter capacity: identify the primary factors governing filtrate throughput for a given installation and slurry.

Introduction / Context:
Rotary drum vacuum filters are widely used for continuous solid–liquid separation in inorganic chemicals, fertilizers, and minerals. Filtration capacity (filtrate volume per time) depends on both operating setpoints and the nature of the slurry. Understanding the dominant levers helps troubleshoot low throughput and optimize cycle parameters (submergence, rotation speed, vacuum, wash).

Given Data / Assumptions:

• Constant vacuum operation with periodic cake formation, dewatering, washing, and discharge.
• Slurry properties influence cake resistance and formation rate.
• Cake thickness directly changes resistance and drainage path length.

Concept / Approach:
Darcy's law for flow through porous media states that filtrate flux decreases with higher cake resistance and thickness. Slurry particle size distribution, compressibility, and solids loading govern cake structure and permeability. Thus both cake thickness and slurry characteristics are principal determinants of capacity, alongside secondary factors like cloth condition and vacuum level.

Step-by-Step Solution:
Relate filtrate flow to pressure drop and total resistance (medium + cake).Note that thicker cakes increase resistance linearly (for incompressible cakes) or even more (compressible cakes).Recognize slurry characteristics set the cake permeability/compressibility; both govern capacity.

Verification / Alternative check:
Startup optimization usually tunes drum speed (hence cake thickness) for a given slurry to maximize throughput while achieving target moisture—confirming the joint role of (a) and (b).

Why Other Options Are Wrong:
Cake thickness only or slurry only omits a coequal driver.“Neither”: contradicts fundamental filtration theory.

Common Pitfalls:
Running with excessively thick cakes to chase dryness, which collapses capacity; or ignoring slurry pretreatment (coagulation/conditioning) that can improve permeability dramatically.

Final Answer:
Both (a) & (b)