Filtration of compressible cakes What is the typical range of the compressibility coefficient (s) for commercial compressible cakes encountered in industrial filtration?

Introduction / Context:
In solid–liquid separation, cake compressibility strongly influences filtrate throughput and energy requirements. The compressibility coefficient s (sometimes denoted n) characterizes how cake resistance changes with applied pressure, a key concept in chemical engineering operations.

Given Data / Assumptions:

• Commercial cakes formed from fine, deformable particles (e.g., biological sludges, pigments)
• Constant-pressure or constant-rate filtration models
• Definition: specific cake resistance α ∝ (ΔP)^s, where s indicates compressibility (s = 0 for incompressible)

Concept / Approach:
For industrial, compressible cakes, s typically lies well above zero. Experience shows values in the broad range 0.2–0.8 depending on structure, particle size, and binding. This explains why increasing pressure often yields diminishing returns in flow rate when dealing with soft cakes.

Step-by-Step Solution:

Verification / Alternative check:
Operational data from filter presses, rotary vacuum filters, and leaf filters show that doubling pressure seldom doubles flow for compressible slurries, consistent with s in the 0.2–0.8 band.

Why Other Options Are Wrong:

• 0.01–0.1 and 0.1–0.3: Too low for most commercial compressible cakes; closer to mildly compressible or near-incompressible behavior.
• 0.2–0.4: Possible for some systems but too narrow; does not cover many highly compressible cakes encountered in practice.

Common Pitfalls:
Over-pressurizing in hopes of linear gains; for compressible cakes, dewatering aids (flocculants), precoat or filter aids, and conditioning can be more effective than just raising pressure.

Final Answer:
0.2 to 0.8