In filtration theory, what is the compressibility coefficient (s) for an absolutely compressible filter cake?

Introduction / Context:
Filter cake compressibility is central to predicting how specific cake resistance changes with applied pressure in constant-pressure or constant-rate filtration. The compressibility coefficient s (sometimes n) characterises the sensitivity of cake resistance to pressure.

Given Data / Assumptions:

• Definition: α = α_0 * (ΔP)^s, where α is specific cake resistance and s is the compressibility coefficient.
• Absolutely compressible cake implies maximum sensitivity to pressure.
• Absolutely incompressible cake implies no sensitivity to pressure.

Concept / Approach:
By convention, s = 0 corresponds to an incompressible cake (α independent of ΔP). As compressibility increases, s increases toward unity. An absolutely compressible cake exhibits a direct proportionality of resistance to pressure on a log-log basis with slope equal to 1.

Step-by-Step Solution:

Verification / Alternative check:
Experimental plots of ln(α) versus ln(ΔP) give slope s. Highly compressible colloidal cakes show slopes close to 1, matching the limiting idealisation.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing s with porosity exponent; misreading absolute compressibility as infinite resistance instead of maximum pressure sensitivity.

Final Answer:
1