Filter-cake structure: in a compressible cake formed during filtration, where is the porosity highest across the cake thickness?

Introduction / Context:
As a cake forms on a filter medium, pressure drops across the cake thickness. If the cake is compressible, its structure (porosity and permeability) is not uniform; it varies with the local effective pressure. This spatial variation strongly influences filtration rate and washing efficiency.

Given Data / Assumptions:

• Cake compressibility is significant.
• Pressure is highest at the medium surface and decreases toward the slurry side.
• Steady filtration under constant pressure or constant rate conditions.

Concept / Approach:
Compressible cakes compact more where the applied stress is greatest. Because the maximum pressure occurs near the filter medium, pores there are most compressed (lowest porosity). Moving toward the upstream slurry interface, the local pressure is smaller and the cake is looser (higher porosity). Thus, porosity is highest at the upstream side and lowest at the medium side, giving a porosity gradient through the cake.

Step-by-Step Solution:
Recognize pressure gradient across cake thickness.Compressibility implies porosity decreases with increasing local pressure.Therefore, porosity is highest upstream (low pressure) and lowest at the medium (high pressure).

Verification / Alternative check:
Experimental washing data often show poorer wash efficiency near the medium due to tighter, lower-porosity layers.

Why Other Options Are Wrong:
Maximum at medium: contradicts compressibility behavior.Uniform porosity: valid only for incompressible cakes.

Common Pitfalls:
Assuming cake properties are constant; design models frequently incorporate a compressibility coefficient to reflect this gradient.

Final Answer:
maximum porosity at the upstream side