Cake washing in filtration — behavior of resistances:\nDuring the washing step of a formed filter cake, how do the hydraulic resistances generally behave as washing proceeds under constant conditions?

Introduction / Context:
After cake formation in filtration, a washing step is often applied to displace mother liquor and soluble impurities. Engineers must understand how hydraulic resistance evolves, because it governs wash time, pressure drop, and pump energy. Although detailed behavior depends on cake compressibility and wash chemistry, a common trend is that resistance does not fall; instead, it tends to increase or at best remain steady as washing proceeds.

Given Data / Assumptions:

• Cake has already been formed on the medium.
• Washing is performed at roughly constant pressure difference and steady temperature.
• No cake removal between wash passes, and no drastic dissolution of the solid matrix.

Concept / Approach:
Total resistance is the sum of medium resistance and cake resistance. As washing continues, the cake structure may compact due to continued hydraulic loading, reducing porosity and increasing specific resistance. Fines migration can also block pores near the medium. While displaced liquor composition improves, the hydraulic pathway rarely becomes easier. Therefore, the most common textbook expectation is an increase in overall resistance during washing, particularly for compressible cakes.

Step-by-Step Solution:

Verification / Alternative check:
Pilot tests of compressible cakes (e.g., precipitates, biological sludges) show rising pressure drop with wash throughput, requiring longer times or higher driving force to achieve target wash ratios.

Why Other Options Are Wrong:

• Decrease/constant: possible only with unusual cake dissolution or rigid incompressible cakes; not the general rule.
• Oscillation: lacks a physical basis under steady conditions.
• “None of these”: unnecessary; “Increase” matches practice.

Common Pitfalls:
Assuming improved liquor purity implies lower resistance; purity rises while permeability can fall.

Final Answer:
Increase