Depth filtration performance metric: in the context of microbial removal by filters, what does the symbol X90 represent for a filtration system?

Introduction:
Depth filters remove particulates and microorganisms by mechanisms such as interception, diffusion, and adsorption within a porous matrix. Performance can be expressed using removal as a function of filter depth. The notation X90 is a convenient way to specify how much thickness is needed to achieve a given log reduction.

Given Data / Assumptions:

• Microbial population decreases with increasing depth due to capture within the filter.
• We are discussing removal as a function of thickness, not exposure time or temperature.
• 90% reduction corresponds to a one-log decrease in population for filtration-depth metrics.

Concept / Approach:
In depth filtration models, removal is described via exponential decay with distance: C(x) = C0 * exp(−K * x). The thickness that achieves a 90% reduction (C/C0 = 0.1) satisfies 0.1 = exp(−K * X90), so X90 = 2.303 / K. Thus X90 directly denotes a required depth, not a time parameter, to attain 90% removal.

Step-by-Step Solution:
Write the depth-removal relation: C/C0 = exp(−K * x).Set C/C0 = 0.1 to define 90% removal.Solve for x: X90 = 2.303 / K.Interpret the result: X90 is a thickness requirement at given flow and media properties.

Verification / Alternative check:
Plotting log(C/C0) versus depth yields a straight line with slope −K. One log cycle corresponds to X90 depth, consistent with the exponential model.

Why Other Options Are Wrong:

• Time-based options (a, b): Conflate thermal survivor curves with depth filtration metrics.
• 99% removal depth (d): Refers to X99, not X90.
• Pressure requirement (e): Pressure influences flux but does not define X90.

Common Pitfalls:
Mixing up time–temperature lethality (D-value) with depth-based removal constants; always check context and units.

Final Answer:
the depth required to reduce population by 90%