Single-fiber impaction efficiency correlation (Friedlander model): which expression gives the impaction collection efficiency ηimp in terms of the Stokes number NSt?

Introduction:
For aerosol filtration by fibrous media, single-fiber collection efficiency can be decomposed into contributions from diffusion, interception, and inertial impaction. Empirical correlations relate impaction efficiency to the particle’s Stokes number NSt, which captures inertia relative to viscous drag around a fiber.

Given Data / Assumptions:

• NSt increases with particle size and density and with approach velocity; it decreases with fluid viscosity.
• Correlation sought is the Friedlander-type fit expressing ηimp as a power of NSt.
• Low to moderate NSt regime typical of air filtration around fibers.

Concept / Approach:
Empirical fits take the general form ηimp = A * NSt^m, with A and m determined experimentally. A commonly cited Friedlander correlation gives m ≈ 1.2 and A ≈ 0.75 for impaction on single fibers under representative conditions, enabling quick estimates within design calculations.

Step-by-Step Solution:
Identify target mechanism: inertial impaction.Recall the Friedlander-style power-law dependence on NSt.Choose the option with exponent 1.2 and coefficient consistent with literature (≈0.75).

Verification / Alternative check:
Comparisons across correlations (e.g., Lee–Liu, Pich) show similar NSt exponents in certain regimes; the selected expression aligns with widely used design heuristics.

Why Other Options Are Wrong:

• Other coefficients (0.25, 0.075, 0.025) underestimate impaction over typical ranges.
• Rational form NSt/(1+NSt) represents a different functional dependence and not the stated Friedlander power-law fit.

Common Pitfalls:
Applying a single correlation outside its calibration range; always validate against experimental data for the specific fiber geometry and flow regime.

Final Answer:
ηimp = 0.75 NSt^1.2