For particle capture by inertial impaction in fibrous filtration, the collection efficiency is primarily a function of which dimensionless numbers?

Introduction:
Inertial impaction occurs when particles deviate from streamlines due to inertia and collide with collector surfaces (e.g., filter fibers). Predicting impaction efficiency requires non-dimensional groups that capture the competition between particle inertia and viscous forces, as well as the flow regime around the collector.

Given Data / Assumptions:

• Discrete particles entrained in a fluid (air) approach a cylindrical fiber.
• Flow near the fiber can be described by a local Reynolds number.
• Particle–fluid relative inertia is represented by the Stokes number.

Concept / Approach:
The Stokes number (Stk) compares the particle relaxation time to a characteristic flow time around the collector; higher Stk increases impaction. The Reynolds number (Re) describes the flow field and influences streamline curvature and stagnation zones. Models of fibrous filtration express impaction efficiency in terms of Stk and Re; Schmidt (Sc) and Grashof (Gr) are more relevant to diffusion or buoyancy, not direct impaction trends.

Step-by-Step Solution:

Verification / Alternative check:
Experimental data for cyclone inlets and fibrous filters demonstrate impaction increases with Stk; at fixed Stk, Re variations alter stagnation region size and capture probability, corroborating the dependence.

Why Other Options Are Wrong:

• Stokes–Schmidt: Sc describes diffusion, not inertia.
• Grashof–Reynolds or Stokes–Grashof: Gr accounts for buoyancy (natural convection), irrelevant in typical filtration.

Common Pitfalls:
Confusing increased velocity effects on impaction with interception or diffusion regimes; each mechanism has distinct controlling parameters.

Final Answer:
Stokes and Reynolds number