Particle Deposition Mechanisms
Learning Objectives
Students will be able to:
- Describe the four primary mechanisms of particle deposition
- Explain how particle size determines which deposition mechanism dominates
- Calculate gravitational settling velocities using Stokes' law
- Apply deposition concepts to respiratory tract deposition and filtration
- Analyze the "minimum efficiency" particle size range
The Big Question
"How do particles in air eventually end up on surfaces, and why are particles in the 0.1-0.3 um range so difficult to remove?"
Four Deposition Mechanisms
1. Gravitational Settling
Particles fall under gravity at their terminal settling velocity. Dominates for particles > 1 um.
vs = (rhop - rhof) g d2 / (18 eta)
2. Inertial Impaction
Particles with high inertia cannot follow air streamlines around obstacles. Dominates for particles > 1 um at high velocities.
Stokes number: St = rhop d2 v / (18 eta L)
3. Interception
Particles following streamlines contact a surface when they pass within one particle radius. Important for fibers and filter media.
Interception parameter: R = dp / dfiber
4. Diffusion
Brownian motion causes particles to wander across streamlines and contact surfaces. Dominates for particles < 0.1 um.
Peclet number: Pe = v L / D
Gravitational Settling: Stokes' Law
For spherical particles settling at low Reynolds numbers (Re < 1), the settling velocity is given by Stokes' law:
vs = (rhop - rhoair) g d2 / (18 eta)
| Particle Diameter | Settling Velocity | Time to Fall 1 meter |
|---|---|---|
| 100 um | 25 cm/s | 4 seconds |
| 10 um | 0.3 cm/s | 5.5 minutes |
| 1 um | 0.003 cm/s | 9 hours |
| 0.1 um | ~0 (diffusion dominates) | Indefinite |
The Most Penetrating Particle Size (MPPS)
Filtration efficiency has a minimum at a specific particle size where neither diffusion nor interception/impaction is effective:
The Efficiency Minimum
- Small particles (<0.1 um): Efficiently captured by diffusion
- Large particles (>1 um): Efficiently captured by impaction/interception
- MPPS (~0.1-0.3 um): Too large for efficient diffusion, too small for efficient impaction
Note: HEPA filters are rated at 99.97% efficiency specifically at the MPPS (0.3 um) because this represents worst-case performance.
Respiratory Tract Deposition
The same deposition mechanisms determine where inhaled particles deposit in the respiratory system:
Nasal/Throat
Particles > 10 um
Impaction at bends and bifurcations
Tracheobronchial
Particles 1-10 um
Impaction and settling
Alveolar
Particles < 1 um
Settling and diffusion in deep lung
The 0.1-0.3 um MPPS range also has low deposition efficiency in the respiratory tract, meaning these particles are both hardest to filter and often exhaled without depositing.
Activity: Deposition Analysis
Problem Set
- Settling time: Calculate the settling velocity and time to fall 2 meters for a 5 um particle with density 2.5 g/cm3.
- Room clearance: A room is 3 m tall. How long would it take for all 10 um particles to settle out (assuming no air currents)? What about 1 um particles?
- HEPA analysis: Why do HEPA filters specify 99.97% efficiency at 0.3 um rather than at a larger particle size where impaction is more effective?
- Virus particles: SARS-CoV-2 is approximately 100 nm in diameter. Which deposition mechanisms would be most important for removing these particles from air? From the respiratory tract?
Key Takeaway
Particle deposition occurs through multiple mechanisms whose relative importance depends on particle size and local flow conditions. The existence of the most penetrating particle size (MPPS) around 0.1-0.3 um has profound implications for air filtration and respiratory health. Understanding these mechanisms is essential for designing effective air cleaning systems and understanding aerosol exposure pathways.