MECH6019 Chap.6 Particle Behaviour and Size Distributions
Particle Behaviour and Size Distributions
Particle motion depends on diameter, density, shape and the surrounding gas. A settling calculation balances gravitational force, buoyancy and drag. After release, a particle accelerates until drag equals effective weight and terminal velocity is reached.
That velocity controls settling distance, residence time and the performance expected from devices that rely on gravity or inertia.
Stokes' law provides a simple terminal-velocity equation for spherical particles at sufficiently low Reynolds number. Velocity rises with the density difference and diameter squared, and falls as gas viscosity increases. The diameter-squared relationship makes sizing errors expensive.
The calculated velocity must be used to check Reynolds number afterwards because the regime assumption and result depend on each other.
Larger particles can leave the Stokes regime, making drag coefficient dependent on Reynolds number. The solution then becomes iterative: assume or estimate velocity, calculate Reynolds number, select the drag relationship, update the force balance and repeat until consistent.
Very small particles can require a slip correction because the continuum assumption becomes inaccurate relative to molecular motion. One equation therefore cannot span every size.
Irregular shape complicates geometric diameter. Aerodynamic diameter expresses the behaviour of a particle as an equivalent reference-density sphere, allowing collection and respiratory behaviour to be compared.
It is not necessarily the size seen by microscopy. Density and shape can cause equal geometric diameters to behave differently, so the diameter definition must accompany any distribution or device curve.
A distribution also needs a weighting basis. Number weighting emphasises abundant small particles. Mass weighting emphasises large particles because individual mass scales approximately with diameter cubed.
Surface weighting falls between them and can matter for reaction or adsorption. A mean diameter without its weighting can misrepresent the property relevant to a collector.
Work problems in the order force balance, regime check, diameter definition and distribution weighting. State assumptions before substitution and carry units through viscosity, density and diameter.
Finish by asking whether the predicted direction is physical: larger Stokes particles settle faster, denser particles settle faster, and more viscous gas slows them. If the direction fails, the algebra or basis needs review.
What this chapter covers
- 01
Terminal settling
- 02
Stokes law
- 03
Reynolds number
- 04
Drag coefficient
- 05
Aerodynamic diameter
- 06
Size-distribution weighting
Worked example · free
Scale Stokes settling velocity
- 1Use velocity proportional to diameter squared.
- 1Form the diameter ratio 2.
- 1Square it to obtain 4.
Key terms
- Terminal velocity
- Steady speed reached when drag balances effective weight.
- Stokes law
- Low-Reynolds-number relation for viscous drag on a sphere.
- Aerodynamic diameter
- Diameter of a reference-density sphere with equivalent aerodynamic behaviour.
- Slip correction
- Adjustment for small particles when continuum drag becomes inaccurate.
Particle Behaviour and Size Distributions FAQ
Why does diameter matter so strongly?
In the Stokes regime settling velocity scales with diameter squared, while particle mass scales approximately with diameter cubed. Small sizing errors can therefore change predictions greatly. Convert diameter units before applying the power and confirm that both compared particles remain within the same drag regime.
Why check Reynolds number afterwards?
The velocity is needed to estimate Reynolds number, but Reynolds number determines whether Stokes law was valid. The calculation is therefore followed by a regime check. If the assumption fails, use the appropriate drag correlation and iterate until velocity and drag coefficient agree.
Why do number and mass distributions differ?
A large population of tiny particles can dominate number, while fewer large particles dominate mass because each carries much more material. Surface weighting can emphasise another range, so every mean and distribution should state the property used for weighting.
Exam move
Practise proportional changes before full substitutions. Attach a validity line to every Stokes result and label the weighting of every distribution. Begin with the Stokes relationship and vary one property at a time: double diameter, change density difference or increase viscosity. Predict the direction and factor before using numbers. Convert diameter to metres before squaring and keep the unit line visible.
After calculating terminal velocity, estimate Reynolds number and write an explicit valid-or-invalid conclusion. If invalid, outline the iteration using drag coefficient rather than forcing the Stokes result to stand. Create a separate card for very small particles and the reason a slip correction appears. Compare geometric and aerodynamic diameter with examples of equal-size particles that differ in density or shape.
Next draw the same hypothetical aerosol as a number distribution and a mass distribution. Explain why abundant small particles dominate one while larger particles can dominate the other. Label every mean with its weighting and use log-scale thinking when sizes span orders of magnitude.
For device questions, identify which behaviour matters: settling velocity for gravity, inertia for cyclones or electrical migration for precipitators. In final revision, use a regime checklist beside each equation: spherical assumption, steady terminal motion, low Reynolds number and continuum validity. A correct substitution without this check is incomplete engineering reasoning.
