Compute settling velocity, diffusion coefficient, Stokes number, Cunningham correction, aerodynamic diameter, and lung deposition fraction for particles from 0.01 to 100 μm in real time.
What exactly is "settling velocity"? I see it's the first output in the simulator, but what's it telling me?
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Basically, it's the constant speed a particle reaches when the force of gravity pulling it down equals the drag force from the air resisting its fall. In practice, for tiny aerosol particles, this speed is surprisingly slow. For instance, a 10-micron dust particle might settle at about 3 mm/s, meaning it would take over 5 minutes to fall 1 meter! Try moving the "Particle Diameter" slider in the tool to see how dramatically the speed changes with size.
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Wait, really? So for very small particles, they barely settle at all? What happens to them then?
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Exactly! For sub-micron particles, Brownian diffusion—random kicks from air molecules—becomes the dominant transport mechanism, not gravity. That's why smoke seems to hang in the air. The simulator calculates a "Diffusion Coefficient" to quantify this. A common case is a 0.1-micron virus-laden droplet; its settling is negligible, but diffusion allows it to wander and potentially be inhaled. Change the diameter slider down to 0.1 µm and watch the settling velocity plummet while the diffusion coefficient value shoots up.
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I see the "Lung Deposition Fraction" output. How does the tool know if a particle gets stuck in someone's lungs? That seems complex.
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It uses the other calculated values—settling, diffusion, and inertia—to estimate the probability. In practice, each deposition mechanism targets a different particle size. Sedimentation catches mid-sized particles in the small airways, diffusion catches the very small ones, and impaction (related to the Stokes Number) catches large, fast-moving particles at airway bends. When you select different "Breathing Scenarios" in the dropdown, you're changing the flow conditions, which shifts which size particle is most likely to deposit. It's a key calculation for designing inhaler medicines or assessing air pollution risk.
Physical Model & Key Equations
The core equation governing gravitational settling for small, spherical particles in a fluid is the Stokes' law, corrected for very small particles where air can no longer be treated as a continuous medium.
Where $v_s$ is the settling velocity (m/s), $\rho_p$ is particle density (kg/m³), $\rho_f$ is fluid (air) density, $d_p$ is particle diameter (m), $g$ is gravity (9.81 m/s²), $\mu$ is air dynamic viscosity (Pa·s), and $C_c$ is the Cunningham slip correction factor.
The Cunningham correction factor is crucial for particles approaching the mean free path of air molecules (~0.066 µm). It accounts for "slip" at the particle surface, which reduces drag and increases settling speed compared to classic Stokes' law.
Here, $\lambda$ is the mean free path of air. For large $d_p$, $C_c$ approaches 1 (no correction). For a 0.01 µm particle, $C_c$ can be >20, meaning it falls over 20 times faster than standard Stokes' law would predict!
Frequently Asked Questions
Please check if the particle diameter is less than 0.01 μm or greater than 100 μm. Also, verify that the particle density or fluid density is not set to an extremely small value (0 or negative). If the values are entered correctly, the calculation results will be updated in real time.
It is important for fine particles with a diameter of 1 μm or less (especially 0.1 μm or less). In this range, particles are comparable in size to the mean free path of air molecules, so Stokes' drag law does not hold, and correction is necessary. This tool automatically calculates the factor from the Knudsen number and reflects it in the settling velocity and diffusion coefficient.
The lung deposition rate in this tool is a reference value based on a representative ICRP model. For actual assessment, factors such as breathing conditions (flow rate, frequency), particle shape, and hygroscopicity must be considered. We recommend using it only for relative trend understanding or educational purposes.
The Stokes number is a dimensionless number that indicates how well a particle can follow changes in flow. It is useful, for example, for evaluating particle collection efficiency in filters or impactors, or for predicting particle deposition in pipe bends. When the value is greater than 1, particles are less likely to follow the flow.
Real-World Applications
Pharmaceutical Inhalers: Drug efficacy depends on particles depositing in specific lung regions. Engineers use these dynamics calculations to design aerosol particles with the perfect size (often 1-5 µm) to maximize lung deposition via sedimentation and minimize exhalation.
Indoor Air Quality & Ventilation: Understanding how fast virus-laden aerosols settle or remain airborne informs ventilation guidelines and safe exposure times. For example, large droplets settle quickly, but sub-micron "aerosol" particles can drift across a room.
Industrial Emission Control: Scrubbers and filters are designed based on the size distribution of emitted particles. The Stokes number determines if a particle will impact on a baffle or follow the gas stream, guiding pollution control device design.
Climate Science: The lifetime of atmospheric aerosols (like sea salt or sulfate particles) in the air before they settle or are washed out by rain is governed by these dynamics. This residence time directly impacts their radiative forcing and effect on climate.
Common Misconceptions and Points to Note
First, there's the common assumption that "the particle density can always be taken as 1 g/cm³, the same as water". This can be quite misleading. For instance, between metal oxide dust (density ~4 g/cm³) and pollen (density ~0.5 g/cm³), the settling velocity for the same 10μm particle can differ by several times. Since deposition behavior in the lungs also changes, researching the actual density of the particles you're dealing with is the essential first step.
Next, there's the tendency to assume "air conditions are fixed at standard state (20°C, 1 atm)". At high altitudes (lower pressure) or in high-temperature environments, the air viscosity μ and density ρ_f change, affecting your calculation results. For example, at an altitude of 2000m, air density is about 80% of sea-level density, reducing buoyancy and slightly increasing the settling velocity. When simulating real-world conditions, remember to adjust the temperature and pressure parameters accordingly.
Finally, beware of the oversimplified interpretation that "a Stokes number (Stk) greater than 1 means the particle immediately falls to the floor". Stk is an indicator of behavior at airflow "bends". Even if a particle has high inertia, if its initial velocity is zero, its settling will be gradual. For example, a large particle (Stk>1) carried by ventilation duct airflow is more likely to impact the wall at a duct bend, whereas the same particle in still air would simply undergo Stokes settling. Get into the habit of considering how each parameter calculated by the tool applies within your specific flow field context.
Industrial hygiene standards reference impaction and sedimentation in the tracheobronchial region; validate results against ISO 12103-1 test dust (≈4 µm count median diameter)