Adjust particle size, density, and temperature to calculate Stokes settling velocity, Brownian diffusion coefficient, Cunningham correction factor, and Stokes number in real time. Visualize dominant deposition mechanisms by particle size range.
Particle and medium conditions
Presets
Deposition mechanism: —
Results
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Stokes settling velocity vs (mm/s)
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Cunningham correction Cc
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Diffusion coefficient D (m²/s)
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Stokes number Stk
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Reynolds number Re
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Relaxation time τ (ms)
Settling Velocity vs Diameter
Particle diameter 0.01-100 μm and Stokes settling velocity on a log scale. The dot marks the current setting.
Mech
Relative strength of dominant deposition mechanisms by particle-size range: diffusion, gravitational settling, and inertial impaction.
Sens
Change in settling velocity and diffusion coefficient with temperature (10-80°C) for the current particle diameter.
Theory & Key Formulas
Stokes settling velocity with Cunningham correction:
Fundamentals of Aerosol Engineering — Understanding Through Conversation
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What is an 'aerosol'? Is it the same as fog?
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It's a general term for tiny solid particles or liquid droplets suspended in air. Fog is a type of liquid droplet aerosol. Cigarette smoke (solid particles + droplets), yellow dust (solid), and mist from medical inhalers are all aerosols. In engineering, the main focus is on particle sizes from 1 nm to 100 μm, which are deeply related to air pollution, cleanrooms, inhalation drugs, and filter design.
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Does the settling speed vary a lot with particle size? Why do smaller particles stay suspended longer?
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Stokes' settling velocity is vs = d²(ρp-ρf)g/(18μ), which is proportional to the square of the particle diameter. A 10 μm particle settles 100 times faster than a 1 μm particle. Small particles have very little weight, so they are supported by air's viscous forces and also affected by Brownian motion (thermal agitation), making them slow to settle. That's why PM2.5 (2.5 μm or smaller) lingers in the atmosphere for a long time.
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What is the Cunningham slip correction factor? Why is it needed?
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Stokes' law treats the fluid as a 'continuum,' but when the particle size approaches the mean free path of air molecules (about 65 nm at room temperature and pressure), that assumption breaks down. For particles below 100 nm, 'slip flow' occurs relative to air molecules, and the actual drag becomes smaller than predicted by Stokes' law. By multiplying by the Cunningham correction factor Cc ≥ 1, we get a faster settling velocity and a larger diffusion coefficient.
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I hear particle size is really important for inhalation drugs. Why is that?
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Because the deposition site in the lungs changes significantly with particle size. Particles above 10 μm are captured in the nasal and oral cavities. 5–10 μm reach the bronchi. 1–5 μm (MMAD, mass median aerodynamic diameter) can reach the terminal bronchioles and alveoli. Inhalation drugs target this 1–5 μm range. Particles below 0.5 μm reach the alveoli but are easily exhaled, reducing efficiency. That's why the design of metered-dose inhalers (MDIs) requires very precise particle size control.
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What is the 'Stokes number' that's important in cleanrooms?
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The Stokes number Stk = τU/L (τ: particle relaxation time, U: flow velocity, L: characteristic length) is an indicator of whether particles can follow a curved airflow. When Stk >> 1, particles continue straight and collide with walls even when the flow turns (inertial impaction deposition). When Stk << 1, they follow the flow and pass over surfaces. Cleanroom filters combine inertial impaction, diffusion, interception, and electrostatic attraction to capture particles.
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How do you simulate aerosol deposition with CFD?
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There are two main approaches. ① Lagrangian particle tracking (DPM: Discrete Phase Model): Tracks individual particle trajectories. High accuracy for inertial impaction and gravitational settling. ② Eulerian method (solving convection-diffusion equations): Treats particles as a continuum and calculates concentration distribution. Suitable for diffusion deposition. OpenFOAM's lagrangianParticle and Fluent's DPM model are used in practice. They are applied to predict particle deposition in respiratory airways, factory ducts, and cleanrooms.
Frequently Asked Questions
The particle Reynolds number Re = ρf × vs × d / μ < 1 is valid in the Stokes flow regime. For d < 50 μm (in air, standard density particles), it is generally applicable. When Re > 1, flow separation occurs and Stokes' law overestimates drag. For larger particles, corrected drag coefficient models such as Schiller-Naumann are used.
PM10 (particle diameter < 10 μm) deposits in the nasal cavity to bronchi. PM2.5 (< 2.5 μm) can reach the bronchioles and alveoli, potentially entering the bloodstream. WHO guidelines (2021 revision): PM2.5 annual mean 5 μg/m³, daily mean 15 μg/m³. PM10 annual mean 15 μg/m³. Japan's environmental standards: PM2.5 annual mean ≤ 15 μg/m³, daily mean ≤ 35 μg/m³.
HEPA filter collection mechanisms are diffusion (small particles), interception, and inertial impaction (large particles). Diffusion is more effective for smaller particles, inertial impaction for larger ones, and the intermediate size around 0.3 μm is the most penetrating particle size (MPPS). HEPA standards (JIS) require a collection efficiency of 99.97% or higher at this 0.3 μm size.
For hood design near a source, the Stokes settling velocity by particle size allows calculation of the minimum face velocity required to capture particles before natural settling. Particles ≥ 10 μm settle quickly and can be captured even at low face velocities, while particles ≤ 1 μm are dominated by Brownian diffusion, making it important to entrain them in the exhaust flow. Use the settling velocity and Stokes number from this tool as design references.
This is a mechanism where charged particles are attracted to a surface by an electric field. Airborne particles are often naturally charged, following the Boltzmann charge distribution. Electrostatic precipitators (ESPs) intentionally exploit this by charging particles with high voltage and depositing them on collection electrodes. They are used for dust control in cleanrooms and flue gas treatment in chimneys. This simulator does not calculate electrostatic deposition, but it is an important consideration in practical design.
CFD analyses using realistic geometries based on CT data of the upper respiratory tract (nasal cavity to trachea) are widely performed. Airflow is computed using LES (Large Eddy Simulation), and particles are tracked using the Lagrangian method. This is used for in silico evaluation in inhaler device design and pharmaceutical regulatory submissions (FDA/EMA guidance). Optimizing the deep lung deposition efficiency for particles in the 0.5–5 μm range is a central research topic.
What is Aerosol Deposition?
Aerosol Deposition is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind Aerosol Deposition Calculator. Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind Aerosol Deposition Calculator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.
Set particle diameter (sl_d) from 0.01 to 100 micrometers using the slider or numeric input (sl_dNum)
Adjust particle density (sl_rp) between 1000 and 2500 kg/m³ via slider (sl_rpNum) for materials like polystyrene or silica
Configure absolute temperature (sl_t) from 250 to 350 K using slider (sl_tNum) to account for ambient or elevated conditions
Input air velocity (sl_u) from 0 to 2 m/s with slider (sl_uNum) representing bulk flow conditions in ducts or chambers
Click calculate to obtain Stokes settling velocity, Brownian diffusion coefficient, and Cunningham correction factor
Worked Example
For pharmaceutical inhalation studies: 5 micrometer polystyrene particles (density 1050 kg/m³) at 298 K in quiescent air (0.1 m/s). The calculator yields Stokes velocity approximately 0.055 cm/s, Brownian diffusion 4.2×10⁻⁶ cm²/s, and Cunningham factor 1.16. In a 10 cm settling chamber, particles deposit in roughly 180 seconds, critical for dry powder inhaler formulation validation.
Practical Notes
Sub-micrometer particles (0.01-0.1 μm) show dominant Brownian diffusion; use low velocities to maximize residence time in deposition devices
Cunningham slip correction becomes significant below 1 micrometer—essential for accurate filtration and electrostatic precipitator design
Temperature affects air viscosity and diffusivity; elevated conditions (320+ K) accelerate diffusional transport in pharmaceutical aerosol chambers
Validate results against experimental TSI or cascade impactor data for your specific aerosol system