Filter Testing Simulator
Educational filtration scenarios — efficiency and pressure drop over time.
Calculator
Test dust
Filter efficiency curve
Operating conditions
Educational model with stated assumptions: the collection curve is a monotonic S-curve and does not reproduce the diffusion minimum (MPPS, ~0.1–0.3 µm) of fibrous filters; pressure drop assumes constant flow and an incompressible dust cake (Δp = Δp₀ + K₂·V·W); K₂ presets are illustrative, not certified values.
Theory & method
This simulator links three things a filtration test measures: the particle size distribution of the challenge dust, the gravimetric collection efficiency of the filter, and the growth of pressure drop as captured dust builds a cake on the medium. It is an educational model — every equation and assumption is stated below, and none of the outputs are certified performance data.
The filter is described by an empirical fractional-efficiency curve η(d) = η_min + (1 − η_min)·Φ(ln(d/d50)/ln σE), where Φ is the standard normal CDF, d50 is the size collected with 50% efficiency and σE controls how steep the transition is. This monotonic S-curve represents capture by sieving and interception. It deliberately does not reproduce the efficiency minimum caused by diffusion in fibrous media (the most-penetrating particle size, typically 0.1–0.3 µm): below that size real efficiency rises again, which this model cannot show.
The challenge dust is a mass-based size distribution: either a log-normal defined by its mass median diameter (MMD) and geometric standard deviation σg (the representation of ISO 9276), or a tabulated ISO 12103-1 test dust (A2 fine, A4 coarse) interpolated from the published cumulative curves. A2 is bimodal, which is why the standard grades are kept as tables instead of being forced into a log-normal fit.
The total gravimetric efficiency is the integral of the fractional efficiency weighted by the dust distribution, computed here as E = Σ wᵢ·η(dᵢ) over ~200 logarithmic size bins. Because the filter removes coarse particles preferentially, the penetrating dust is finer than the feed — the simulator reports the downstream mass median diameter to make that shift visible.
Pressure drop follows the classic linear cake-filtration model at constant flow (Darcy's law applied to an incompressible cake): the captured areal mass grows as W(t) = E·C_in·V·t and the pressure drop as Δp(t) = Δp₀ + K₂·V·W(t), a relation verified experimentally for HEPA media by Novick, Monson & Ellison (1992) and refined by Endo, Chen & Pui (1998). K₂, the specific cake resistance, depends strongly on the dust and the medium; the presets offered here are order-of-magnitude illustrations, not certified coefficients.
How to use
- 01Choose the test dust: a standard ISO 12103-1 grade (A2 fine or A4 coarse) or a custom log-normal defined by MMD and σg. Enter the inlet dust concentration in g/m³.
- 02Describe the filter with d50 (the particle size collected at 50%) and σE (curve steepness). Optionally add an efficiency floor for media that never drop to zero efficiency.
- 03Set the operating conditions: face velocity in cm/s, clean-media pressure drop Δp₀ in Pa, and a cake resistance K₂ preset — or enter your own K₂ value.
- 04Enter the test duration in minutes. Results update as you type: the fractional efficiency curve, the pressure-drop history, total efficiency, penetration and the upstream/downstream median sizes.
- 05Export the tables as CSV (raw values) or a PDF report with the efficiency chart. All model assumptions are printed in the report footer.
Frequently asked questions
Why doesn't the efficiency curve show a dip at small sizes (MPPS)?
Real fibrous filters collect very small particles by Brownian diffusion, so efficiency rises again below ~0.3 µm and the curve has a minimum (the most-penetrating particle size). This simulator uses a monotonic S-curve that only represents sieving/interception capture, so it understates efficiency below the MPPS. That limitation is stated instead of hidden — treat sub-micron results as out of the model's scope.
What is K₂ and why is it labelled "illustrative"?
K₂ is the specific resistance of the dust cake — how many pascals of extra pressure drop each g/m² of captured dust adds per m/s of face velocity. It varies by orders of magnitude with dust type, particle size, humidity and medium. The presets (20/200/2000 Pa·m·s/g) exist so the time behaviour is visible, not to represent any certified product; enter a measured K₂ if you have one.
Why is the downstream MMD smaller than the upstream MMD?
The fractional efficiency increases with size, so coarse particles are captured preferentially and the dust that penetrates is enriched in fines. The downstream mass median diameter is recomputed from the penetrating distribution wᵢ·(1 − η(dᵢ)).
Can I use these results for filter certification or compliance?
No. This is an educational simulator with a declared simplified model. Filter performance ratings come from standardized laboratory tests such as ISO 16889 (multi-pass, hydraulic filters), ISO 29463/EN 1822 (HEPA) or ASHRAE 52.2 — use certified test data for any engineering or compliance decision.
Normative references
- ISO 12103-1:2016 — Road vehicles — Test contaminants for filter evaluation — Part 1: Arizona test dust (A2 fine and A4 coarse cumulative distributions).
- ISO 9276-1 — Representation of results of particle size analysis (log-normal mass distributions).
- A. S. Novick, P. R. Monson, P. R. Ellison (1992). The effect of solid particle mass loading on the pressure drop of HEPA filters. Journal of Aerosol Science 23(S1).
- M. Endo, D.-R. Chen, D. Y. H. Pui (1998). Effects of particle polydispersity and shape factor during dust cake loading on air filters. Powder Technology 98, 241–249.
- H. Darcy (1856). Les fontaines publiques de la ville de Dijon — linear flow-resistance law underlying the cake model.