How to translate cascade impactor data easily starts by recognising that the instrument does not photograph or individually weigh particles while they fly past a sensor. A cascade impactor sends a controlled aerosol flow through a sequence of jets and impaction surfaces. Different particles depart from the airstream according to inertia, so collected material is apportioned into operational aerodynamic-size fractions. The mass on a plate or filter becomes a meaningful air concentration only after blanks, sampled volume, cutpoint behaviour and losses have been considered.
An impactor stage has a nominal cutpoint, often expressed as d50: the aerodynamic diameter at which 50% of the tested particles are collected by that stage under calibrated conditions. It is not a perfect gate where one side is collected and the other side entirely escapes. Each stage has a collection-efficiency curve, and the aerosol changes as it passes through preceding stages. Particle bounce, wall deposition, evaporation and flow error can distort the apparent size distribution even when the weighing balance operates perfectly.
This guide shows what the instrument really separates, how to translate aerodynamic diameter into plain English, how to calculate stage concentrations, and how to recognize mistaken comparisons with PM2.5, APS or SMPS results. Every calculation here uses declared illustrative numbers, not unpublished measurements. The aim is to make a technical impactor report understandable without discarding the very qualifications that protect its meaning.
Start with inertia, not with a chart legend
An aerosol-laden gas must change direction when it approaches an impaction plate. Particles with sufficient inertia cannot follow every bend of the gas stream, so they continue towards the plate and may deposit. Smaller or more easily entrained particles follow the diverted flow and pass towards a subsequent, usually higher-velocity stage. This separation depends on particle aerodynamic behaviour, gas properties, nozzle geometry and flow. It is not equivalent to mechanical sieving through holes sized to the particle diameters printed on the data sheet.
If a manufacturer labels a plate as a ‘2.5 micrometre stage’, that label should be read through its calibration curve and nominal cutpoint definition, not as a guarantee that every deposited particle measured exactly 2.5 µm. An incoming distribution spans sizes, and some particles above and below the nominal point can be recovered on that plate. The correct question is how the calibrated stage collection efficiency varies with particle size, not whether a single particle’s diameter matched the plate’s convenient name.
Why the cascade stages run from larger to smaller material
A multistage impactor generally removes easier-to-impact, aerodynamically larger particles upstream. Air then passes through successive nozzle stages designed to capture progressively smaller fractions. A backup filter, when present and functioning, collects a final downstream fraction that passes the previous plates, subject to the filter’s own collection efficiency and losses. The collection sequence does not mean that particles mechanically shrink while passing through the sampler; the upstream stages change what remains in the flow.
The order matters for interpreting stage masses. If a large amount lands on an early stage, later stages receive a depleted distribution, not an identical copy of the inlet aerosol. To derive a size distribution, each collected stage must be associated with the proper aerodynamic-size interval or efficiency-response model. Simply treating the plates as independent parallel samplers double-counts the conceptual supply of particles. The downstream stages are conditional on upstream separation and must be interpreted as one integrated sampling train.
Aerodynamic diameter is a property of motion
Aerodynamic diameter describes how a particle behaves in a fluid relative to a reference spherical particle with an adopted density under defined conditions. It packages the effects of physical dimensions, effective density and shape into a useful motion-related size. An irregular dust particle and a dense compact particle can have similar aerodynamic diameters without having identical geometric diameters or chemical identities. A plotted aerodynamic-size distribution therefore does not reveal particle morphology by itself.
For a teaching comparison, consider a porous particle and a compact particle of the same geometric width. Different effective densities and shapes can produce different inertial responses at the same gas flow. An impactor separates by that response, whereas an SMPS primarily measures electrical mobility and an optical counter uses scattering behaviour. Never rewrite aerodynamic diameter as an unqualified physical particle width when comparing those systems. The noun after the word diameter matters because it tells the reader which measurement process produced the number.
The meaning of a 50% collection cutpoint
At a given d50, a reference population of that aerodynamic diameter has 50% collection efficiency on the calibrated stage, after applying the definition used for that method. Particles substantially larger are generally collected with greater efficiency, while smaller ones are usually more likely to pass, but the transition is not an ideal mathematical step. The curve’s steepness is a property of the design and operating conditions. A sharp-looking nominal boundary on a figure may conceal overlapping collection probabilities.
Imagine a purely illustrative stage whose measured efficiency at 2.0 µm is 15%, at its nominal 2.5 µm d50 is 50%, and at 3.0 µm is 85%. These numbers are chosen to show a graded response, not supplied as calibration for any product. A 2.4 µm particle is not magically assigned only downstream, nor is a 2.6 µm particle guaranteed to stay on the plate. A technically responsible stage label identifies the calibration flow and cutpoint while leaving room for the real transition curve.
Flow rate is a physical calibration parameter
The velocity through a stage’s nozzles affects the inertia needed for deposition. If operating flow differs from the calibrated value, collection efficiency and effective cutpoints may shift. Flow also determines the sample volume used to convert deposited mass into ambient concentration. A report should therefore contain actual flow measurements, not just a nominal pump setting. Changes in filter loading, tubing pressure and atmospheric conditions can influence the flow achieved in practice.
For example, a nominal 10 L/min system operating at 9 L/min over ten hours samples 5.4 m³, not 6.0 m³. If 54 µg of blank-corrected material were collected and no further corrections were needed, the reported concentration should be 54/5.4 = 10 µg/m³. Dividing by the nominal 6.0 m³ would instead produce 9 µg/m³ and systematically understate the value by 10% relative to the correct 10. This is a denominator error, not an issue of analytical balance sensitivity.
Read a complete collection-efficiency curve
A cutpoint is a convenient summary, but a properly characterized impactor stage has an efficiency curve, sometimes influenced by particle properties and the measurement procedure. A stage may show a less-than-perfect maximum collection fraction or an unexpected efficiency tail. Its calibrated curve allows a distribution reconstruction more faithfully than a diagram with vertical boundaries. Under some research conditions, inversion or response-matrix methods are used to account for overlaps and losses rather than treating every deposited mass as belonging to one exclusive interval.
This matters especially when the incoming distribution is narrow and lies near a stage boundary. A tiny shift in aerodynamic size can redistribute material between adjacent plates without a large change in total aerosol mass. If one day’s 2.5 µm stage decreases while the adjacent stage increases, the plume may have changed size, the flow may have shifted or a deposition artifact may be present. Do not infer an environmental removal process from one stage’s movement until the entire collection train has been examined.
Stokes number: the reason velocity and nozzle size matter
The Stokes number compares a particle’s tendency to continue its motion with the characteristic timescale or dimension of the gas-flow change. In simple impactor design reasoning, it incorporates particle aerodynamic properties, nozzle velocity, gas viscosity and characteristic jet dimension. Greater particle inertia relative to the turning airflow tends to favour impaction. The exact relationships require attention to particle slip correction, Reynolds number, nozzle geometry and the calibrated design rather than an unqualified formula copied across instruments.
For readers outside fluid mechanics, the everyday analogy is a heavy object resisting a sharp turn, but the analogy has limits: microscopic particles experience drag differently from large projectiles, and particle density, shape and the gas properties matter. Describe the mechanism through momentum and flow diversion, then return to the actual efficiency calibration for numerical interpretation. A neat theoretical value cannot override a measured efficiency curve that includes nonideal losses, nozzle conditions and particle behaviour.
The backup filter has a bounded meaning
A downstream backup filter may collect particles that passed the preceding impaction stages. Its mass is a portion of the same original inlet aerosol after upstream collection and any transport losses. Calling this the ‘nanoparticle concentration’ is unsafe without knowing the final cutpoint, diffusion losses, filter efficiency and size distribution. It can contain material from overlapping tails of the preceding efficiency curves, and some particles may be lost before reaching it.
A backup filter also needs its own blank, conditioning and handling procedure. If its net gain is only a few micrograms, small balance drift, transport contamination or volatile losses can materially affect the calculated fraction. The phrase ‘not captured on the plates’ is closer to the operational truth than ‘all particles below a sharp diameter’. A report should state whether the backup is a physical filter, its type, collection protocol and whether the blank correction is based on matched field materials.
Plate bounce and re-entrainment
A particle striking an impaction surface may not remain there. Dry, hard particles can bounce and be carried further downstream, causing an apparent transfer from a larger aerodynamic-size fraction to a smaller one. Deposited material can also be re-entrained under changing flow or excessive loading. Some systems use coatings, special substrates or alternative surfaces to improve retention; those interventions can themselves affect chemical recovery or gravimetric analysis. Method choice must match the intended particle and analytical task.
An example illustrates the interpretation danger. Suppose a stage that should collect much of a coarse mode instead retains only 70% of incident mass because of hypothetical bounce. The remaining portion may contaminate a smaller-stage deposit or be lost. A downstream rise does not necessarily mean that atmospheric fine-particle mass rose; it may be an artifact created inside the instrument. To diagnose it, inspect substrate condition, load, flow, collection efficiency, chemical signatures and suitable laboratory checks rather than merely adjusting a plotted histogram until it looks smooth.
Wall losses remove material without appearing on a plate
Some particles deposit on the inside walls, nozzle backs or other internal surfaces rather than the intended collection substrates. That material may be omitted from the analyzed stage mass, biasing the reconstructed concentration low and potentially distorting the distribution. Wall losses depend on design and particle characteristics, and small particles can be especially subject to diffusion-related losses through a long or complex path. The relevant question is whether the stated method quantified those losses or bounded them experimentally.
The reviewed research on round-nozzle impactor design discusses losses on internal surfaces and the implications of geometry and particle properties. This is not a license to borrow a single literature percentage as a universal correction. A laboratory assessment may use controlled particles to characterize the particular impactor at its operating flow. If no correction is validated, a published distribution should state that wall losses could affect recovery. The missing mass must not be silently treated as having passed into the atmosphere untouched.
Evaporation and semivolatile particles
Collected ammonium nitrate and some organic material may evaporate from a substrate during a long collection, especially as temperature, pressure or gas composition changes. In a reduced-pressure impactor, evaporative behaviour can differ from ambient conditions. This can make measured substrate mass lower than the amount that initially reached the surface. The downstream filter may not simply catch the evaporated molecules as particles; they may remain in gas phase or be lost by other mechanisms.
If nitrate mass on a plate declines during a warm sampling period, the analyst should consider whether this reflects ambient nitrate change or sampler partitioning artifacts. The chemistry of collected material, sampling duration, substrate temperature and later storage all matter. Comparing a cascade impactor with an AMS can help, but the AMS has its own vaporization and collection-efficiency assumptions. Two imperfect instruments do not automatically make a perfect reference by agreeing or disagreeing with one another.
Hygroscopic growth and the meaning of dry size
Atmospheric particles can take up water as relative humidity rises. Their aerodynamic behaviour can therefore change with conditioning and humidity, even if dry solute mass stays similar. A sampling inlet that dries the aerosol may select a different apparent size distribution from one admitting humid ambient particles. The impaction surface itself may collect water under some conditions or lose water during conditioning before weighing. Distinguishing wet aerosol properties from dry filter mass is essential.
Consider a hygroscopic particle that grows in diameter upon humidification. Its mass, effective density and shape properties may change with water content; the relation to aerodynamic behaviour must be evaluated rather than calculated solely from geometric diameter. If the study reports stage cutpoints calibrated with dry test material, the reader should check how ambient humidity was controlled. Link this question with the verified HTDMA growth-factor guide, which discusses why water uptake changes apparent particle dimensions without requiring proportional changes in dry chemical mass.
Gravimetric mass needs conditioning and blanks
A gravimetric result uses the difference between post-sampling and pre-sampling mass of a collection substrate, usually after a specified conditioning process. A blank-subtracted mass is then divided by sampled air volume. The blank may account for handling, transport or laboratory background, and its uncertainty can be proportionally large when sample mass is small. Balance precision is important, but so are stable temperature, humidity, static charge, substrate identification and evidence that collected material remained on the substrate.
Suppose a stage’s initial conditioned mass is 30.0000 mg and its final mass is 30.1000 mg, giving 0.1000 mg = 100 µg apparent gain. A matched blank gains 0.0100 mg = 10 µg. The corrected stage mass is 90 µg. If sampled volume is 14.4 m³, the concentration assigned to that stage is 90/14.4 = 6.25 µg/m³. This calculation is valid only if the balance results, matched blanks, sampling time and volume describe the same stage and procedure. It does not correct bounce or wall losses automatically.
Chemical recovery differs from substrate mass
Some studies use impactor substrates for later elemental or ion analysis rather than only gravimetric mass. Recovery then involves extraction efficiency, digestion, laboratory blanks, analyte stability and the distinction between dissolved or extracted material and total collected material. A chemically measured sulfate mass does not equal the entire deposited stage mass, and some compounds may be transformed in storage or analysis. If a stage is coated for collection, the coating itself may interfere with particular chemical assays.
An analyst should ask whether the reported number is physical substrate mass, a concentration of one extracted ion, a sum of selected chemical species or an inferred total. The denominator may be sampled air volume, extract volume or substrate area depending on the table. To convert an extraction result, multiply solution concentration by extraction volume, apply validated dilution and recovery factors, subtract appropriate blanks and divide by air volume. Skipping any of these steps can produce values with plausible-looking units but incorrect physical meaning.
Sample volume: a full worked conversion
Suppose a hypothetical impactor runs at a verified constant 10 L/min for 24 hours. Its air volume is 10 × 60 × 24 = 14,400 L, or 14.4 m³. If one blank-corrected plate contains 144 µg of retained material, the corresponding stage concentration is 10 µg/m³. If a second stage contains 72 µg, it contributes 5 µg/m³ under the same air volume. The stage labels tell you which aerodynamic fractions are represented; the division by volume gives ambient concentration.
If flow fell during the day, use the integrated flow history instead of the simple multiplication. An instrument running for half the time at 10 L/min and half at 8 L/min samples 12.96 m³ over 24 hours, because the average flow is 9 L/min. For a mass of 144 µg, that denominator gives approximately 11.11 µg/m³, not 10. A difference in flow history can therefore change the concentration even when the collected mass is identical. Both numerator and denominator need provenance.
Build the stage mass sum without mixing definitions
Imagine a five-fraction simplified dataset with blank-corrected masses 8, 16, 30, 20 and 6 µg collected over an identical 2.0 m³ air volume. The retained total is 80 µg and the sum concentration is 40 µg/m³. Stage contributions are 4, 8, 15, 10 and 3 µg/m³. Their percentages of the retained sum are 10%, 20%, 37.5%, 25% and 7.5%, respectively. The fractions sum to 100%, which is an internal arithmetic check rather than proof all sampled particles were retained.
Notice the denominator in those percentages: total material measured on the included stages and backup. If wall losses or bounce caused unmeasured loss, the percentages describe only retained material. If the last filter is excluded from a chart but included in a table, the fractions no longer share the same denominator. A trustworthy figure caption states the included stages, backup policy, blank correction and whether apparent fractions have been adjusted using a calibrated collection-efficiency matrix.
Stage totals are not automatically dM/dlogD
A histogram may plot stage mass concentration, a differential mass distribution such as dM/dlog10(D), or normalized fractions per diameter interval. These forms have different units and must not be confused. If the stage width spans 0.30 decades in logarithmic diameter and contains 12 µg/m³, the approximate differential density over that interval is 12/0.30 = 40 µg/m³ per decade. Conversely, multiplying a differential value by its bin width recovers the concentration represented by that interval.
If two stages have different logarithmic widths, plotting their unnormalized concentrations as equal-width bars can misrepresent the distribution’s shape. The visually tallest bar may not indicate the largest concentration density. A correct chart either uses appropriate widths or clearly labels that each bar is a retained stage total. Reconstructing a continuous size distribution may require an inversion that considers overlapping efficiency curves rather than a rectangular histogram, especially near narrow peaks or cutoff thresholds.
Percentage of PM2.5 requires an independently aligned definition
It may be tempting to sum nominal stages below 2.5 µm and label the result PM2.5. But a reference PM2.5 method has its own inlet performance, conditioning and specified operating procedures. An impactor’s stage efficiency transitions and losses may differ. If a stage straddles 2.5 µm, one cannot simply count all its mass on one side of the threshold. A study may use calibrated cutpoint estimates to calculate comparable fractions, but the assumptions must be given explicitly.
Consider an impactor sum of 20 µg/m³ on stages provisionally classified as fine and a co-located reference PM2.5 measurement of 22 µg/m³. Their ratio 20/22 ≈ 0.909 is descriptive. It is not proof that 9.1% of particles bounced or were lost. The difference could involve size-response curves, semivolatile chemistry, measurement uncertainty, time mismatch and sampling artifacts. The correct next step is to test comparable intervals, valid flows, blanks and calibrated inlet response before proposing a mechanism for the 2 µg/m³ gap.
Compare with APS carefully
An aerodynamic particle sizer (APS) uses particle time-of-flight measurements to estimate size distributions in its calibrated range, whereas an impactor deposits particles according to inertial separation at multiple stages. Both use aerodynamic concepts, but their response functions, size coverage and measured outputs differ. An APS typically reports number-related size distributions from counted detection events; impactor plates commonly yield retained mass or chemical content. Number cannot be equated to mass without assumptions about particle size and effective density.
For a useful comparison, align size intervals, sampling conditions and time periods. Convert number to mass only with a stated particle property model, and account for counting efficiency and coincidence where applicable. A shared aerodynamic-diameter label is helpful but does not erase model and technique differences. Continue with the verified APS time-of-flight and coincidence guide when a graph of deposited stage mass is compared against a counted particle spectrum. A disagreement may be an interpretive clue rather than a defect.
Compare with SMPS carefully
An SMPS classifies particles by electrical mobility and reconstructs a number size distribution using charging and inversion procedures. A cascade impactor uses inertial deposition. Both can characterize an aerosol population, but the diameter metrics and primary y-axes often differ. Converting an SMPS number spectrum to mass requires effective density and morphology assumptions; the smallest particles may also be subject to diffusion losses in the impactor, while a particular SMPS may not cover an impactor’s coarse range.
When readers see two different peaks, they should first ask whether the plots share units, size definitions, sampling windows and corrections. The verified SMPS mobility-diameter guide helps unpack the other instrument’s inversion and multiple-charge questions. The comparison becomes scientifically meaningful only after converting between physical observables with appropriate assumptions. Merely aligning two x-axis scales in graphic software cannot accomplish that conversion.
Recovering a cumulative distribution
A cumulative mass distribution sums contributions below or above specified size boundaries. With impactor data, the direction depends on how stages are ordered and how their fractions are assigned, so carefully check whether a plot reads cumulative finer-than or coarser-than. If the total retained concentration is 40 µg/m³ and the two finest fractions contribute 10 and 3 µg/m³, their combined contribution is 13 µg/m³, or 32.5% of the retained total. That is a stage-based cumulative statement, not a precise universal fine-particle mass fraction.
The mass median aerodynamic diameter would correspond to the size at which half of the relevant mass lies on either side. Estimating it requires reliable stage interval assignments and often interpolation or a fitted distribution. If a cutpoint lies in a broad efficiency transition, a precise median may be model dependent. State whether the median is calculated from retained stage mass, a response-corrected distribution or some other representation. An extra decimal place cannot compensate for uncertain bin response.
Laboratory blanks and field blanks answer different questions
A laboratory blank tests background from handling and analytical processes under a specified workflow. A field blank can capture additional contamination from transporting and installing a substrate without normal sample collection. The appropriate subtraction depends on the protocol and can be decisive for low-mass or trace-chemical fractions. A negative blank-corrected result is not physically negative atmospheric mass; it indicates that signal, blank and uncertainty interact near a method’s ability to resolve a small net gain.
Suppose a stage gain is 12 µg and a matched field blank gain is 9 µg. The net result is 3 µg, but if each balance and blank determination has several micrograms of uncertainty, the positive point estimate may not establish a reliable above-background concentration. A responsible report includes method detection and reporting limits rather than celebrating an apparently precise 3.000 µg value. The correct choice of blank is part of the definition of the final result, not a detail to bury in supplementary material.
Spatial and temporal interpretation has limits
A 24-hour impactor sample integrates conditions across its collection duration. It may combine morning traffic, midday secondary aerosol and a distant overnight plume into one size-resolved average. If a nearby real-time sensor shows a short peak, the deposited sample generally cannot uniquely assign a separate chemical mass to that short interval. More frequent filters or a complementary real-time instrument may help, but the time support of each observation must be stated.
A strong event within a long sample can dominate total retained mass while remaining impossible to isolate temporally. To argue for a source, bring meteorology, source tracers, paired monitoring, appropriate temporal comparisons and uncertainty. A high coarse-stage mass is not by itself proof of construction dust; a high fine-stage mass is not proof of vehicle combustion. Particle size can narrow questions, but it does not uniquely identify source or chemical identity.
Diagnosing an unexpected fine-stage rise
Imagine a dataset where a nominally fine stage suddenly gains mass while the upstream coarse-stage value drops. Consider at least four alternatives before interpreting the change as atmospheric growth: actual aerosol-size redistribution, stage bounce from coarse particles, flow-related cutpoint movement, and changes in aerosol hygroscopic or volatile behaviour. The direction of a stage trend is an observation; the proposed process is a hypothesis. Independent physical evidence is needed to choose among plausible causes.
Check whether pump flow changed, whether deposits visibly overloaded or dried, whether substrates were coated, and whether the chemistry of the two stages is unexpectedly similar. Repeating a controlled laboratory comparison may distinguish retention artifacts from real aerosol variation. If the data do not include sufficient checks, write that the shift is consistent with multiple processes and mark the uncertainty. Such an explanation helps the reader more than selecting a dramatic story solely because it fits the chart.
Diagnosing poor mass closure across the collection train
If a co-located total particulate measurement is higher than the summed impactor retention, compare the physical size ranges and inlet conditions before calling the difference a loss fraction. Then examine blanks, balance conditioning, wall losses, particle bounce, semivolatile loss, filter recovery and collection-efficiency response. A poorly matched optical PM estimate is not automatically a reference mass. The method by which the comparison number was derived belongs in the audit.
Suppose an impactor retains 75 µg across all stages while a comparable independent sampler suggests 90 ± 10 µg during the same period. The difference is 15 µg, but the uncertainty and operational mismatch may be substantial. A retained-to-comparison ratio of 0.833 does not by itself prove 16.7% internal loss. Report the ratio as a diagnostic and state what physical measurements are required to close the balance. If stage chemistry is being studied, cross-check selected ions or elements as additional independent evidence.
Reconstructing a size distribution is a modelling act
A response-matrix inversion can distribute mass over size bins while accounting for overlap among stage collection curves. Such a procedure may improve the physical description, but it introduces a model and sometimes regularization choices that affect smoothness and peak location. A plotted smooth curve should not be described as more directly observed than the actual plate masses. Readers deserve to know whether they are seeing measurements, reconstructed concentrations or a fitted parametric distribution.
For a narrow mode near a boundary, two different regularization settings might produce slightly different peak shapes while explaining the same plate measurements. If conclusions about sources or health exposure depend on a specific narrow peak, quantify that sensitivity. A reliable report can show raw stage masses in a table alongside the reconstructed curve. This lets the audience distinguish the data from the mathematical transformation and prevents a smooth line from concealing underdetermination.
Transfer problem: check a missing volume conversion
An illustrative impactor collects 180 µg of blank-corrected material during six hours of constant verified 12 L/min sampling. Calculate the sampled volume in cubic metres and the mass concentration. Then explain why dividing by 72 rather than the correct number of cubic metres would be incorrect even if the resulting unit were typed as µg/m³. This exercise is about recovering the actual physical denominator rather than relying on a spreadsheet label.
Solution: 12 L/min × 60 min/h × 6 h = 4,320 L = 4.32 m³. Concentration is 180/4.32 ≈ 41.67 µg/m³. The mistaken number 72 comes from mixing the units: 12 × 6 yields litre-minutes per hour without converting hours to minutes. A cell can be labelled with any text while its arithmetic remains dimensionally invalid. Write a full unit chain during checks so the cause is obvious and independent readers can reproduce the answer.
Transfer problem: interpret an impactor stage histogram
A simplified, blank-corrected set of stage concentrations is 2, 6, 9, 5 and 3 µg/m³. Find the retained sum and determine the fractional contribution of the third stage. Then explain why the third stage’s percentage should be labelled as a fraction of retained impactor mass rather than a percentage of all ambient PM10. Finally, name one reason the true distribution near that stage’s boundaries may be more complex than the bar appears.
The retained sum is 2 + 6 + 9 + 5 + 3 = 25 µg/m³. The third stage contributes 9/25 = 36%. It is 36% of the measured retained sum under the stated corrections. PM10 has a separate inlet and reference definition; the impactor could have missed material through walls, bounce or a different upper size range. Its cutpoint is a graded collection curve, not an infinitely thin division. The arithmetic is easy; the scientifically meaningful part is resisting an unsupported denominator.
Transfer problem: determine a log-size density
A stage holds a concentration of 15 µg/m³ across an illustrative logarithmic diameter interval of 0.25 decades. Estimate the average dM/dlog10D value over that interval and state the units. Explain why that value must not be added directly to a stage’s total µg/m³ without first accounting for its width. Then identify an assumption that could limit this rectangular approximation for a real impactor.
The average differential concentration is 15/0.25 = 60 µg/m³ per decade. Multiplying that differential value by 0.25 decades returns the 15 µg/m³ bin contribution. Differential values from bins of unequal widths cannot be summed as if they were bin totals. The rectangular approximation assumes a suitable effective assignment of the mass to that interval; actual impactor response curves overlap, and wall losses or bounce can bias retained mass. The stage width and calibrated efficiency profile matter to the reconstruction.
Transfer problem: calibrations can invert an apparent trend
Suppose an impactor’s nominal flow is 10 L/min for both sample days. On Day A the actual flow is 10 L/min for 10 hours and retained mass is 100 µg. On Day B the actual flow is 8 L/min for 10 hours and retained mass is 90 µg. Calculate mass concentrations and decide whether the concentration increased or decreased despite lower collected mass. Use litres-to-cubic-metres conversion and ignore other losses only for this illustration.
Day A sampled 6.0 m³ and yields 100/6.0 ≈ 16.67 µg/m³. Day B sampled 4.8 m³ and yields 90/4.8 = 18.75 µg/m³. Concentration increased even though collected mass fell, because the second sample passed less air. It would be wrong to infer declining ambient mass from substrate gain alone. Flow histories, durations, efficiency and handling are inseparable from the concentration calculation. This exercise is directly transferable to filter samplers, canisters and many environmental measurement methods.
Practical questions that reveal hidden assumptions
Is a stage d50 a guaranteed cutoff? No, it marks 50% collection on the relevant calibrated curve. Is the backup filter all nanoparticles? Not necessarily, because earlier stages, downstream efficiency and losses matter. Can retained stage mass be summed? Yes, with compatible blanks and sampling volume, but the sum may not represent all inlet mass. Is aerodynamic size the same as geometric or mobility size? No, unless a validated conversion and particle property model justify that description.
Does an impactor identify the source of the aerosol? Size separation alone does not. Does chemical extraction automatically recover all retained material? No, recovery and analyte stability must be checked. Does a high downstream mass prove fine particles increased outdoors? Not without evaluating bounce, wall losses, humidity and flow. Can two samplers with nominal 2.5 µm labels be interchanged? Their collection-efficiency curves and regulatory method definitions must first be compared. These questions turn vague instrument vocabulary into practical checks.
Translate the result without erasing uncertainty
A useful public description might read: ‘During the specified interval, the cascade impactor retained 25 µg/m³ of blank-corrected material over its analyzed stages. Approximately 36% of that retained sum was assigned to its third operational fraction. The nominal aerodynamic cutpoints and potential deposition losses limit how precisely these values describe the full ambient size distribution.’ This is clearer than calling a stage ‘all particles of one diameter’ or assigning a source without evidence.
All data in this article’s exercises are teaching numbers. For broader particle methods, continue into the verified APS aerodynamic time-of-flight guide, SMPS mobility distribution guide and eduKate exact-language guide. Different operational measurements can become more informative when their boundaries are preserved rather than flattened into one supposed particle size.
Original methodological sources and reading
Demokritou and colleagues, Development of a High Volume Cascade Impactor, indexed by US EPA
US EPA, Ambient Air Monitoring Quality Assurance
ISO 10473:2000, background on beta-ray mass versus sample volume and size-selective inlets