Why a UV Lamp's Dose Does Not Depend on the Flow

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Yes, and almost all of the benefit is the filter rather than the lamp. In the same airstream a MERV 16 filter does about 152 times as much per pass as a UV-C lamp does, and a HEPA stage about 412 times. More importantly, they are not doing the same job: a filter takes the particle out of the air, and UV leaves it exactly where it was with its DNA damaged. For dust, dander and pollen, which is most of what you want gone, the lamp contributes nothing, because most of that mass was never alive and inactivation is not removal.

There is a second and more interesting result underneath that one, and it applies to every UV device in water or air. The dose a UV lamp delivers to a whole system does not depend on the flow rate at all. The flow cancels, exactly, and the advice everyone gives about high flow is advice about something else.

Why the flow cancels

A UV dose is a fluence rate multiplied by an exposure time, measured in millijoules per square centimetre. In a treatment chamber the exposure time is the chamber's volume divided by the flow through it. So the dose each pass delivers falls in inverse proportion to the flow, which is where the usual worry comes from.

But the number of times the whole system passes through the chamber per unit time is the flow divided by the system volume, and that rises in exactly the same proportion. Multiply the two together and the flow disappears:

Cumulative dose rate equals fluence rate times chamber volume divided by system volume.

No flow term. The things that matter are the lamp's output, the chamber's size, and the volume of water or air you are trying to treat. What flow changes is whether anything gets left out, which is a different and genuinely important question.

The clarifier, and the number it does not publish

An Aquatic Eden 3W mini UV-C clarifier light for aquariums publishes a usefully specific set: 3 watts, UV-C, suitability for 10 to 20 gallon tanks and low bio-load setups up to 30, four timer modes of 3, 6, 12 and 24 hours, a pre-filter sponge, in-filter rather than in-tank placement, and a maker recommendation of 2 to 3 hour sessions 3 to 4 times weekly.

Take a representative chamber for a unit of that size: a 50 millimetre lamp of 8 millimetre diameter sitting in a 20 millimetre bore, which gives an annulus of 13.19 cubic centimetres and a mid-radius cylinder area of 21.99 square centimetres.

Now the figure that is missing, and it is the only one that matters. A low-pressure mercury lamp turns roughly 30 percent of its input into 254 nanometre light. A UV-C LED turns roughly 3 percent of its input into its emission band. So a 3 watt unit delivers either 0.9 watts or 0.09 watts of germicidal output, and the listing says only "3W UV-C".

Put those through the cancellation. On a 20 gallon tank, which is 75.7 litres:

The mercury reading gives a cumulative dose rate of 40.9 milliwatts per square centimetre times 13.19 over 75,700, which is 25.7 millijoules per square centimetre an hour. The LED reading gives 2.57.

Against a representative 30 millijoules per square centimetre for free-floating algae, the mercury version needs 1.17 hours and the LED version needs 11.7.

Which lands squarely on the product's own timer. The shortest mode is 3 hours, so on the mercury reading the shortest available setting delivers 2.6 times the target, and on a 2 to 3 hour session 2.6 to 3.9 times. On the LED reading the correct mode is the 12 hour one. A single unstated word about the lamp spans the entire range of settings the product offers. Full record in our review of the Aquatic Eden clarifier.

On the mercury reading the maker's schedule checks out with real margin, which is worth saying plainly. And the 30 gallon ceiling turns out to be in the right place too: at 113.6 litres the dose rate falls to 17.1 millijoules an hour, so a 2 hour session delivers 1.14 times the target rather than 2.6, which is exactly where a qualifier like "low bio-load" belongs.

One small oddity. The advice is 2 to 3 hour sessions and the four timer modes start at 3 hours, so there is no setting at the bottom of the recommended range. You can have the top of it or double it.

What flow actually does, demonstrated

A fishkeeper 4-in-1 submersible aquarium internal filter rated 135GPH publishes 135 gallons an hour with an adjustable flow, an 80 to 300 gallon range, a biochemical sponge, a magnetic rotor, four suction cups, a rain shower pipe and an air hose. Its own drawbacks are honest and relevant: "135GPH is modest for the top of its range."

Run the clarifier in that filter's flow. 135 gallons an hour is 511 litres an hour, which is 141.9 millilitres a second, so a 13.19 cubic centimetre chamber gives a residence time of 0.0930 seconds. On the mercury reading the per-pass dose is 40.9 times 0.0930, which is 3.80 millijoules per square centimetre: 7.9 times short of a 30 millijoule target.

Run it instead in a canister-class 581 gallons an hour. The residence time falls to 0.0216 seconds and the per-pass dose to 0.883, 34 times short.

A factor of 6.6 in per-pass dose. And the time to reach any cumulative target is 1.17 hours in both cases, because the faster flow sends the water round 6.6 times more often.

So the per-pass dose, which is the number everybody worries about, is not the number that decides the outcome on a tank. What does decide it is the three terms in the cancellation, and the only role flow plays is in the two conditions the cancellation requires.

The first is no bypass. Water that never enters the chamber receives zero dose, and no number of passes helps it. The second is mixing: the cancellation assumes every litre is equally likely to be the next one through, and a tank with dead corners violates that. Both of those are genuine arguments for strong circulation, and neither is an argument about dose.

The correction, in our own words and the maker's

Our guide to using a UV clarifier to keep aquarium water clear puts it like this, under a heading that says it twice: "Install it in high flow. UV needs water passing close to the lamp to work. Place the unit in a sump, top filter box, or external chamber where flow is strong. Slow or bypassed flow wastes the effect."

Three of those four sentences are right and one is the wrong way round. Water does need to pass close to the lamp, because UV is absorbed by water and the fluence rate falls steeply with distance from the tube. Bypassed flow genuinely does waste the effect, for the reason above. A sump or filter chamber is the right place, because that is where the water is confined near the lamp.

But "where flow is strong" is not an argument about dose, and "slow flow wastes the effect" is the opposite of the per-pass arithmetic and irrelevant to the cumulative arithmetic. Slow flow raises the per-pass dose and lowers the number of passes, and the product of the two is unchanged. The sentence that would be right is about mixing: enough flow that no part of the tank is left unvisited, and no particular benefit beyond that.

The product listing says the same thing in its own voice, and its drawbacks repeat it: "Results depend heavily on high-flow placement." That claim is doing two jobs, one correct and one not, and the correct one is about geometry rather than speed.

Here is the honest limit on all of this, and it is the reason the cancellation is a model rather than a law. It assumes first-order inactivation with no recovery between exposures. Organisms do repair ultraviolet damage, by photoreactivation in visible light and by dark repair, so fifty passes at a fiftieth of a dose is not strictly the same as one pass at the whole dose. No listing in this category publishes anything about repair, and neither does any reasonable product description, so this page does not attempt to quantify it. What can be said is the direction: repair makes the per-pass dose matter somewhat, so very high flow is not perfectly free, and the right reading of the cancellation is that flow is a weak variable rather than a strong one.

Now the air, which is where the question started

A TOOLBOOX 970CFM air scrubber publishes up to 970 cubic feet a minute through three-stage HEPA-grade filtration, a rotomolded polyethylene shell, an auto-foldable handle, lockable 360 degree wheels, a stackable design, negative air operation, and "Built-in UV-C light technology" that "works alongside the filtration". It publishes no UV wattage and no wavelength, which means the dose cannot be computed from the listing at all.

So take a representative lamp. Ten watts of input at 30 percent gives 3 watts of UV-C, spread across a duct section of 0.3 by 0.3 metres and half a metre long, which is 0.045 cubic metres with a 1,500 square centimetre illuminated plane. That gives a fluence rate of 2.0 milliwatts per square centimetre.

At 970 cubic feet a minute, which is 0.4577 cubic metres a second, the residence time in that section is 0.0983 seconds, and the per-pass dose is 0.197 millijoules per square centimetre. Against a 10 millijoule target for ordinary bacteria that is 51 times short.

Run the cancellation on a 50 cubic metre room and the cumulative dose rate is 2.0 times 0.045 over 50, which is 6.48 millijoules per square centimetre an hour, so an hour and a half to reach 10 millijoules. On its own that does not sound hopeless.

It is hopeless in context, and the context is the filter sitting in the same duct. Convert both stages to log reduction, which is the only common currency. At a representative rate constant of 0.1 square centimetres per millijoule, a 0.197 millijoule dose leaves 98.05 percent of organisms viable, which is 0.00855 logs per pass. A MERV 16 filter removes about 95 percent of particles in the critical size band, which is 1.301 logs. A HEPA stage at 99.97 percent is 3.52 logs.

So the MERV 16 does 152 times what the lamp does per pass, and the HEPA stage 412 times. The lamp is adding about 0.7 percent to what the furnace filter already achieves.

And the decisive point is not that ratio. A filter removes the particle from the air; UV leaves it in the air with damaged DNA. Dust, dander, pollen, skin flakes and combustion particles are not alive and never were, so UV does not act on them at all. Our page on why an air cleaner's square footage is a time works out what air changes buy against particles, and our pages on why a bag is the filter and a cyclone is not and why two 5 micron filters are not the same filter work out what filtration efficiency means. Between them they are the answer to the original question, and the UV lamp is a rounding error on it.

Three bands, three jobs, one published wavelength

Germicidal action follows the absorption spectrum of DNA, which peaks near 265 nanometres. The 254 nanometre mercury line sits close enough to that peak to be the industry standard, which is why UV-C means what it means.

A 365nm rechargeable UV black light flashlight for pet urine publishes the wavelength explicitly, and argues for it: the maker states its 365 nanometre LED gives purer, more uniform output and far greater accuracy than a 395 nanometre flashlight. That is correct, and the reason is worth stating. Shorter-wave UV-A excites more organic fluorophores while emitting less visible violet of its own, so the stain glows against a darker background and the contrast is better.

It is also, at 365 nanometres, below a thousandth of the germicidal peak in effectiveness. The photon energy is 1,239.8 electronvolt nanometres divided by 365, which is 3.40 electronvolts, against 4.88 at 254: a ratio of 1.437 in energy per photon, and a far larger ratio in what the photons do, because DNA simply does not absorb much at 365. So this light is about a thousand times less germicidal per watt than the clarifier above, and that is not a defect. It is the correct band for fluorescence, and the listing is unusually clear about which band it is in. Our page on why red light does not ruin your night vision makes the same kind of argument at the other end of the spectrum, where a wavelength rather than an intensity decides the outcome.

A Pestrols indoor LED bug zapper and insect trap publishes energy-efficient LED light tubes, a built-in timer, a remote with dimmable lighting modes, soft eye-friendly lighting, flame-resistant ABS, and no wavelength at all. Which for a light trap is the whole mechanism, because what a light trap does is exploit phototaxis, and phototaxis has a spectrum.

Fly and moth attraction peaks somewhere around 350 to 400 nanometres, which is the same UV-A band as the urine light and not the germicidal band. So all three of these products are called ultraviolet devices and two of the three are in a band that inactivates nothing, which is correct for their jobs and invisible from their listings.

Its drawbacks get the important limitation right: "Light traps are less reliable for mosquitoes." That is true and the reason is that mosquitoes orient on carbon dioxide, body heat and skin volatiles rather than on light, so a photon-based trap is working on the wrong sensory channel entirely. A trap aimed at mosquitoes needs a carbon dioxide or heat lure, and this one does not claim to have either.

There is one more thing in that feature list that is not what it looks like. A light trap's catch rate scales with its radiant flux, because the flux sets how far away an insect can detect it and the catchment area goes as the square of that distance. So the dimmable remote is a capture rate control wearing a comfort label. Turning it down for the bedroom is a perfectly reasonable thing to want and it is also turning the trap down, and nothing says so.

What this category refuses to publish

A UV device is normally specified in one of three ways: a dose in millijoules per square centimetre, a fluence rate, or a rated flow at a stated dose. Not one UV product in this catalogue publishes any of the three.

The clarifier publishes a wattage and a band, which is two thirds of the way there and stops short of a lamp type, and the lamp type is a factor of ten. The air scrubber publishes an airflow and the words UV-C, with no wattage, no wavelength and no chamber dimension, so nothing about it can be computed. The insect trap publishes no wavelength. The inspection light publishes a precise wavelength and is the only one of the four that does, and it is also the only one whose job does not depend on a dose.

That pattern is worth naming. The one product here that publishes its wavelength is the one for which the wavelength is a marketing advantage rather than a performance limit. The three where a number would expose a shortfall publish a band name instead.

The honest limit, and the three numbers to carry

What is exact here is the cancellation. A per-pass dose of fluence rate times chamber volume over flow, multiplied by a pass rate of flow over system volume, leaves fluence rate times chamber volume over system volume, and the flow is gone. That is algebra rather than estimation, and it holds for any recirculating system with a treatment chamber in it. The log reduction conversions are logarithms. The photon energies are a division.

What is representative is nearly everything else, and two items carry most of the weight. The chamber geometry, 13.19 cubic centimetres with a 21.99 square centimetre illuminated area, is a reasonable guess for a mini in-filter unit and no listing publishes a chamber dimension, so every absolute dose scales with it. The lamp efficiencies, 30 percent for mercury and 3 percent for a UV-C LED, span the real range for the two technologies and the listing says which it is for neither. The 30 and 10 millijoule targets, the 0.1 square centimetre per millijoule rate constant, the 10 watt duct lamp and its 0.045 cubic metre section, the 50 cubic metre room, the 95 percent MERV 16 and 99.97 percent HEPA figures, and the spectral effectiveness at 365 nanometres are all in the same category. Every ratio on this page is far more robust than any absolute figure, because the ratios divide the uncertain terms out.

What this page deliberately does not compute is three things. It does not compute repair, and that is the real limit on the cancellation: organisms recover from sub-lethal ultraviolet damage by photoreactivation and dark repair, so many passes at a small dose is not perfectly equivalent to one pass at a large one, and there is no rate constant for that in any product listing or any specification a maker would publish. It does not compute what dose any particular organism needs, beyond using representative figures for algae and ordinary bacteria, because dose requirements span more than an order of magnitude across organisms and a page that picked one would be pretending to a precision the inputs do not support. And it does not compute whether a UV lamp is safe to look at, in any of these products, because that is an exposure limit question about people rather than a dose question about water, and the only honest instruction is the one the listings already give: UV-C belongs inside the filter or inside the duct, never where anyone can see it.

Three numbers to carry. The cumulative dose rate on a system is the fluence rate times the chamber volume divided by the system volume, with the flow cancelled out, so flow is about bypass and mixing and not about dose. A 3 watt UV-C unit is either 0.9 watts or 0.09 of useful output depending on a lamp type nobody states, which is the difference between a 3 hour setting and a 12 hour one. And in air, a filter does one to three and a half logs per pass while a lamp in the same duct does under a hundredth, and only one of the two actually takes the particle away.