Tools

Improved bell-type
CO₂ diffuser

Simple, reliable, stable, safe, cheap & non-overdosable CO₂ dosing device

In my opinion, dissolving carbon dioxide (CO₂) using the device described below is one of the simplest and most accurate ways of dosing it, and is particularly suitable for smaller (or experimental) aquariums.

Note: As far as I know, the principle of this device was first formulated and published under the German name Paffrathsche Rinne (Paffrath's channel) or Paffrathschale (Paffrath's dish), named after the German developer Kurt Paffrath, in the German book Bestimmung und Pflege von Aquarienpflanzen (1978). See References at the end of the article for additional sources of information on this device.

The principle of this device

An inverted container (in my case I used a glass beaker) is placed below the water level in the aquarium and fixed to the side of the aquarium, for example with suction cups. Carbon dioxide is fed into this vessel [from a cylinder or fermentation vessel] and accumulates there, forming a so-called gas pocket (a giant CO₂ bubble). The carbon dioxide spontaneously passes (diffuses) into the aquarium water at the contact surface [of the formed CO₂ bubble] with the aquarium water. So [logically] the larger the contact area, the more carbon dioxide will transfer into the water (i.e. the higher the resulting CO₂ concentration in the aquarium water). Since excess carbon dioxide constantly tends to escape through the water surface into the atmosphere, its resulting amount in the water is determined not only by the size of the container [from which it diffuses into the water], but also by the size of the water surface [from which it diffuses into the atmosphere]. The size of the container must therefore be adapted to the size of the water surface. The dissolution efficiency can be significantly increased if the contact surface of the vessel is subjected to a strong flow (e.g. through the outlet of a filter or water pump). The velocity of the water flow at the contact surface [of the gas bubble] is therefore another factor that influences the resulting CO₂ concentration.

Calculation of the container size

Initial assumption

Current CO₂ concentration in air and its equilibrium concentration in water:

425 ppm CO₂_(air) (= 0.0425%) = 0.616 ppm CO₂_(aq)

Logic behind this calculation

If the air above the aquarium contains 0.0425% CO₂, its equilibrium concentration in the water will be 0.616 ppm CO₂. How much does the concentration of CO₂ above the surface have to rise for its concentration in the water to increase to, for example, ppm?

Calculating the required CO₂_(air) concentration

0.0425%	CO₂ in atmosphere	=	ppm	CO₂ in water (at equilibrium with atmosphere)
X%	CO₂ in atmosphere	=	ppm	CO₂ in water

X = / (0.616 / 0.0425) = %

So, if we want to have ppm CO₂ in the aquarium water, we need to have % (= ppm) CO₂ in the air above the aquarium. How to achieve this higher CO₂ concentration [above the aquarium]?

Problem

The problem with this option is that such a high CO₂ concentration (= ppm) in the air [above the aquarium] would not only be difficult to ensure (and maintain) in the long term, but would also be toxic to humans (i.e., could poison us). Fortunately, there is a workaround to this problem:

Solution

We can move this much more CO₂-concentrated atmosphere underwater. And not only that, we can increase this concentration to the maximum (i.e. 100%).

The logic behind this solution is as follows:

If there were 100% CO₂ above the entire aquarium, then the CO₂ concentration in the aqurium water would rise to 1,450 ppm (100 * 0.616 / 0.0425). But, as we only want to achieve a concentration of ~ ppm CO₂, then the contact area of the container with that 100% CO₂ needs to be only % of the water surface area ( * 100 / 1,450).
Given our aquarium has a water surface area of say * cm = cm², then the underwater container with 100% CO₂ only needs to have a surface area of ~ cm² (% of cm² or * / 1,450).

Thus, a contact area of cm² is [theoretically] required to achieve the target concentration of ppm CO₂_(aq).

In other words, to achieve a concentration of ppm CO₂ we need a CO₂ container with a contact area of cm².

Consideration of other factors

However, as the above calculation does not take into account some factors (which will reduce the efficiency of CO₂ diffusion), it is advisable to increase the contact area by a certain coefficient.

Factors negatively affecting CO₂ diffusion in water:

The air inside the diffuser won't be 100% CO₂ for long, other gasses dissolved in the water will enter the diffuser.
- Yugang attempts to solve this problem by using what is called an "overflow" → a small cutout in the bottom edge of the container, through which the excess gas escapes from the container in the form of small bubbles. He assumes that these escaping bubbles contain "old" gas (i.e. other gases besides CO₂ that diffuse into the container from the water over time => e.g. N₂, O₂), and that their removal has a self-cleaning function => thanks to their removal the gas in the container remains 100% pure and concentrated.
- The problem I see with this assumption is that other gases that diffuse from the surrounding water into the container are lighter than CO₂ (molar mass of CO₂ is 44 g/mol while the molar mass of O₂ is 32 g/mol and that of N₂ is 28 g/mol), and therefore will accumulate in the upper part of the container, not in the lower part where the excess gas escapes as bubbles. The bubbles that escape from the bottom part of the container will therefore contain nothing but pure CO₂.
- In order to solve this problem, some sort of gas venting would have to be done at the top (and not at the bottom) of the vessel as e.g. Kurt Paffrath had in his original design →
  
  Entlüftung = deaeration (air removal)
- This can be a problem especially with low (shallow) containers. If a taller container (e.g. a beaker) is used, in my experience no significant accumulation of foreign gases will occur (at least not within a few months). Still, it may be a good idea to manually empty the container from time to time (i.e. every few months) and fill it completely with fresh carbon dioxide.
There is a difference in speed between CO₂ dissolving from the diffuser into the water, and from the water in to the air at the rest of the surface. This can also be influenced by water movement, etc.
The water in an aquarium is not 100% pure, it contains small amounts of salts that have a negative effect on the solubility of CO₂.
Consumption/production of CO₂ by plants, bacteria and fish is not accounted for.

Calculating contact area

Based on the above factors and practical measurements, it seems appropriate to increase the diffuser contact area by about 1/3 = %

PS: Using Yugang's alternative method of calculation, it comes out to 37%.

Thus, the calculated [theoretical] value of the diffuser contact area (= cm²) should [in reality] be approximately cm² ( * 1.).

Calculating container size

Round container (diameter)

Ø = 2 * √ ( surface-size / π )
Ø = 2 * √ ( / 3.14 ) = cm

Square container (width x length)

Dimensions = √ ( surface-size )
Dimensions = √ = x cm

Yugang's alternative method of calculation:

S = water-surface / ( cA * cB )

water surface = the surface area of our aquarium (in cm²)
- length and width of my aquarium (height is not important here): 30 x 25 cm
- water surface area = 30 * 25 cm = cm²
coefficient A = 17.7
- determined experimentally
coefficient B
- for a pH drop of 1.5 (~60 ppm CO₂) = 1
- for a pH drop of 1.2 (~30 ppm CO₂) = 2
- for a pH drop of 0.9 (~15 ppm CO₂) = 4
container surface
- for 15 ppm CO₂: 750 / (17.7 * 4) = 10.6 cm²
- for 30 ppm CO₂: 750 / (17.7 * 2) = 21.2 cm²
- for 60 ppm CO₂: 750 / (17.7 * 1) = 42.4 cm²
conversion to square or circle
- round container (diameter): 2 * √ ( S / π )
  - for 15 ppm CO₂: 2 * √ ( 10.6 / 3.14 ) = 3.7 cm
  - for 30 ppm CO₂: 2 * √ ( 21.2 / 3.14 ) = 5.2 cm
  - for 60 ppm CO₂: 2 * √ ( 42.4 / 3.14 ) = 7.35 cm
- square container (size): √ S
  - for 15 ppm CO₂: √ 10.6 = 3.3 x 3.3 cm
  - for 30 ppm CO₂: √ 21.2 = 4.6 x 4.6 cm
  - for 60 ppm CO₂: √ 42.4 = 6.5 x 6.5 cm

Conditions to be met

Important: It is important that (1) the beaker is filled with gas to the brim, (2) the hose supplying CO₂ to the beaker is inserted inside it, (3) the neck of the beaker is the correct size (= diameter), (4) the water, which is in contact with the carbon dioxide inside the beaker, is flowing, and (5) the beaker is placed bottom up and as straight as possible.

(1) CO₂ supply in slight excess

The first condition is achieved by supplying a little more gas into the beaker than will dissolve spontaneously into the water, with the excess gas escaping through the spout (overflow) away to the surface.

(2) Hose ends inside the beaker

Even if it doesn't seem like it, it is not only CO₂ from the tubing that will get into the gas in the beaker, but also various other gases from the aquarium water (e.g. oxygen or nitrogen). This will cause the concentrated carbon dioxide in the beaker to dilute slightly over time. By inserting the tubing into the beaker, we ensure that the new gas that is fed into the beaker is dissolved without any residue, so that only the old (slightly diluted) gas escapes through the overflow. If we were to place the end of the tubing under the beaker, the bubbles escaping from the tubing into the beaker might not get into the beaker when they hit the gas surface in the beaker, but might slide along the surface to the spout (overflow) where they could escape to the water surface. Although this problem is likely to occur only in very small containers, it is better to try to prevent it.

(3) Correct diameter of the beaker

As for the required diameter of the beaker, see the "Calculation of the container size" section above.

(4) Suitable water flow

A standard aquarium filter or a jet pump is sufficient to ensure a suitable water flow.

(5) Suitable fixing of the beaker

Although not the most aesthetically pleasing solution, the easiest way of attaching the beaker to the aquarium wall seems to me to be by means of two zip ties with suction cups [used to hold the glass thermometer].

References

Books

Paffrath, Kurt. Bestimmung und Pflege von Aquarienpflanzen. 2. Auflage. Landbuch Verlag GmbH, 1979. ISBN 3-7842-0220-9. (pp. 142-146) → click to show …
Identification and care of aquarium plants

The behaviour of carbon dioxide in water

Carbon dioxide is present in water in a bound form with calcium. A certain amount of free, i.e. unbound, CO₂ is needed to keep the calcium in solution. If this content is too low, the calcium precipitates and often forms a coarse white coating on aquarium plants. The so-called equilibrium carbon dioxide varies considerably depending on the calcium content of the water.

Here are some values to illustrate these different needs. For example
- up to 4 KH in water = under 1 mg free CO₂ per litre
- 9 KH in water = approximately 11 mg free CO₂ per litre
- 15 KH in water = more than 50 mg free CO₂ per litre
The more concentrated CO₂ in the water is always balanced by the lower content in the free air ([see] an open bottle of mineral water). The higher the carbonate hardness of the water, the faster the carbon dioxide escapes. This process is accelerated [also] by the use of air stones, specifically by circulating the water and absorbing the less saturated air bubbles in the water on their way up. The earlier theory that aquarium water always contains sufficient or too much CO₂ is not correct.

Natural sources are not always sufficient

Tap water is always pumped by the waterworks into our water supply network in an equilibrium state. Otherwise, scale would precipitate and clog the pipes over time. The aquarium equilibrates with free air, the CO₂ content decreases and the pH value increases. According to previous measurements, the content stabilizes itself at around 5 mg per litre of water through natural carbon dioxide sources. Fish and soil bacteria release carbon dioxide when they respire or convert organic matter. The resulting level is generally sufficient for normal plant growth, provided the water is not too hard and no air stone is used. In hard water, conditions are different. The reduced carbon dioxide content causes the pH value to rise above 8. This creates a barrier and many plants cannot use such a small amount. Under certain conditions, therefore, the naturally produced CO₂ is not enough. Plant growth stagnates or remains restricted to robust species.

What can [be] done [about this]?

Again, there are several options to choose from. We can adapt the plant selection to these conditions and use a standard range of robust plants. One option is to reduce the calcium content by mixing with rainwater with a lower calcium content. Another option to achieve better plant growth and more species in the aquarium is CO₂ fertilization, which produces quite surprising results. Sometimes even a small amount has an excellent effect, as the pH value is brought into more favourable limits. Plants that usually grow in soft water can now grow healthily in harder tap water without any problems. This makes it possible to grow more plant species and more plants than before.

Equipment on the market

Mineral water is not the solution. Frequent water changes can only compensate hard water conditions to a limited extent. Carbon dioxide bombs or water decarbonisation are expensive and difficult [to use]. Specialist retailers offer various devices. The so-called diffusion device is attached to the aquarium and is fed from a cartridge. CO₂ enters the water through a membrane. In another device, CO₂ is produced via a marble stone and hydrochloric acid ([this is] dangerous) and fed into the water. Due to the small diffusion area, both devices are limited to smaller tanks or low calcium tanks.

Fermentation method

For yeast fermentation, a 10% sugar solution (100 g of sugar per 1 litre of water) is mixed with 2 g of dry yeast and filled into a tightly closed plastic container. The minimum size of the container is 1 litre. A larger fermentation vessel (over 10 litres for large aquariums and very hard water) has advantages in terms of maintenance, duration of the fermentation process and daily CO₂ production. During alcoholic fermentation, carbon dioxide is released for approximately four weeks. It is fed through a thin plastic air tube into the aquarium, where it can escape through the air stone and the water is enriched from the rising bubbles. In smaller tanks, extreme caution is required as the content rises too quickly and is harmful to the fish.

It is better to feed CO₂ into a storage container (reservoir) from which the water can [naturally] enrich itself with CO₂. I have been using the method described below successfully for more than 10 years in very hard water with a carbonate hardness of 16°. As a result, even sensitive plants grow excellently. The container is a U-shaped channel made of three strips of Plexiglas and sealed at both ends (use special Acrifix glue), each 3 cm wide and 3 cm high (measured inside). This container is attached on the inside to the front top frame of the tank (using offset narrow strips of Plexiglas) and does not interfere with the appearance of the aquarium. The side of the container that is open at the bottom protrudes about 1 cm into the water, which is automatically enriched by direct contact with the gas. Levels of up to 80 mg CO₂ per litre can be achieved, thus maintaining the carbon dioxide balance even in very hard water. This level has not yet been shown to be harmful to the fish in the aquarium.* Care should be taken to increase the dosage slowly at first.

* Note: Most modern science literature states 20 ppm CO₂ as the maximum permissible [long-term] concentration of CO₂ for warmwater species, and <10 ppm for salmonid fishes. See (1) „Physiology of fish in intensive culture systems“ (Wedemeyer, 1996 → pp. 67-69), (2) „Hydrochemistry“ (Pitter, 2015 → p. 321), (3) DOI: 10.1016/j.aquatox.2010.12.014.

Schematic illustration of carbonic acid fertilization using the fermentation method. Carbon dioxide is produced in a fermenter (1) with water, sugar and yeast. The gas is led through a plastic air tube (2) into a storage channel (3) which is attached to the upper frame of the aquarium (4).

The length of the intake channel or the size of the contact area depends on the amount of water in the aquarium and its carbonate hardness. To achieve a balance between calcium and carbonic acid (as the ideal condition for plant growth), the contact area between water and gas for every 100 litres of water content is calculated as follows: up to 10° KH = 30 cm² = approx. 10 cm channel length. Above 10° KH, increase the contact area by 20 cm² for every 1° KH.

The table shows the individual values in absolute numbers. These should be adjusted to the size of the tank. Tank size: 100 litres.

Carbonate hardness --- Contact area (cm²) --- Channel length (cm)
- 10 KH --- 30 --- 10
- 11 KH --- 50 --- 18
- 12 KH --- 70 --- 25
- 13 KH --- 90 --- 30
- 14 KH --- 110 --- 40
- 15 KH --- 130 --- 45
- 16 KH --- 150 --- 50
Allgayer, Robert & Teton, Jacques. The complete book of aquarium plants. London: Ward Lock Limited, 1987. ISBN 0-7063-6614-X. (pp. 41-43)

Online resources

Paffrathsche Rinne. Online. In: Wikipedia: the free encyclopedia. San Francisco (CA): Wikimedia Foundation. 2008. Available from: wikipedia.org. [cit. 2024-12-26].
Old school co2 method (post #86) [@akwarium]. Online. 2019. Available from: ukaps.org. [cit. 2024-12-26].
Horizontal CO2 Reactor - Yugang 鱼缸 Reactor [@Yugang]. Online. 2023. Available from: scapecrunch.com. [cit. 2024-12-26].
CO2 Spray Bar – a summary [@Yugang]. Online. 2023. Available from: scapecrunch.com. [cit. 2024-12-26].