Water vapor diffusion in bee hives and hollow trees

Water vapor diffusion

Wood is a diffusible material That means it has low resistance to water vapor diffusion. If there is a different water vapor pressure on one component on different sides, the water vapor pressure tries to balance itself by diffusion through the component. The component itself opposes this diffusion with a resistance (water vapor diffusion resistance Z, depending on the material-specific water vapor diffusion resistance value µ and the component thickness). The largest possible water vapor pressure in air (with constant air composition and geographical location/height) is only variable by the temperature.

An example:  At 15°C the water vapor saturation pressure is 1706 Pascal. If the relative humidity is 60%, the water vapor pressure is 60% of the water vapour saturation pressure (0,6×1706=1024 [Pa]). If a temperature of 4°C and a relative humidity of 100% is present on the other side of the component, the water vapor pressure is 813 Pa. The water vapor pressure is clearly higher on the warmer side despite lower relative humidity. Moisture is transported by diffusion from the warmer to the colder side.
This example illustrates that there is usually a moisture transport from the warmer to the colder side. In inhabited houses as well as in bee hives and tree caves.

Hollow tree

Water vapor diffusion plays a minor role in tree caves. Although there is a clear difference in temperature to the outside air in the upper part of the cave, the thickness of the outer walls allows only a small amount of water vapor transport.

For the purposes of the rough calculation, we take the following assumption:

  • The tree cave in a beech has the shape of a cylinder with the dimensions 20cm diameter and 1.44m height, the average wall thickness is 40cm.
  • Diffusion upwards/down is neglected, the outside is too far away for significant external transport
  • The bee cluster retreats to the top 30cm of the tree hollow, the temperature in this area is 12°C
  • In the area below the bee cluster, the temperature is likely to be only slightly higher than outside, we do not take this area into account
  • Relative humidity inside is 70% and outside 90%
  • water vapour diffusion resistance coefficient of beech (radial) is assumed to be µ=10, due to the very humid outer areas of the tree
A=2×π×0,1×0,3=0,188 [m²]

surface through which water vapor diffuses

ρi=1403×0,7=982,1 [Pa]

water vapor pressure on the inside

ρa=813×0,9=731,7 [Pa]

water vapor pressure on the outside

Z=1,5×106×μ×d=6×106 [m²hPakg]

water vapor diffusion resistance coefficient

g=ρiρaZ=41,73×106 [kgm²h]

water vapor diffusion current density

m=41,73×106×6×30×24×0,188=0,034 [kg]

diffusing water quantity in 6 months

Under the assumed conditions, 34g of water diffuse outwards through the side walls of the tree-cave in the cold 6 months. This is equal to 1% of the moisture released by bees during this time by metabolism (approx. 3400g). This model calculation shows the magnitude of the reduction of moisture in tree hollows by diffusion.

Modern bee hive

With the modern bee hives it looks a bit different. Theoretically, large amounts of water could escape the beehive through the thin walls by means of vapor diffusion. As it usually does not:

  • There is no temperature difference at the side walls due to the poor thermal insulation. Indoor and outdoor temperatures are almost identical (see HOBOS temperature graph). With higher relative humidity on the outside (approx. 90% in winter), this even places an additional load on the interior. For this reason it makes sense to paint thin-walled magazine hives on the outside.
  • There is a temperature difference at the lid, but here the diffusion is usually completely prevented by cover sheets and aluminium lids.
Temperature curves, HOBOS beehive Schwartau
Temperature curves, HOBOS beehive Schwartau

The graph shows the temperature curves of a beehive in Schwartau during the first week of January 2017. The diagram shows the temperature of the middle comb aisle (red), the temperature of the two outermost comb aisles and the temperature of the outside. Although the temperature inside the hive is about 20°C, the temperature in the vicinity of the side walls is at the same level as the outside air.

In the following, I will show with a model calculation how much water can theoretically be carried away through a diffusible lid. For the calculation I make the following assumptions:

  • average outdoor temperature 4°C
  • average temperature under the lid 12°C
  • relative humidity inside 80%, relative humidity outside 90%
  • construction of the lid as described under diffusion lid with an insulation layer of 4cm hemp insulation wool
  • geometry of  a Dadant Blatt hive
A=0,48×0,48=0,23 [m²]

surface through which water vapor diffuses

ρi=1403×0,8=1122,4 [Pa]

water vapor pressure on the inside

ρa=813×0,9=731,7 [Pa]

water vapor pressure on the outside

Z=1,5×106×μ×d=1,5×106×1,5×0,04=90000 [m²hPakg]

water vapor diffusion resistance coefficient

g=ρiρaZ=390,790000=4341×106 [kgm²h]

water vapor diffusion current density

m=4341×106×6×30×24×0,23=4,31 [kg]

diffusing water quantity in 6 months

The amount of water would correspond to about two thirds of the total moisture produced. If the moisture was only removed via this lid, the humidity would increase below the lid, as more water is produced than is removed. As a result, the vapour pressure difference would increase and thus the diffusing water quantity would increase. At 95% rH inside there would be a vapor pressure difference of about 600Pa. The diffusing amount of water would increase to 6.6kg. This corresponds approximately to the total amount of water in time. This means that even if the moisture produced had to be removed exclusively through the lid by diffusion, condensation would not occur under the lid. There would become a balance at 95% RH inside.

This is a model calculation. Even changes in the assumed temperature by a few degrees can significantly change the result. Soon I will start with the evaluation of measurement data, I will then adjust this calculation. However, the calculation clearly shows the magnitude of the diffusing water quantities in a diffusion-open construction.