Can temperature gradient keep concrete wall below 100% RH in 100% RH atmosphere?

Question

Consider a high and wide concrete wall of say 30 cm thickness, covered with a sheet of vapor barrier on one side, and a sheet of say 30 cm thick and effective insulation on the other side.

The vapor barrier completely blocks water vapor. The insulation lets water vapor through and leads away any condensed water downwards where it is drained away. The concrete lets vapor vapor through, albeit slowly.

The air on the vapor barrier side (the inside of a hypothetical building) is 25°C with 50% Relative Humidity, and the air on the insulation side (the outside of a hypothetical building) is 10°C with 100% RH. See illustration above which shows the wall from above.

According to some vendors of basement insulation, a setup like this will cause the concrete wall to become relatively dry due to vapor pressure towards the insulation in which the water vapor will condense and allow the water to drip down and then be drained away.

But I can't make myself understand how this process works from a physical point of view. I thought an infinite source of water vapor spreads out until all air is saturated with water, so I would expect the wall to end up having 100% RH.

Will the wall end up relatively dry, at say 70% RH? If yes, how exactly?

Answer 1

I have had to repair the concrete walls because of severe leaks and sometimes the replacement of a pipe, etc.

There were walls totally wet and even dark with water oozing out, and there were walls in much dryer condition.

It has to do with the quality and the aggregate grading of the concrete. Some concrete are dense and almost seal the infiltration of water vapors, some porous and so defective that they even bleed cement and expose the sand under sever humidity.

Answer 2

I am an electrical engineer but took some time to study pyschrometric charts which allow you to work out much of this stuff graphically quite quickly. I'm not an expert but here's my understanding.

This section of the answer is based on the incorrect understanding that it's 25°C outside and 10°C inside.

Figure 1. The relevant points on a psychrometric chart. Chart source: Wikipedia Commons. Double-click for full resolution.

• The outside RH is irrelevant as the membrane is impermeable. For that reason I've put the red dot on the 25°C, 0% RH point to avoid any confusion.

• There's going to be a temperature gradient across the insulation and the wall. The water vapour at the barrier will be heated to the outside air temperature (or close to).

• The psychrometic chart tells us that your air contains 0.008 g H₂ per g of dry air. This is about 8 g/kg or 10 g/m³ of air. I like to think of this as two teaspoons of water per m³ of air.
• As the air gets heated (follow the black arrow) the water content doesn't change but the RH decreases in your case from 100% to just below 40%.

According to some vendors of basement insulation, a setup like this will cause the concrete wall to become relatively dry due to vapor pressure towards the insulation in which the water vapor will condense and allow the water to drip down and then be drained away.

I can't see why any condensation would be expected at the membrane. The dew point at that humidity ratio (water to air ratio) is 10°C so vapour should not condense on the membrane.

I thought an infinite source of water vapor spreads out until all air is saturated with water, so I would expect the wall to end up having 100% RH.

If the first part of your sentence were true then the earth's atmosphere would be saturated everywhere. The humidity is regulated by the minimum temperature the air reaches. If the air cools to 0°C it will have about 4 g/kg humidity ratio. If it then warms up to 20°C the RH will fall to about 30%. (Again, note that the actual mass of water hasn't changed.)

Will the wall end up relatively dry, at say 70% RH? If yes, how exactly?

I suspect that the RH will vary with the temperature gradient.

Maybe someone who actually knows what they're talking about can comment on this answer!

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One comment though: In my diagram, the outside is the 10° side. You seem to have assumed the outside is the 25° side.

Right-ho. Here we go.

Figure 2. The reversed situation.

• Here we see that as the air gets closer to the vapour barrier its temperature rises towards 25°C. As it does so the RH drops from 100% to below 40% (black arrow). Condensation should not form because the RH is below the dew point. With my (limited) understanding I can't see why any condensation would occur in the concrete wall or insulation.

What about condensation on the inside of the vapour barrier?

For this to occur the RH has to rise to 100%. Since the humidity ratio won't be changing (the right axis reading on the chart will be constant) we would have to cool the vapour barrier to < 15°C (as shown by the orange arrow) before the air becomes saturated and condensation forms.

Answer 3

After some research, I managed to come up with an answer myself. I will wait with accepting it to allow time for feedback.

Let's first calculate the RH of the concrete. First, we need to calculate the temperature distribution.

Temperature distribution

We will assume the following thermal conductivity values:

• concrete: 1,5 W/mK
• insulation: 0,04 W/mK

this gives us R (thickness divided by thermal conductivity) values of:

• concrete R_c = 0,3 m / 1,5 W/mK = 0,2 m²K/W
• insulation R_i = 0,3 / 0,04 = 7,5 m²K/W

The flow of heat from the warm side to the cold side is given by

q = ΔT / ΣR = (25 - 10) / (0,2 + 7,5) ≈ 2 W/m²

To calculate the temperature drop over the concrete which we can call ΔT_c, we use the above formula but solve for ΔT and only use R_c for ΣR, which gives us

ΔT_c = R_c × q = 0,2 * 2 = 0.4 K = 0.4 °C

For demonstrative purposes, let's round this up to 1 °C. So we have:

• temperature in concrete right next to the vapor barrier = 25 °C
• temperature between concrete and insulation = 24 °C
• temperature at insulation outside = 10 °C

Water vapor distribution

To be able to calculate RH in the concrete, we need to know how the water vapor is distributed. Water vapor diffusion occurs so that concentration of water molecules becomes evenly distributed. Temperature only affects the speed of the diffusion^*. Since RH is 100% outside of the insulation at 10 °C, we know that water vapor content is 9,40 g/m³.

If the air in the concrete has more than 9,40 g/m³ water molecules, the water molecules with diffuse in the direction of the insulation, since the concentration of water vapor is lower there. And since the water vapor content is fully saturated, it will condense and flow away.

If the air in the concrete has less than 9,40 g/m³, water molecules will diffuse into the concrete, but only up to 9,40 g/m³.

To calculate relative humidity in the concrete, we need to know maximum water vapor capacity of air at 24 °C and 25 °C which is 21,75 g/m³ and 23,02 g/m³ respectively. So the RH in the concrete becomes 9,40/21,75 ≈ 43% and 9,40/23,02 ≈ 41%.

^* Temperature itself does have a small impact of diffusion, but in the domain of building physics, it is negligible.

Answer summary

Will the wall end up relatively dry, at say 70% RH? If yes, how exactly?

The RH of the wall will become ≈ 40% because water vapor diffusion is driven by difference in water molecule concentration, not difference in RH.