Air is saturated with water vapor when the Relative Humidity is at 100%. Temperature and pressure affect how much water vapor can be in the air for it to reach saturation/100%RH.
If you mean “water vapor is removed faster or as fast as the rate at which it is being put into the system”, then that is not ‘saturation’, or at least, not the correct word. It would be like saying the sink is ‘saturated’ with water because as much is running down the drain as coming in from the tap.
The room’s Relative Humidity is 20%. That is no where near saturation. However, given the draftiness of many households, a small portable humidifier probably can’t keep up with the air replacement to budge the RH of the room. The room isn’t saturated… it’s leaky.
while the situation is dynamic i doubt it will ever be at an equilibrium (that’s just scientific speak, i would bet my left nut that it never will be if the room is being used in a household as a bedroom). the OP did not mention time duration or other factors like type of heat/ventilation, room air exchange, amount and type of material in the room.
there is likely air leakage in and out of the room. the window is cooling air and causing circulation, the vaporizer is pushing air. if the heating is air flow then there are air changes. there may be much moisture still being absorbed by clothes, bedding, carpet and so on.
I am assuming that the vapor diffuses pretty quickly throughout the room and mixes pretty evenly, in no more than a few minutes. Is this not the case? Does it take hours for the vapor to get from the humidifier to the window?
The volume of air needs to move across the window surface for it to dehumidify it. Most rooms do not have circulation such that that occurs. Even with air leakage and drafts air will tend to have layers and a volume of air will stay relatively stuck near the surfaces. Maybe Chronos or someone else with a greater physics knowledge can explain it clearer but it is more like fluid dynamics than diffusion at work.
Yes. But not enough to cause complete mixing of air throughout the room. Possibly not even significant mixing of the air. There is at least no reason to assume it would be.
Fluid dynamics of air flow is above my pay grade but just looking at the visualizations in this article illustrates how mixing is often extremely incomplete and how various boundry conditions occur.
there is likely air circulations and gradients of temperature and humidity all over the room.
the window much colder than the bulk of the room. the exterior wall likely colder than the bulk of the room. the door to a hallway may be warmer than an exterior room. the heating system will create a convective flow. the vaporizer will create a flow.
there may be steep gradients near the window and near the vaporizer.
there could be eddys and unmixed areas throughout the room.
the dynamics of this situation is hard to predict; it will depend on indoor and outdoor temperatures, amount of insulation, air leakage, materials in the room, did the person go out to take a drink during the night because of the dry air (did they leave the door open?), did they later pee at night because they drank too much water (did they leave the door open?).
This sounds reasonable. Expecting mixing “pretty evenly, in no more than a few minutes” however does not. And assuming that (if the air was constantly completely mixed) the window surface has the dehumidification capacity to take out humidity at the same rate that a vaporizer also does not seem reasonable.
Meanwhile here is a source that tells us the real answer. A typical existing home completely changes its air volume from 0.5 to 1.25 times each hour. An older leaky home (which this one sounds like), from 1.0 to 2.5 times an hour.
Condensation will occur so long as the humidity is above dew point at the window surface. Single pane, no storm, 30% indoor relative humidity will do that at any outside temperature much below 34F. It is not a significant issue for where the water is going.
The fact that all the air in the house, the complete house, is being exchanged at least every hour, OTOH, is.
In case you doubt that one site’s claim, and I wouldn’t blame you, it is to me a surprisingly large number, the same figures are repeated bu a variety of sources. Here’s another: