Short explanation
You're basically seeing this:
In this picture fog appears because air is humid and the ground is colder than air. In your case humidity from the air has condensed into water droplets because of a temperature drop in the cabin, near the AC vents.
Air is a mix of invisible gases, of which water vapor. Water is air-soluble, but only to a certain extent for a given temperature. Humidity is measured by the relative humidity index, the ratio between the mass of water vapor dissolved and a mass of dry air: 0% for dry air, 100% for saturated air, i.e. containing the largest quantity possible given the temperature.
If drying time is considerably reduced in summer, this is because hot air can absorb much more vapor than cold air, as depicted on this psychrometric chart calculated for sea level and 100% RH:
(Source)
Read this curve as: For temperatures -18°C, 20°C and 28°C, one kg of dry air can be saturated (100% RH) with respectively 2g, 17g and 27g of water vapor. When the mass of water vapor exceeds this ratio, water vapor in excess condensates into liquid droplets which separate from gaseous air and form with it an aerosol.
This condensation can occur after two events:
- A large quantity of water vapor is introduced in air, e.g. by boiling water or by evaporating water.
- Air temperature is lowered, mechanically increasing the RH, this is a way to get water in dry deserts.
From left to right: Boiling water, evaporation tower, liquid nitrogen. All cause water in air to condense after reaching 100% RH. This same mechanism is able to create mist, fog, clouds and dew.
The other parameter that can decrease water capacity and induce condensation is a significant change in pressure. In aviation this can be seen in case of explosive decompression, fog fills the whole aircraft in 1/10s, and more casually in the low pressure areas of the wing:
(Source: JetPhotos, by Seth Jaworski)
Calculation for your case
In your case:
- Ambient air temperature is 28°C, it means 100% RH corresponds to 27g of water vapor in one kg of air, and 23g/kg for a RH of 85%.
- The temperature for which 23g/kg represents 100% RH is 27°C (the dew point).
- The spread between current temperature and dew point is only 1°C, condensation is going to happen easily.
- Around the AC vents, air is cooled at 20°C, this is far below the dew point. For this temperature there are 6g/kg of gaseous water vapor in excess, they are condensed into 6g of visible water droplets. This happens only around the AC vents, remote from the vents the temperature is warm again, water droplets are evaporated accordingly.
- Water (either vapor or liquid) is progressively eliminated from the cabin by the AC system, RH is maintained around 20%, condensation cannot occur anymore.
Condensation appears near the AC inlets:
Air circulation in large pressurized aircraft, from this answer
Dew point
Psychrometrics, the branch of physics studying how liquids and solids boil or condense, revolves around the notion of equilibrium vapor pressure, but for us mere mortals, the notion of dew point is more practical.
The quantity of vapor air can contain before being saturated is called its water vapor capacity, it increases exponentially with temperature. Let's define two cases:
Full saturation: If the quantity of vapor is the maximum allowed for the current temperature (100% relative humidity), decreasing the temperature or adding vapor will cause some vapor to condensate into water.
Partial saturation: If air is not fully saturated, there is a (lower) temperature for which it becomes saturated. This temperature is referred to as dew point. So whatever the current temperature, fog can be created by decreasing the temperature until the dew point is reached.
For sake of accuracy: When water vapor is present in air, it is continuously condensed and evaporated. The dew point is the point where condensation occurs at a greater rate than evaporation and water droplets start accumulating.
Whether fog will form depends on the the dew point spread, that is the difference between current temperature and dew point. When the spread is large, the change in humidity or in temperature must be large. In your case, the spread is small, because air is wet and temperature is high.
Measuring the dew point
The dew point may be determined with a psychrometer (a system with dry and wet thermometers):
Whirling (how to use it) and digital psychrometers
Pressure, dry and wet temperatures, dew point and relative humidity are linked by the mean of vapor pressure. By knowing three elements, the two other can be determined. So knowing pressure, dry temperature and wet temperature allows to determine the dew point. It exists precalculated charts (Mollier diagrams) to read dew point directly. There are also online calculators.
Dew point and fog/mist information
KLAX ASOS report:
As previously mentioned, when the dew point is close to the ambient temperature and the humidity percentage is high, the visibility is low and fog occurs.
When water vapor changes into ice
When the dew point is below 0°C, water vapor is not condensing into water droplets, it is converted directly into ice crystals (frost).
This effect is particularly dangerous and can lead to icing in the carburetor of a piston engine. This condition can happen in areas of low pressure and low temperature, commonly created by the sudden pressure drop in the throttle venturi, due to venturi effect and the temperature drop due to fuel vaporization.
For a typical piston engine, this effect is centered on a external temperature around 10°C but extends to a large range of temperature when the engine is slowed down (descent):
Induction icing conditions
The remedy to carburetor induction icing is to heat the carburetor and raise the due point to a safe area, especially when descending.
For jet engines, induction icing (not to be confused with flying in atmosphere with ice crystals or supercooled water droplets) can cause ice to form at the engine inlet. Blocks of ice can then break, causing damage to blades, compressor stall and/or combustor flameout. It can also cause EPR probe (PT2) reading errors and subsequent FADEC fatal behavior.