Obviously, the rate of evaporation depends on the temperature. Put a drop of water in a hot frying pan and it will sizzle and change into a vapour almost immediately. Place that drop on your countertop and it will stay there for a while.
The dishes in a dishwasher get hot, but how well they retain the heat after the heating element is turned off depends on the material of which they are made. “Heat capacity†is a physical property, and is defined as the amount of heat that has to be supplied to an object to produce a unit change in its temperature. This value also determines how well a substance retains the heat. Glass and metal absorb and retain heat longer than plastic, so residual water will evaporate more quickly from glass or metal.
Now for the more captivating science. This is where “surface energy†comes into play. You will notice that if you place a drop of water on a plastic surface it forms a bead, while on a glass surface it spreads out into a thin layer. This has to do with the strength with which atoms at the surface of a substance are attracted to the bulk of the substance relative to being attracted to an adjacent surface. Substances that have a low surface energy show weak bonding of the surface atoms to the bulk, and therefore have a greater tendency to be attracted to another surface. Glass has a lower surface energy than plastic, so molecules at its surface will have a greater attraction for water than a plastic surface has for water. Since the rate of evaporation of water is a function of the area in contact with air, a thin layer such as forms on glass will evaporate more readily than a bead that forms on plastic.
If you are troubled by wet plastic, the addition of a rinsing agent will help. Such products contain “surfactants†such as “alcohol ethoxylates†or “sodium cumene sulfonate†that reduce the attraction of water molecules for each other by getting in-between them. This reduction in “surface tension†means that water is less likely to bead, and therefore evaporates more readily.
As far as putting plastics in the dishwasher in the first place, well that’s a thorny issue. The question is whether any potentially undesirable chemicals leach out. Plastics are chemically very complex with various additives used in their manufacture that can conceivably leach out at high temperatures. Then there is the added problem of the polymer breaking down with heat and releasing some of the breakdown products. In any case, whatever does leach out will end up going down the drain.
However, there is the possibility that the heat will have altered the properties of the plastic in such a way as to enhance the release of its components into any food subsequently stored inside. In the context of everything to which we are exposed in our daily lives, this is of no great consequence. Still, in general, only plastics that are “dishwater safe†should be placed in the dishwasher. Polypropylene (#5 on the recycling logo) is probably the most common plastic used in food containers and is dishwasher safe. Polyester (#1) and polyethylene (#2, #4) are fine, but polystyrene (#6) and plastics in category #7 should not be placed in a dishwasher.
There is of course another way to eliminate the concerns discussed. Wash your dishes by hand and dry them with a towel. That works well whether you are dealing with plastic or glass. And you will also be saving energy. Dishwashers with their high requirement for electricity are not exactly environmentally friendly.