In general, the presence of suds is a good indicator of the presence of soap. Technically it is an indicator of a chemical which modifies the surface tension, many chemicals fall into this category (some sugars, etc) but mainly this category is surfactants from soap. Other components have the opposite effect of reducing suds even when there is a surfactant (soap) present. An example of this is alcohol. Lack of suds means that there is either not enough agitation/scrubbing to produce bubbles, or something is acting to rapidly burst the bubbles, such as alcohol.



My argument for mechanical action over dissolving is that you're scrubbing. One surface touches another and what is stuck to the surface is mechanically moved off it and left floating in the surrounding water or (disgustingly) stuck to the sponge. Dissolving is more important in rinsing, but since the water is generally turbulent, not a smooth cohesive flow, you're dealing with a lot of mechanical action by the water. If a contaminant is stuck to the surface of a dish when you start rinsing, either the water's bulk velocity will be great enough to grab it and take it off the dish, or it will slowly dissolve into the stream of water. In this situation, the water grabbing the contaminant from the surface will be more effective with cold water, but the dissolving part will be better with hot water. Now speaking from experience as a chemical engineer i can say that in the rinsing situation the time scale for diffusion is long versus turbulent time scales. If you're waiting for diffusion (dissolving) to wash something off the surface of a dish, you'll probably be waiting for a matter of minutes holding that dish under the stream of water. Of course truth be told with an actual dirty dish scenario there are a huge variety of possible types and arrangements of contaminants on a dish surface and many types of surfaces so there is some guessing involved. If you're dealing with a dish that has a significant solid stuck on layer that you think will take a long time to get off, hot water could be more useful since you'll need the help of diffusion, and since you can rely on thermal expansion to separate the two dissimilar layers. Overall i believe dissolving has a smaller effect than mechanical action, so the benefits of cold water through decreased viscosity especially could in theory win over hot water's decrease in diffusion time.