You said that there is no obvious relationship between density and viscosity. I disagree. If you heat a liquid, you increase it's volume because as the molecules are heated, they move & take up more space. The mass of the liquid, on the other hand, has not changed. Since the formula for density is mass divided by volume, the density of a heated liquid may change because its volume has changed, very slightly, but changed.
There is a relationship between density and temperature, and we need only look at density tables in scientific literature to see that your statement is correct. In addition, for paints and coatings there is a relationship between viscosity and temeprature, but that relationship is not always predictable because viscosity is not only a function of the resin used in the paints, but it is also dependent on some of the ingredients introduced into the paint formulation.
Despite that, I understand that for each unique coating formulation it is possible to plot a curve of viscosity versus temperature, and those who use paints on a regular basis know that a small temperature increase can result in a large viscosity decrease. In my work I have found that even a 2oF temperature increase can have a marked effect on viscosity. Unfortunately, the same cannot be said for density versus temperature. For most liquids a small temperature increase results in a minute change in density.
I believe the person who asked the question was interested in being able to use coating density as a proxy for viscosity as a method for ongoing monitoring of paint viscosity. He was hoping that by measuring density he could in effect determine viscosity. In practical terms I don't think it is possible to do this. What makes the relationship of density and viscosity even more difficult to measure is the fact that in many cases solvents evaporate from paints as they are being used. Therefore, even at constant temperature the paint density can change if the paint reservoir is not tightly sealed.
In summary, you might be correct in stating that there is a relationship between density and viscosity, but I do not believe one can measure it in practical day-to-day painting operations.
