Evaporation of a non-ideal solution and its application to writing ink aging

The evaporation of a solution consisting of a non-volatile solute dissolved in a volatile solvent has been previously treated using a simple model called the beaker model. This model considers the solution to be in a non-porous container that has vertical walls like a glass beaker and assumes the solution is an ideal solution so that Raoult's law is obeyed. A particular novel finding was that under a certain condition, the evaporation or aging curve of the solution has a point of maximum acceleration. Prior to this point, the solution is in its fast drying mode and after this point, it is in its slow drying mode. This phenomenon is observed in the drying of many writing inks. In this work this model is modified to consider the evaporation of (a) a non-ideal solution, (b) a solution that become saturated, (c) a solution on a glass slide, and (d) a solution on a porous substrate. In each of these cases, the existence and location of the point of maximum acceleration of the drying process are examined. These modifications lead to a description of the dying process of a solution that is remarkably similar to that of writing inks but obtained via an entirely different physical model.