Abstract Natural sciences have experienced important developments when the insights into both matter and its interaction with the environment advanced to the next scale in space and time – irrespective whether the direction was towards larger or smaller scales. A landmark advance took place at the end of the 19th century when the understanding of matter as composed of atoms eventually outranged the perception of matter as an energetic continuum. Although physical and mathematical discontinuities always pose serious problems, the atomistic perception of matter had the advantage of providing a valuable microscopic aside to thermodynamics, a new perspective to study the interaction between matter and radiation, and a better understanding of numerous properties of solids and liquids. Additionally, the concept of atoms has been proven to be a key to understand and quantify the kinetics of chemical reactions. The atomic age had begun. However, the advances derived from the idea of atoms not only led to new insights into matter, they also made it necessary to develop new models for the reactions of a solid composed of atoms ( i.e. composed discontinuously) with a liquid phase composed of the same or a different component ( i.e. melt or solvent). Among the reactions that can occur between a solid and a liquid, growth and dissolution are ubiquitous and very important to understand. Growth can be described as the formation of a (crystalline) solid from a liquid phase whereas dissolution can be perceived as the decomposition of a solid and the transfer of its constituents into a liquid phase.