Diffusion: Macroscale Dwarf and Nanoscale Giant

Diffusion processes of particles or energy exhibit a characteristic scaling behavior with space and time. In this contribution, the background of this scaling behavior will be shortly described and its consequences in physics, chemistry, biology and various areas of technology shall be explored. Furthermore, some demonstration experiments for different aspects of diffusion and its scaling behavior will be discussed in the course of the article. A standard demonstration of diffusion processes in German experimental physics lectures involves a large (up to 1 m high) glass cylinder the lower part of which is filled with a blue, concentrated solution of copper sulfate which then is carefully overlaid with colourless demineralized water. If done by a skilful experimentalist, the interface between both solutions is initially quite sharp (with a transition zone of maybe 1 to 2 millimeters and with the density difference between the water and the solution additionally stabilizing the original stratification. Over the course of a two-hour lecture, one can already recognize some widening of the interface region due to interdiffusion of blue copper ions (and their colorless sulfate counterions) into the demineralized water region. The interface zone may grow to about 1 to 2 cm in this time. In some places, especially in the State of Saxony, the cylinder is then carefully positioned into a wooden rack and kept on public display for the remaining term or even longer (see fig. 1). There is even a special name for this rack with the cylinders in it: It is called "Semesteruhr", i.e. "term clock". This name illustrates quite well that major changes in the distribution of the copper ions over the cylinder may take several terms, coming close to equilibration even years. The appearance of a "term clock" a few weeks after filling perfectly represents the typical perception of diffusion on the macroscale: It may lead to some blurring of formerly sharp interfaces, but is slow and it does not reach very far, and in order to 1