Personal tools

## UMR 5672

You are here: Home / Scaling: from the atomic bomb to drops and cells

# Scaling: from the atomic bomb to drops and cells

Marc-Antoine Fardin (CNRS, Institut Jacques Monod)
When May 16, 2023 from 11:00 to 12:00 Salle des thèses Marc-Antoine Fardin vCal iCal

According to standard dictionaries, "scaling" refers to the removal of scales from fishes or of tartar from teeth. The word is used in a different way by physicists. Scaling has to do with the algebra of dimensions. For instance, if a size is proportional to a duration, then the coefficient of proportionality must be a speed. If this speed is, in turn, proportional to a surface tension, then the coefficient of proportionality must be the inverse of a viscosity. If the speed was proportional to the square root of an energy, the coefficient of proportionality would be the inverse of the square root of a mass. From these different combinations emerge a host of mechanical quantities: mass, force, energy, stiffness, stress, viscosity, density, power, etc. In a particular situation, knowledge of the pair of mechanical quantities--either impelling or impeding motion--is sufficient to lead to a "scaling solution". Three years ago Vivek Sharma, Mathieu Hautefeuille, and I started to discuss ways to teach scaling concepts to biologists since the methods can be quite effective and require a very limited mathematical background. In the process, we discovered how much we had underestimated these methods ourselves. This lead us to experiment with the confection of video lectures on this topic (https://www.youtube.com/@naturesnumbers). A complete series on the scaling of explosions is already available. I will only say a few words about explosions to focus instead on the scaling of freely spreading, coalescing, and pinching droplets of Newtonian fluids. These capillary flows provide a great example of the breadth and depth of scaling methods.