Applications of Statistical Physics to Mixing in Microchannels: Entropy and Multifractals

Abstract

We apply rigorous measures of mixing based on entropy in conjunction with fractals to the field of microfluidics. First we determine the entropy and multifractal dimensions of images of mixing a fluorescent and a non-fluorescent fluid in a microchannel. We find the microstructures to be self-similar (fractals). Second we propose a new approach for patterning the walls of microchannels using the Weierstrass function. We have evidence from numerical simulations that by properly adjusting the dimension of the Weierstrass function one can get microfluidic devices that exhibit better mixing than the current ones.