APPLICATIONS OF STATISTICAL PHYSICS TO MIXING IN MICROCHANNELS: ENTROPY AND MULTIFRACTALS M. KAUFMAN 1* , M. CAMESASCA 2 , I. MANAS-ZLOCZOWER 2 , L.A. DUDIK 3 , AND C. LIU 3 1 Department of Physics, Cleveland State University, Cleveland, OH.44115, USA 2 Department of Macromolecular Science, Case Western Reserve University, Cleveland OH.44106, USA 3 Electronics Design Center, Case Western Reserve University, Cleveland OH.44106, USA Abstract – We apply rigorous measures of mixing based on entropy in conjunc- tion 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. Keywords: Microfluidics, entropy, fractals, mixing 1. Introduction Microfluidic systems operate in a pressure driven flow regime with no moving parts to drag the fluids. Since the flows are laminar and diffusion is in general small, mixing can be achieved in such devices by patterning the channel walls. 1 To design microchannels that are efficient mixers it is important to develop rigorous assessment and quantification tools of mixing. To this end we proposed 2 to use Shannon and Renyi entropies. To further our understanding of mixing, we also characterize the geometric structures generated by the flow by using ______ * To whom correspondence should be addressed: M. Kaufman, email: m.kaufman@csuohio.edu A. Vaseashta and I.N. Mihailescu (eds.), Functionalized Nanoscale Materials, Devices and Systems. © Springer Science + Business Media B.V. 2008 437