Characterization of transverse channel concentration profiles obtainable with a class of microfluidic networks

We analyze mathematically a previously reported class of passive microfluidic mixing networks. The networks produce nonhomogeneous concentrations in the output channel, resulting in diverse concentration profiles. We formally prove that all profiles obtainable with this class of networks can be described as polynomials of degree no higher than the number of input channels less one. We derive explicit formulas for the calculation of resultant output concentration profiles and conversely for the calculation of input concentrations needed to obtain set output profiles.