Generation of complex concentration profiles in microchannels in a logarithmically small number of steps

We describe the principles of design and the architecture of planar microfluidic networks producing concentration gradients with the shape of any given monotonic function. Each microfluidic network is fed by two separate source solutions and delivers to its outlet a set of N solutions that all differ in concentration. Inside the network, the source solutions flow through a series of k = log(2)(N-1) stages, where they are repeatedly split and mixed. Streams of the solutions emerging from the network are combined to create a single stream with the desired shape of the concentration profile across the direction of flow. To demonstrate the functionality of the proposed architecture, we have built and tested three networks with k = 4 and N = 17 that generate an exponential concentration profile, a linear profile, and a profile with a shape of two fused branches of a parabola.