Diffusive intertwining of two fluid phases in chemically patterned microchannels

Via a coarse-grained model, we simulate the flow of a pressure driven binary AB fluid through a three-dimensional microchannel, which is decorated on both top and bottom with distinct A- and B-like patches. The advection is "frustrated" because A-like patches are placed in the path of the B stream and similarly, B-like patches are placed in the path of the A fluid. A competition between two factors, the advection caused by the imposed flow and the interactions between the confined fluids and the patterned substrates, introduces nonlinearity into the system. This nonlinear behavior gives rise to a temporally periodic state, where the A and B fluids are intertwined. In effect, the simple pattern of chemically distinct patches introduces positive feedback, which is responsible for the instability of the interface separating the injected fluids.