Fluid flow through a complex array of channels and analogies with electron and spin transport in nanoscale

Abstract This work discusses the flow regimes through an array of channels with a single inlet and a single outlet. The fluid considered in the simulations is classical, viscous, Newtonian and incompressible. We obtain numerical solutions of the Navier–Stokes equations in different flow regimes using the Finite Volume Method in a complex domain mimicking the lattice of a graphene slab, which contains sequences of bifurcations and junctions. The simulations consider a wide range of pressure unbalances to create laminar and turbulent flows. The results permit concluding that: (i) even with small inflow velocities the probability for the fluid to flow through a specific path changes from route to route, what we understand as a signature of the interaction among neighboring channels; (ii) as the pressure unbalance increases, the flow enter the transition to turbulence, becoming a stochastic process, and producing a change in the transport regime. The response function transforms from a constant to a negative power law. We explore analogies of the flow in complex arrays with electron and spin transport in nanoscale structures.