The kinematics of bend-induced mixing in micro-conduits

The absence of turbulence and the difficulty associated with introducing moving components into micro-fluidic systems make the mixing problem in micro-devices challenging. We studied steady, laminar, incompressible flow through a sequence of conduits with rectangular cross-sections aligned to form 90° with each other. The feasibility of taking advantage of bend-induced vortices to stir the fluid and enhance the mixing process was evaluated theoretically and experimentally. Since at very low Reynolds numbers the bend-induced vortices decay rapidly, it was necessary to utilize a large number of bends to achieve the desired effects. Since it is not practical to directly simulate the flow through a large number of bends, we borrowed Jones et al.’s [J. Fluid Mech. 209 (1989) 335–357] idea of constructing a two-dimensional map to project fluid particles from a cross-section upstream of the bend to a cross-section downstream of the bend. This map was then applied repetitively to trace particle trajectories in various bend arrangements. Under certain conditions, chaotic advection was predicted. A prototype of a stirrer was fabricated with low temperature co-fired ceramic tapes.