The Kinematics of Bend-Induced Stirring in Micro-Conduits

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Abstract
The absence of turbulence and the difficulty associated with introducing moving stirrers into microfluidic systems make the mixing problem in microdevices challenging. We studied theoretically 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. 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 (1989) 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 observed.

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