Poiseuille flow and drop circulation in microchannels

Microfluidics aims to control precisely the transport of fluids and suspended particles or drops. Two characteristics of such transport in rectangular microchannels are addressed here, as a function of the cross-sectional aspect ratio. First, we highlight a convenient expression for the ratio of the centerline to bulk flow velocities, which is relevant for controlling the flow of suspended or flow-focused objects. Then, using the theory of Nadim and Stone, the droplet circulation fountain-flow pattern in such channels is evaluated explicitly, and implications for interfacial mobility measurements are discussed. For example, when the interface is retarded, part of the fountain reverses direction, thus alleviating stagnation, promoting mixing, and reducing interfacial concentration gradients.