Characterisation of Stability Criteria for Pressure Driven Flows in Small Length Scale Fluidic Devices

This paper develops criteria for the prediction of two distinct instabilities in microflows, one isothermal, the other with heat transfer. The engineering objective is to transport droplets that act as micro-reactors and are carried through various processes in a carrier fluid to prepare sample reactants or complete a chemical reaction. The requirement is that the carrier fluid flow be stable so that droplet trajectories can be accurately controlled. The popular two-dimensional microfluidic geometry of three streamlines merging at a junction is chosen for this analysis. A dimensional analysis of the governing flow-field and boundary conditions is undertaken to derive the non-dimensional groups upon which the flow characteristics of the junction are dependent. The emerging parameters are the Grasshof number (Gr) and Reynolds numbers (Re) of both inlet streams. Experimental flow visualisation images are used to determine the relationship between these scaling groups for both isothermal flow and buoyancy opposing mixed convection. The experimental range of inlet Re’s is from 1 to 100. It is found that the ratio of the inlet Re’s is sufficient to describe isothermal flows and that a parameter referred to as W* (the product of the Richardson number (Ri) and Re of the centreline stream) provides a good correlation for buoyancy opposing mixed convection. Inertia dominated flow regimes are seen to exist for W* values below approximately 2 and re-circulation zones are observed when W* is increased above this value. It was also observed that buckling flow was attainable at a critical Re of 65 for isothermal flow and that this critical Re is significantly reduced as W* is increased. An analogy is drawn from the results between the flow studied in this paper and that of cross flow over bluff objects such as a cylinder. Finally, based on the results of this work a design envelope is developed for predicting the stability of scaled models of the fluidic junction.