On the out-of-plane divergence of streamtubes in planar mini-scale flow focusing devices

In this paper, criteria for the prediction of a 3-D divergence of streamtubes within the entrance region of developing laminar flows between merging streams is presented. This divergence has a direct impact on the application of microscale flow cytometers based upon a 2-D design, as the exact downstream position of the sample population may not be accurately predictable. Also, the phenomenon could adversely affect the efficiency of fluidic sorting systems that have been incorporated into such devices. In this study a mini-scale flow cytometer with three streams merging at a single junction is analyzed to investigate the existence of any three-dimensional divergence of the inlet streams. This is achieved by visualizing dyed inlet streams from both isometric and planar views. A theory to predict this phenomenon is presented and validated using flow visualization and Particle Image Velocimetry (PIV). It is noted that the Reynolds numbers of the inlet streams are the only characterizing parameters for such a device under isothermal pressure driven flow conditions. A range of inlet flow ratios from 1 to 10 between the merging streams are examined. These flow ratio observations were carried out over a Reynolds number range of 23-53. The results show that a three-dimensional divergence of the inlet streams exists within the entrance region. The divergence was found to be almost non-existent at flow ratios of unity but becomes more apparent as the flow ratio is increased. It was also observed that the higher the magnitude of the Reynolds number, the more apparent the divergence became for each flow ratio investigated. Finally, the effect of this phenomenon on the development of microfluidic devices incorporating a similar geometry is discussed and conclusions are drawn