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Parameters affecting the shape of a hydrodynamically focused stream

MansoorNasir*, David R. Mott†, Matthew J. Kennedy‡, Joel P. Golden*, and Frances S. Ligler*

*Center for Bio/Molecular Science and Engineering, †Lab for Computational Physics and Fluid Dynamics, ‡ Chemistry Division

Naval Research Laboratory, 4555 Overlook Ave SW., WashingtonDC20375, USA

Corresponding author email:

The simulations demonstrated the effect of increasing Re as well as the concentration distribution of the focused stream for different cases of sheath-to-sample flow-rate ratios. The shape of the interface between sheath and sample was flat the flow rate in the two streams was same regardless of the range of Re tested. With flow focusing, increasing the Re made the cusps larger with the focused stream completely separating for the flow-rate ratio of 50 with Re = 50.

Fig.S1COMSOL simulations show concentration distributions of three flow-rate ratios (1, 5, 50) at three different Re (1, 10, 25). The sample/focused stream is in shades of red while the sheath stream is in shades of blue. The intermediate colors at the interface between the two fluids show the diffusion region. The diffusion constant in all cases was 1x10-10m2/s. A 90º symmetric channel design was used in all cases. The channel dimensions were 500 μm x 500 μm (height x width).

The sheath and sample flow rates (µL/min) used in each case in Fig. S1 are shown in the following Table S1:

Table S1. Flow rates used in simulations.

Flow-rate ratio / Re = 1 / Re = 10 / Re = 25
Sample / Sheath / Sample / Sheath / Sample / Sheath
1 / 15.0 / 15.0 / 150.0 / 150.0 / 375.0 / 375.0
5 / 5.0 / 25.0 / 50.0 / 250.0 / 125.0 / 625.0
50 / 0.6 / 29.4 / 5.9 / 294.1 / 14.7 / 735.3

Simulations were conducted to verify the backflow into the sample inlet that was observed in Particle Image Velocimetry (PIV) experiments. The simulations showed that the backflow region was present at low Re but diminished as Re increased. The sheath fluid momentum carried it across the junction into the main channel at higher Re and pushed the sample stream away from the center of the channel.

Fig.S2Channel cross-sections from COMSOL simulations were used to plotvector field with normalized velocity field and contours showing the velocity magnitude for 90º symmetric channel designs. The cross-sections were taken at the mid-height along the Z-direction. The simulated channels were 500 μm x 500 μm. The sample and sheath were 1.2 and 29.0 µL/min for Re = 1 and 29.0 and 725.0 µL/min for Re = 25. Flow-rate ratio was 25 in both cases. The colorbars indicate the velocity at different point in the streamlines for the simulated channels in units of m/s.

Simulations and experiments were conducted to understand the effect of channel symmetry on the shape of the interface between sheath and sample streams. Asymmetric channels resulted in larger deviations from a flat interface than symmetric channels when the angle of confluence was the same. Increasing the angle of confluence or the Re exacerbated the cusps.

Fig.S3Channel cross-sections from COMSOL simulations (columns 1 and 2) and confocal microscopy (columns 3 and 4) show the concentration profiles for symmetric and asymmetric channel designs. Two angles of confluence (45º, 90º) and two Re (10, 25) were used for comparison. The dimensions of the channel used in confocal experiments were 380 μm x 600 μm. The sample and sheath flow rates, respectively, were 11 and 283 µL/min for Re = 10 and 28 and 707 µL/min for Re = 25. For simulations the simulated channels were 500 μm x 500 μm. The sample and sheath flow rates, respectively, were 11.5 and 288.5 µL/min for Re = 10 and 28.8 and 721 µL/min for Re = 25.

The inertial effects demonstrated for 500μm square (simulated) and 600μm x 380μm rectangular (confocal) channels are seen in channels with smaller cross-sections. If the channel size is decreased then the flow velocities must be decreased accordingly to maintain Re. The flow focusing behavior is similar in the smaller channels albeit the diffusive mixing at the interface of sheath and focused streams is more pronounced since the fluid velocities are slower and this leads to longer residence times.

Fig.S4 Concentration profiles from COMSOL simulations with 90º symmetric inlet designs are shown for two Re (10, 25) for comparison. The dimensions of the simulated channel used in confocal experiments were 100 μm x 100μm. The flow-rate ratio in each case was 25. The sample and sheath flow rates, respectively, were 2.3 and 57.7 µL/min for Re = 10 and 5.8 and 144.2 µL/min for Re = 25.

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