Liquid-liquid plug flow. (a) Schematic of microvortices which develop in a plug as it moves through the channel at a velocity VP. The plug radius is RP, the channel radius is RC, and the wetting film has a thickness h. (b) Analytical model illustrating forward and reverse flow in the reference frame of the plug. The flow can be approximated as a classic Poiseuille profile.
Schematic of the 3 flow regimes, described by the dimensionless Shields parameter θ (column 1). In each flow regime, the circulation effect and the aggregation effect are illustrated in columns 2 and 3, respectively. The combined behavior is shown in column 4. Note: all the schematics show a side view of the plug.
Top view comparison of experimental concentration profiles with small, light particles versus large, heavy particles at an identical flow rate of 3 mm/s in a 500 μm diameter circular channel. Both experiments use a high particle loading of >105/ml.
Particle concentration profiles as a function of flow velocity and particle loading (38 μm glass beads). Images shown are high speed video (1200 fps) taken in a circular, 500 μm capillary tubing at the indicated flow velocity. Both the top view and side view are shown. High concentration is defined as >105/ml, and low concentration is defined as <104/ml (enhanced online). [URL: http://dx.doi.org/10.1063/1.3700120.1] [URL: http://dx.doi.org/10.1063/1.3700120.2] [URL: http://dx.doi.org/10.1063/1.3700120.3] [URL: http://dx.doi.org/10.1063/1.3700120.4] [URL: http://dx.doi.org/10.1063/1.3700120.5] [URL: http://dx.doi.org/10.1063/1.3700120.6] [URL: http://dx.doi.org/10.1063/1.3700120.7] [URL: http://dx.doi.org/10.1063/1.3700120.8]10.1063/1.3700120.110.1063/1.3700120.210.1063/1.3700120.310.1063/1.3700120.410.1063/1.3700120.510.1063/1.3700120.610.1063/1.3700120.710.1063/1.3700120.8
Variation in the length of the circulation zone as a function of plug velocity. The data are given in nondimensional form by scaling LC by the plug radius (which gives the aspect ratio of the circulation zone), and expressing plug velocity in terms of the Shields parameter. The dotted lines demarcate the 3 flow regimes. The data are taken with experimental conditions identical to Figure 5.
(a) Schematic of multiple possible trajectories for circulating particles. (b) and (c) Parabolic particle distribution in at 10 and 30 mm/s flow velocity, respectively (top view) (enhanced online). [URL: http://dx.doi.org/10.1063/1.3700120.9]10.1063/1.3700120.9
Very high particle loading (>107/ml) causes the aggregate in the rear cap to extend into the plug, extending the length of the stagnation zone. The channel diameter is 500 μm (top view).
Particle sedimentation velocities.
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