Coalescence and mixing dynamics of droplets in acoustic levitation by selective colour imaging and measurement

Abstract

Acoustic levitation is well-suited to 'lab-on-a-drop' contactless chemical analysis of droplets. Rapid mixing is of fundamental importance in lab-on-a-drop platforms and many other applications involving droplet manipulation. Small droplets, however, have low Reynolds numbers; thus, mixing via turbulence is not possible. Inducing surface oscillation is effective in this regard, however, the relationship between internal flow and mixing dynamics of droplets remains unclear. In this study, we conducted a set of simultaneous optical measurements to assess both the flow field and the distribution of fluid components within acoustically levitated droplets. To achieve this, we developed a technique to selectively separate fluorescent particles within each fluid, permitting the measurement of the concentration field based on the data from the discrete particle distribution. This approach revealed a relationship between the mixing process and the internal flow caused by surface oscillation. Thus, the internal flow induced by surface oscillation could enhance droplet mixing. Our findings will be conducive to the application and further development of lab-on-a-drop devices.

Figure 1

Coalescence of two ethanol droplets. Each image is a combination of images taken by two high-speed video cameras. Scale bar represents 1 mm. At time t = 0, two droplets start to coalesce.

Figure 2

Visualisation of mixing process, number fraction of particles, and flow field in droplets immediately before and after coalescence. Coalescence of two (a) ethanol droplets, (b) 33 wt% glycerol–water solution droplets, and (c) pure glycerol droplets. (i) Photographs. (ii) Number fraction of particles (red and green dots) inside a droplet. (iii) Flow field of a droplet. For (a-c), (ii) and (iii) were calculated from the snapshot at t = 5.0 ms. Scale bar indicates 1 mm. (a-i), (b-i), and (c-i) correspond to Supplementary video S1, S2, and S3, respectively. At t = 0, two droplets start coalescing.

Figure 3

Visualisation of mixing process, number fraction of particles, and flow field in droplets during oscillation. Droplets formed from (a) two ethanol droplets, (b) two 33 wt% glycerol–water solution droplets, and (c) two pure glycerol droplets. (i) Photographs. (ii) Number fraction of particles (red and green dots) inside a droplet. (iii) Flow field of a droplet. For (a) and (c), (ii) and (iii) were calculated from the snapshot at t = 19.1 and 21.3 ms. For (b), (ii) and (iii) were calculated from the snapshot at t = 19.1 ms. Scale bar indicates 1 mm. At t = 0, two droplets start coalescing. (a-i), (b-i), and (c-i) correspond to Supplementary video S4, S5, and S6, respectively.

Figure 4

Visualisation of mixing process, number fraction of particles, and flow field in droplets after oscillation. Droplet formed from (a) two ethanol droplets, (b) two 33 wt% glycerol–water solution droplets, and (c) two pure glycerol droplets. (i) Photographs. (ii) Number fraction of particles (red and green dots) inside a droplet. (iii) Flow field of a droplet. For (a), (ii) and (iii) were calculated from the snapshot at t = 275 and 300 ms. For (b) and (c), (ii) and (iii) were calculated from the snapshot at t = 300 ms. Scale bar indicates 1 mm. At t = 0, two droplets start coalescing. (a-i), (b-i), and (c-i) correspond to Supplementary video S7, S8, and S9, respectively.

Figure 5

Time evolution of mixing index Mc after droplet coalescence. Lower figure shows the first 300 ms of the upper figure. Each solid line shows the moving average of 50 frames; the error band shows the standard deviation. Interruption in the lines correspond to when the droplet was outside the imaging area. Dashed lines correspond to the initial Mc’s when the droplets coalesced at t = 0.

Figure 6

Schematic of experimental setup.

Figure 7

Characteristics of fluorescence and transmittance. (a) Fluorescent of tracer particle. (b) Transmittance of optical system.

Figure 8

Comparison of physical timescales considered for droplet mixing. The mixing time t_mc for Mc = 0.5 (as shown in Fig. 5b) is compared with (a) the particle diffusion time t_tr and (b) the viscous dissipation time, both as functions of the droplet radius r and the kinematic viscosity ν.

Figure 9

Procedure for calculating mixing index. (a) Detection of particles in image. (b) Corresponding Voronoi diagram. (c) Particles adjacent to central black particle. White or black circles represent red or green particles.