Cluster transport

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Appendix 1.(b). Droplets lying along the x axis

4.3 Regime decomposition

4.3.2 Cluster transport

After the droplets enter into the 3D reservoir channel, they are subjected to the flow field. We investigate the behavior of the droplet transport. Interestingly, the rearrange-ment of droplet aggregates is observed which may end with certain stable structures ac-cording to the flow conditions (for the adhesive formulation). In the transport part, we first introduce the way we control the spacing and measure the droplet position in z direc-tion to have a full image of the droplet’s modirec-tion in the reservoir channel. Afterward we describe the experimental cluster formation observations, followed by a numerical anal-ysis of the flow field conditions in the absence of droplets in the reservoir channel. The hydrodynamic assisted clustering process will be further discussed in our preprint paper:

Self-assembly driven by hydrodynamic dipolar interactions.

Cluster spacing control

As we have shown in the cluster production part (see figure 4.11), the number of droplets inside a cluster could be easily predicted by controlling the plug volume pro-duced with the upstream T-junction. Once those droplets enter the microfluidic reservoir, they are immediately subjected to the flow field and be conveyed downstream. Lots of morphologies are discovered with our approach, as shown in figure 4.14.

Figure 4.14: Optical micrographs of different morphologies obtained through our system.

System withh1 = 50µm, h2 = 160µm. n=1.5, 2, 2.5, 3, 4. Scale bar is 100µm.

The spacing of the clusters is one of the key parameters to control the clustering process.

The spacing of the cluster depends on two values: the droplet production frequency and thevelocity field in the reservoir which is mainly dominated by the dilution phase.

The faster the droplets are generated and the more slowly they are conveyed, the higher the risks for the droplets to accumulate at the entrance of the reservoir channel and to lose their identities immediately. Fortunately, the droplet production is not much influenced by the dilution phase (see figure 4.7) which means that there is only a weak dependence between the systems. This makes it easy for us to finely tune the cluster spacing.

We show results of the clusters with different spacing for comparison. In figure 4.15, we keep the Pdilution fixed and change slightly Pdisperse and Pcontinuous simultaneously.

This fine tuning of pressures allows us to have more or less the same length of plug and the cluster transport speed while the droplets production frequency at T-junction is modified. In figure 4.15 (a), droplet generation frequency (f = 1.64 Hz) is higher than that in figure 4.15 (b) (f = 0.31 Hz) and the cluster transport velocity is the same.

Figure 4.16 shows another example in which we control the spacing of triplet clusters by fixing the pressure of the dispersedPdisperseand of the continuous phase Pcontinuouswhile changing the pressure of the dilution phasePdilution. In those experimental conditions, as PdisperseandPcontinuousare fixed, the plug size and generation frequency is nearly the same (f≈1.25 Hz). We increasePdisperseand we observe that it is the transport speed of clusters that control the spacing between cluster entities: In figure 4.15 (a), Pdilution is 5 mbar, it is increased to 10 mbar in (b) and 20 mbar in (c). The spacing distances between the clusters are 100µm, 400µm and 1100µm respectively in those three cases. Similar results can be easily obtained for other microfluidic systems with smaller geometrical dimensions (see figure 4.17; system with W=20µm, h1=10µm, h2=22µm).

4.3. Regime decomposition 91

Figure 4.15: Spacing control of the cluster entities by changingPdisperse and Pcontinuous. System with W=100µm, h1=10µm, h2=160µm. (a) Pdisperse=33mbar, Pcontinuous=10 mbar,Pdilution= 20 mbar.(b) Pdisperse=35mbar, Pcontinuous=10 mbar,Pdilution= 20 mbar.

Scale bar is 100µm.

Figure 4.16: Spacing control of the cluster entities by changing Pdilution. System with W=50µm, h1=10µm, h2=160µm. (a) Pdisperse=38mbar, Pcontinuous=11mbar, Pdilution= 20mbar. The distance between clusters is 100µm.(b) Pdisperse=38mbar, Pcontinuous=11mbar, Pdilution= 80mbar. The distance between clusters is 400µm.(c) Pdisperse=38mbar,Pcontinuous=11mbar,Pdilution= 120mbar. The distance between clusters is 1100µm. The scale bar is 100µm.

Droplet z position measurement Adaptive focus control

We are interested in recognizing the real time z position of the droplets in the reservoir as a function of time to better understand their flow environment. By using the fully automated Leica microscope system with Adaptive Focus Control (AFC), the measurement of the z position of droplets could be realized. We carry out the z position measurement on the smallest microfluidic system which has W = 20µm, h1 = 1µm and h2 = 22µm.

The fully automated AFC is a powerful tool for recordings in combination with multi-positioning, z-stacking and multifluorescence experiments. After setting the focus position of the substrate of our PDMS devise as reference position z = 0µm, we regulate the focus position progressively to screen throughout the whole height of the microfluidic reservoir channel (h2 = 22µm). As the clustering process is reproducible and stationary, we could

Figure 4.17: Spacing control of the cluster entities by changing Pdilution. System with W=20µm, h1=10µm, h2=22µm. (a) Pdisperse=1000 mbar, Pcontinuous=1000 mbar, Pdilution= 5 mbar. The distance between clusters is 300 µm.(b) Pdisperse=1000 mbar, Pcontinuous=1000 mbar,Pdilution= 10 mbar. The distance between clusters is 600µm.(c) Pdisperse=1000 mbar, Pcontinuous=1000 mbar, Pdilution= 20mbar. The distance between clusters is 1600µm. The scale bar is 20µm.

register the videos of the cluster transport at different z positions and follow the z position evolution of the droplets during the transport process in the reservoir channel. Figure 4.18 shows an example of the clusters images taken at a fix distance to the step x ≈ 40µm, with different z position focus from 0µm to 22µm. We can identify the z position of the droplet with the sharpest image, which is in between z =11µm and 15 µm.

Figure 4.18: Optical micrographs of a triplet of droplets located at 40µm away from the step, with different z focus position from the bottom of the microfluidic channel z = 0µm to the top z = 22µm. When the focus is away from the droplets, the cluster’s contour is blurred and it turns clearer if the focus is on its location. The scale bar is 20µm.

With this method, we carried out the measurements of the droplet position under different flow conditions. Results are reported in graph 4.19. A fast evolution towards the middle height z = 11µm is observed within a few tens of micron.

Microscope confocale imaging

Confocal imaging was also carried out to invetigate the droplet z position. This was performed at le Commissariat `a l’´energie atomique et aux ´energies alternatives (CEA), Saclay in France. We produced a stationary train of clusters made of aqueous droplets flowing in the mineral oil. To help visualization, the dispersed phase was mixed with fluorescein isothiocyanate dextran. Rhodamine B red dye (6×10−3% in aqueous solution), was infused into the channels and washed before the experiments to help visulizing the wall of channels. This dye has affinity to the PDMS and permeates the porous polymer matrix. Fluids were pumped into the devices through PEEK tubing using a pressure controller (MFCS Fluident). We performed the experiments with different flow conditions, thePdillution varies from 250 mbar to 700 mbar.

The trajectory of the stationary clusters train appears as a florescent tube due to the long imaging exposure time and the acquisition frequency. Figure 4.20 is the recon-struction of superimposed images with Olympus FLUOVIEW software. Throughout the

4.3. Regime decomposition 93

Figure 4.19: The droplet position in the reservoir channel. (a) Schematic drawing of the xz plan showing the droplet generated at the 3D step is flowing in both x and y direc-tions. (b) The droplet position in z normalized by the reservoir channel height h2 as a function of the distance to the step x. (n) N=4,Pdilution=0 mbar, (l) N=4,Pdilution=10 mbar, (s) N=4,Pdilution=50 mbar, (u)N=4,Pdilution=100 mbar, (m)N=5,Pdilution=20 mbar, (∆)N=6,Pdilution=20 mbar.

experiences, we observed a fast evolution of clusters towards the middle of the reservoir channel. In this reconstructed image, we put the entries in the up side to better visualize the coming flow.

Figure 4.20: A three-dimensional confocal microscopy image of the collective trajectories of doublet clusters shows how the position of the cluster evolute after the step production.

The surface of the channel is labeled for a more vivid observation. We add artificially the doublet clusters in the envelop of their trajectories. Two cross-sections of yz plan are shown in the right: close to the entries at L= 50µm and away from the entries at L=

500µm. A fast evolution towards the mid-plan is observed. PDMS system with W = 50µm, h1 = 10µm and h2 = 163µm. The stable doublet clusters production is obtained withPdisperse=80 mbar,Pcontinuous=90 mbar, Pdilution= 320 mbar.

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