Electrically initiated upstream coalescence cascade of droplets in a microfluidic flow

Two phase microfluidic systems creating size-controlled microdroplets have recently emerged as powerful tools to achieve liquid compartmentalization for high throughput chemical and biological assays. Emulsion electrocoalescence is a destabilization process that can be used in droplet-based platforms for water phase separation to enable lab-on-a-chip applications in biotechnology, including particle or cell recovery. In this paper, we report upon a series of phenomena associated with electrocoalescence of water microdroplet-in-oil populations in microfluidics. In our experiments, we formed microdroplets whose size and dispersion in the channel were varied according to the ratio of the flow rates of the two phases. Different types of electrocoalescence between droplets were obtained. For low applied voltages, drops merged in pairs over the electrode region; for higher values of the applied voltage, a cascade of droplet coalescence was produced against the flow direction, for a range of droplet sizes, lateral distributions of droplets in the channel and localized electric fields.

Figure 1

Device geometry. A $T$ junction (dimensions as reported in inset A) was used to form water emulsions in oil. Further downstream, channel width is $500\mu \text{m}$ (inset B) and microelectrodes were placed perpendicular to the flow direction (dimensions and patterns as reported in inset $E_1$ and $E_2$). Bonding pads were used to contact wires from excitation source. A square waveform was applied at the electrodes, with 1–3 and 2–4 sharing the same potentials.

Figure 2

Emulsions flowing from left to right inside the serpentine channel: (a) $Q_C=3\mu \text{L}/\text{min}$, $Q_D=1\mu \text{L}/\text{min}$; (b) $Q_C=1\mu \text{L}/\text{min}$, $Q_D=1\mu \text{L}/\text{min}$; (c) $Q_C=0.5\mu \text{L}/\text{min}$, $Q_D=1.5\mu \text{L}/\text{min}$. [(d) and (e)] Average droplet area and area fraction, $F$, for different values of $Q_D/Q_T:0.25$ ($Q_D=1\mu \text{L}/\text{min}$, $Q_C=3\mu \text{L}/\text{min}$), 0.33 ($Q_D=1\mu \text{L}/\text{min}$, $Q_C=2\mu \text{L}/\text{min}$), 0.5 ($Q_D=1\mu \text{L}/\text{min}$, $Q_C=1\mu \text{L}/\text{min}$), 0.66 ($Q_D=2\mu \text{L}/\text{min}$, $Q_C=1\mu \text{L}/\text{min}$), and 0.75 ($Q_D=1.5\mu \text{L}/\text{min}$, $Q_C=0.5\mu \text{L}/\text{min}$). Dashed lines are fitting the data with an exponential function (d) and a line (e) using a least square algorithm. [(f) and (g)] Average droplet area and area fraction $F$ of water to oil for $Q_C=Q_D$ and $Q_T=1$, 2, 3, 4, 5, 6, and $8\mu \text{L}/\text{min}$, respectively (dashed line is fitting the data with a line using a least square algorithm). Scale bar is $100\mu \text{m}$.

Figure 3

(a) Mean interdroplet distance $\left(D_{\text{ID}}\right)$ and (b) mean droplet diameter $\left(D_{\text{MD}}\right)$ for different values of $Q_D/Q_T:0.25$ ($Q_D=1\mu \text{L}/\text{min}$, $Q_C=3\mu \text{L}/\text{min}$), 0.33 ($Q_D=1\mu \text{L}/\text{min}$, $Q_C=2\mu \text{L}/\text{min}$), 0.5 ($Q_D=1\mu \text{L}/\text{min}$, $Q_C=1\mu \text{L}/\text{min}$), 0.66 ($Q_D=2\mu \text{L}/\text{min}$, $Q_C=1\mu \text{L}/\text{min}$), and 0.75 ($Q_D=1.5\mu \text{L}/\text{min}$, $Q_C=0.5\mu \text{L}/\text{min}$). (c) ratio $D_{\text{ID}}/D_{\text{MD}}$ over the droplet area (dashed line is fitting the data with a line using a least square algorithm). (d) Average droplet velocity inside the serpentine channel for $Q_C=Q_D$ and $Q_T=1$, 2, 3, 4, 5, 6, and $8\mu \text{L}/\text{min}$, respectively. Mean flow velocity was calculated by dividing $Q_T$ for the cross-sectional area of the channel.

Figure 4

Numerical simulations obtained using COMSOL 3.3. Side view of the electric field distribution inside the channel around the electrode area for a pulsed dc square wave applied at the electrodes (potential values reported in the figure).

Figure 5

Electrocoalescence behaviors of a stream of water droplets in oil under the effect of an applied pulsed dc field at a frequency of 10 kHz: (a) no coalescence occurred without the application of subthreshold electric fields; (b) droplet coalescence originated when a potential threshold $V_1$ was reached; (c) increasing the potential led to drop coalescence that spanned the channel width; (d) drop coalescence is propagated against flow direction when a potential threshold $V_2$ was reached. Scale bar is $200\mu \text{m}$.

Figure 6

(Top) Droplet electrocoalescence behavior as a function of the electric field frequency for total flow rates. $Q_T=3\mu \text{L}/\text{min}$ and $Q_D/Q_T=0.33\mu \text{L}/\text{min}$ ($Q_D=1$, $Q_C=2$), $0.5\mu \text{L}/\text{min}$ ($Q_D=1.5$, $Q_C=1.5$), and $0.66\mu \text{L}/\text{min}$ ($Q_D=2$, $Q_C=1$). Four regions were identified: (i) no coalescence, (ii) downstream coalescence, (iii) upstream coalescence, and (iv) hydrolysis. (Bottom) Droplet electrocoalescence results from over 30 experiments where $Q_T$ varied from 1 to $6\mu \text{L}/\text{min}$, the ratio $Q_D/Q_T$ varied from 0.28 up to 0.7 and the frequency was fixed at 10 kHz. Dashed lines indicate mean values. The following values were calculated for a distance between electrodes of $20\mu \text{m}$ (inset $E_2$ in Fig. 1): obtaining a mean value of 7.24 V for $V_1$ and 16.1 V for $V_2$, which convert in electric field strength values of 3.62 and 8.05 kV/cm, respectively. At 10 kHz hydrolysis never occurred and region of type (i)–(iii) were obtained.

Figure 7

Example of a time sequence showing upstream coalescence induced in a microchannel (sequence was recorded at 2 kHz). Two different types of fusion were observed in upstream coalescence: [(a)–(g)] EE fusion caused only by the electric field strength; [(h)–(t)] HE fusion caused only by localized decompressions and capillary forces between a droplet and the retreating finger. Scale bar is $100\mu \text{m}$.

Figure 8

[(a) and (b)] Two time sequences of droplet fusion induced by the EE fusions. No droplet deformation was observed before fusion.

Figure 9

[(a)–(d)] Time sequence showing an aqueous finger moving toward the electrodes at a velocity higher than the droplet stream. It can be noticed (white dashed lines and arrows) that the finger shortened along the flow direction and, at the same time, became wider along the width of the channel. This effect was caused by surface tension, the finger wanting to minimize the surface in contact with the oil. (e) Average velocity of aqueous finger and droplet for total flow rate, $Q_T=1$, 2, 3, 4, 5, 6, and $8\mu \text{L}/\text{min}$. Scale bar is $100\mu \text{m}$.

Figure 10

(a) Schematic of a time sequence of droplet fusion where $Q_D=1$ and $Q_C=2$. The parameter $D$ is the semi axis of a droplet obtained as the distance between the center of mass of a droplet and the interface of the droplet along the fusion direction and it represents droplet deformation. (b) Examples of evolution of the distance $D$ versus time for a droplet fusing in the first stage (triangles) and second stage (circles) of upstream coalescence. The rightmost of each sequence corresponds to the last frame before fusion occurred. $D\left(t\right)$ has a gradient of $0.03\mu \text{m}/\text{ms}$ ($\pm 0.1\text{std}$, $n=10$) in the moments before fusion in the first case (EE). When coalescence occurred in the second case (HE), $D$ increased with time, yielding a gradient of $1.29\mu \text{m}/\text{ms}$ ($\pm 0.34\text{std}$, $n=10$).