PDMS droplet formation and characterization by hydrodynamic flow focusing technique in a PDMS square microchannel

The MFFDs were fabricated by soft lithography [29, 30] by pouring a well-mixed solution of PDMS and curing agent (5 : 1) onto the SU-8 mold. A thin layer, ~30 μm, of PDMS and curing agent (20 : 1) was spread by spincoating, in a glass slide. This ensures that all the MFFD walls material have the same wetting properties. Both the PDMS mold and the coated glass slide were cured, in an oven, at 80 °C for 20 min. Afterwards, the cured PDMS was peeled off from the SU-8 mold and sealed to the glass coated slide. To ensure a good sealing, the sealed channel was left to cure for approximately 12 h at 80 °C [29].

In the droplet formation experiment, the liquid pre-polymer cannot be in direct contact with the PDMS channel walls, since the pre-polymer PDMS has a high affinity with the hydrophobic PDMS of the channel walls, which is undesirable. With an air plasma surface-treatment, the PDMS surface can be modified from hydrophobic to hydrophilic to have more affinity with the aqueous continuous phase. Plasma treatment was carried out with air in a low pressure Plasma Reactor (Diener^® electronic GMbH, model ZEPTO).

The MFFD, figure 1, consists of three inlet channels—one for the disperse phase, two for the continuous phase—and one outlet channel. All these channels intersect at right angles and have identical dimensions.

Zoom In Zoom Out Reset image size

The continuous phase was an aqueous solution with a surfactant, sodium dodecyl sulfate (SDS L3771-Sigma Aldrich) 2% w/w, and the dispersed phase was the liquid pre-polymer PDMS. The PDMS used for both, channels and disperse phase, was the Dow Corning Sylgard^® 184 kit composed by a base polymer and a curing agent with viscosities, respectively, of 5 and 0.11 Pa s. A base to curing agent ratio of 6 : 4 was chosen for the PDMS pre-polymer disperse phase since, in a previous study, droplets were successfully generated taking this proportion [17].

The viscosity of both phases was characterized using a rotational rheometer (Physica MCR301, Anton Paar) with a Peltier temperature control system. The measurements were performed at 20 °C using a 50 mm diameter plate to plate geometry, PP50, with a gap of 0.1 mm. This gap and the characteristic dimension of the channel are of the same size. As the PDMS pre-polymer cures over time, to avoid drawbacks a 2 h experimental window for the droplet generation was chosen and the PDMS pre-polymer rheology was characterized during an identical period of time (figure 2).

Zoom In Zoom Out Reset image size

The viscosities listed in table 1 are the mean viscosities within 2 h. The density of both phases was measured with a 10 ml pycnometer. The interfacial tension between phases was also measured at ~20 °C in a DuNuoy ring tensiometer. The equilibrium contact angle between the disperse phase and the channels walls is 42° and was measured according to a previous work by Tan et al [31]. The difference between the two wall-fluid interfacial tensions (wall-continuous phase interfacial tension and wall-disperse phase interfacial tension) is ~0.009 N m⁻¹ (as calculated by the Young's equation [32]).

Droplet formation images were captured at a maximum rate of 10 000 frames per second via a high-speed camera (FASTCAM Mini UX100, Photron) mounted on an inverted epifluorescence microscope (DMI 5000M, Leica Microsystems GmbH). Using a dedicated syringe pump, the dispersed and continuous phases were injected into the microchannel. The post-processing of the images was performed using a MATLAB^® custom code.

In this study, due to the small size of the device, inertial forces can be neglected and therefore only capillary and viscous forces are responsible for the different flow patterns. The regimes were characterized by the capillary numbers of both phases, defined as:

$$\begin{eqnarray}&&\text{Ca}=\frac{U\mu}{\sigma}\end{eqnarray} \tag{ 1 }$$

where $U$ and μ are, respectively, the fluid velocity and viscosity and $\sigma$ the interfacial tension.

The flow regime map obtained is presented in figure 3. The identification of the regimes was done according to Cubaud and Mason [24] work and is based only on the capillary numbers of the phases. Since dripping and jetting regimes are those capable of generating droplets, the characterisation study was narrowed to capillary number ranges where these two regimes are reported in the flow regime map and in previous works [24, 25, 28, 33]. Table 2 gathers all the experimental conditions including the regime state representing the flow rates imposed, the flow rate ratio:

$$\begin{eqnarray}&&\varphi =\frac{{{Q}_{\text{c}}}}{{{Q}_{\text{d}}}}\end{eqnarray} \tag{ 2 }$$

where $\varphi$ is the flow rate ratio and ${{Q}_{\text{c}}}$ and ${{Q}_{\text{d}}}$ are the flow rate of the continuous and disperse phases respectively.

Zoom In Zoom Out Reset image size

Table 2. Experimental conditions of both fluids and the respective regimes observed.

$\varphi$	${{Q}_{\text{d}}}$ (ms−3)	${{Q}_{\text{c}}}$ (ms−3)	$\text{C}{{\text{a}}_{\text{d}}}$	$\text{C}{{\text{a}}_{\text{c}}}$	Regime (symbol)
10	1.67  ×  10−12	1.67  ×  10−11	8.89  ×  10−3	1.39  ×  10−4	▪ Dripping
20	1.67  ×  10−12	3.33  ×  10−11	8.89  ×  10−3	2.79  ×  10−4	▪ Dripping
30	1.67  ×  10−12	5.00  ×  10−11	8.89  ×  10−3	4.17  ×  10−4	▪ Dripping
40	1.67  ×  10−12	6.67  ×  10−11	8.89  ×  10−3	5.56  ×  10−4	▪ Dripping
50	1.67  ×  10−12	8.30  ×  10−11	8.89  ×  10−3	6.94  ×  10−3	▪ Dripping
20	5.00  ×  10−12	1.00  ×  10−10	2.67  ×  10−2	8.33  ×  10−4	Dripping
40	5.00  ×  10−12	2.00  ×  10−10	2.67  ×  10−2	1.67  ×  10−3	Dripping
80	5.00  ×  10−12	4.00  ×  10−10	2.67  ×  10−2	3.33  ×  10−3	Dripping
166.67	5.00  ×  10−12	5.00  ×  10−10	2.67  ×  10−2	6.94  ×  10−3	Dripping
333.33	5.00  ×  10−12	1.67  ×  10−9	2.67  ×  10−2	1.39  ×  10−2	Dripping
10	1.00  ×  10−11	1.00  ×  10−10	5.33  ×  10−2	8.33  ×  10−4	▪ Dripping
20	1.00  ×  10−11	2.00  ×  10−10	5.33  ×  10−2	1.67  ×  10−3	▪ Dripping
30	1.00  ×  10−11	3.00  ×  10−10	5.33  ×  10−2	2.50  ×  10−3	▪ Dripping
40	1.00  ×  10−11	4.00  ×  10−10	5.33  ×  10−2	3.33  ×  10−3	▪ Dripping
50	1.00  ×  10−11	5.00  ×  10−10	5.33  ×  10−2	4.17  ×  10−3	▪ Dripping
6	1.67  ×  10−11	1.00  ×  10−10	8.89  ×  10−2	8.33  ×  10−4	▪ Dripping
12	1.67  ×  10−11	2.00  ×  10−10	8.89  ×  10−2	1.67  ×  10−3	Jetting
24	1.67  ×  10−11	4.00  ×  10−10	8.89  ×  10−2	3.33  ×  10−3	Jetting
50	1.67  ×  10−11	5.00  ×  10−10	8.89  ×  10−2	6.94  ×  10−3	▪ Dripping
100	1.67  ×  10−11	1.67  ×  10−9	8.89  ×  10−2	1.39  ×  10−2	▪ Dripping
4	2.50  ×  10−11	1.00  ×  10−10	1.33  ×  10−1	8.33  ×  10−4	Jetting
8	2.50  ×  10−11	2.00  ×  10−10	1.33  ×  10−1	1.67  ×  10−3	Jetting
16	2.50  ×  10−11	4.00  ×  10−10	1.33  ×  10−1	3.33  ×  10−3	Jetting
33.3	2.50  ×  10−11	5.00  ×  10−10	1.33  ×  10−1	6.94  ×  10−3	Jetting
66.67	2.50  ×  10−11	1.67  ×  10−9	1.33  ×  10−1	1.39  ×  10−2	▪ Dripping
2.4	4.17  ×  10−11	1.00  ×  10−10	2.22  ×  10−1	8.33  ×  10−4	Δ Visc. displament
4.8	4.17  ×  10−11	2.00  ×  10−10	2.22  ×  10−1	1.67  ×  10−3	Jetting
9.6	4.17  ×  10−11	4.00  ×  10−10	2.22  ×  10−1	3.33  ×  10−3	Jetting
20	4.17  ×  10−11	5.00  ×  10−10	2.22  ×  10−1	6.94  ×  10−3	Jetting
40	4.17  ×  10−11	1.67  ×  10−9	2.22  ×  10−1	1.39  ×  10−2	◊ Threading

Low capillary numbers for the dripping region (below 10⁻² for the disperse phase, $\text{C}{{\text{a}}_{\text{d}}}$, and 10⁻³ for the continuous phase, $\text{C}{{\text{a}}_{\text{c}}}$) were also studied to determine if there is any major difference from literature near the jetting regime.

The qualitative identification of the regimes, from Cubaud and Mason [24], is as follows:

• The dripping regime (▪), where the thread of the continuous phase breaks and the cap formed stays within the focusing section;
• The jetting regime (), where the thread breaks and the cap stays in the outlet channel;
• The threading regime (Δ), where the thread is stable and doesn't break within a distance of $l<20w$ from the focusing area;
• The viscous displacement regime (◊) characterized by the dispersed phase invading the continuous phase side channels.

In the literature another regime appears before the viscous displacement, the tubing regime, in which continuous phase occupies most of the cross section of the outlet channel [24]. This regime was not observed, maybe due to the nature of the PDMS pre-polymer and the presence of the surfactant.

In figure 3, at a critical $\text{C}{{\text{a}}_{\text{d}}}$  ≈  10^–1 (), a transition between the dripping and jetting regimes occurs. This critical value is widely observed in the literature and it depends slightly on $\text{C}{{\text{a}}_{\text{c}}}\,$ [24, 25, 28, 33, 34]. The frontier between these two regimes is important since it signalizes the change between viscous and capillary effects governing the flow [24]. Above the dripping-jetting transition region, the viscous forces dominate and the viscous thread starts to increase in length as both capillary numbers increase and, eventually, the regime becomes purely viscous (Δ) [24].

Since one of the goals of this study (see Introduction) is to find the best flow conditions for monodisperse and high throughput droplet formation, a quantitative characterization of the flows signalized in the regime map is essential. It is worth noting that this quantitative analysis was $\text{only} ~$ done for jetting and dripping regimes.

An important parameter to measure the amount of droplets generated over time is the droplet generation frequency, f, given by,

$$\begin{eqnarray}&&f=\frac{{{\text{n}}^{{{{\underline{\text{o}}}}}}}\text{droplets}}{\Delta t}\,\left(\text{Hz}\right)\end{eqnarray} \tag{ 3 }$$

which measures the number of droplets generated over a time interval $\Delta t$ of 1 s. This variable is important to the goals of the present work and a regime with a high frequency value is the most desirable.

According to figure 4, frequency increases until a critical $\text{C}{{\text{a}}_{\text{c}}}\,\text{number}$ and from there on decreases. The critical $\text{C}{{\text{a}}_{\text{c}}}$ number is different for each regime, $\text{C}{{\text{a}}_{\text{c}}}$  ≈  2  ×  10⁻³ and $3~\times {{10}^{-3}}~$ for the dripping and jetting regime respectively (dashed lines, figure 4). This change is mainly explained by the overlapping of the viscous over the interfacial forces for increasing $\text{C}{{\text{a}}_{\text{c}}}$ numbers. For very low $\text{C}{{\text{a}}_{\text{d}}}$ 10⁻² numbers, the frequency is almost independent of $\text{C}{{\text{a}}_{\text{c}}}$. As expected, for a given $\text{C}{{\text{a}}_{\text{c}}}\,\text{number}$, the frequency increases as the $\text{C}{{\text{a}}_{\text{d}}}\,\text{number}$ increases.

Zoom In Zoom Out Reset image size

Breakup distance, $l$, is important to assure that droplets are generated near the focusing area, since instabilities can arise if the threads continue to grow [24]. The normalized breakup distance, L, was measured from the end of the focusing area until the location where the thread breaks up and is given by:

$$\begin{eqnarray}&&\text{L}=\frac{l}{w}\end{eqnarray} \tag{ 4 }$$

where $l$ is the length of the thread before breakup and $w$ the characteristic dimension of the channel.

As observed in figure 5, L increases until $\text{C}{{\text{a}}_{\text{c}}}~$  ≈  $3~\times {{10}^{-3}}$ and from there on starts decreasing for both dripping and jetting regime (vertical dashed lines, figure 5). For very low $\text{C}{{\text{a}}_{\text{d}}}$ 10⁻², the normalized breakup distance remains more or less constant as the $\text{C}{{\text{a}}_{\text{c}}}$ number increases. For a given $\text{C}{{\text{a}}_{\text{c}}}$ number, the breakup distance decreases from the second to the third row of $\text{C}{{\text{a}}_{\text{d}}}$ number and then starts to increase during the transition from dripping to jetting regime (horizontal dashed lines, figure 5).

Zoom In Zoom Out Reset image size

One of the most desirable features in droplet generation is the control of the droplet size. A high throughput monodisperse droplet generation for a large variety of applications [9–11, 28, 34] is an imperative. Normalized droplet size, ${{\text{L}}_{\text{d}}}$, is defined by:

$$\begin{eqnarray}&&{{l}_{\text{d}}}=\frac{\underset{i=1}{\overset{n}{\sum}}{{l}_{\text{d}i}}}{n}\end{eqnarray} \tag{ 5 }$$

where ${{l}_{\text{d}i}}$ is the axial size of droplet i and n the number of measures done for each condition. To have an overall statistical description, it is also important to know the coefficient of variance (CV) of the normalized variable, defined by:

$$\begin{eqnarray}&&\text{CV}=\frac{{{\sigma}_{{{\text{L}}_{\text{d}}}}}}{{{\text{L}}_{\text{d}}}}\times 100\end{eqnarray} \tag{ 6 }$$

where ${{\sigma}_{{{\text{L}}_{\text{d}}}}}$ is the standard deviation of ${{\text{L}}_{\text{d}}}$.

As shown in figure 6, normalized droplet size oscillates between 0.90–2.20. For both regimes, there is no clearly defined variation pattern with the capillary numbers.

Zoom In Zoom Out Reset image size

Since the droplet size is a mean value, it is important to analyse the CV. According to figure 7, the jetting regime presents a very high CV, while in the dripping regime the CV is around 3.0% for all the cases measured.

Zoom In Zoom Out Reset image size

The main goal of this study was to find out the best flow conditions to obtain high throughput monodisperse PDMS droplets in a PDMS MFFD. The experimental data obtained proved it possible to attain the proposed goal with the experimental technique developed. By analyzing the different variables, the optimal conditions to obtain high throughput monodisperse PDMS droplets are in the dripping regime, near the critical $\text{Ca}$ number, where the best compromise between a low size coefficient variance, 2.8%, and a high formation frequency  ≈12 Hz is achieved. This frequency number is only valid for the operating scale of this work.