Pulsation of electrified jet in capillary microfluidics

In this work, we investigate the pulsation of an electrically charged jet surrounded by an immiscible dielectric liquid in flow-focusing capillary microfluidics. We have characterized a low-frequency large-amplitude pulsation and a high-frequency small-amplitude pulsation, respectively. The former, due to the unbalanced charge and fluid transportation is responsible for generating droplets with a broad size distribution. The latter is intrinsic and produces droplets with a relatively narrow size distribution. Moreover, the average size of the final droplets can be tuned via the intrinsic pulsating frequency through changing the diameter of the emitted liquid jet. Our results provide degree of control over the emulsion droplets with submicron sizes generated in microfluidic-electrospray platform.

liquid with distinctive frequency and amplitude respectively. In the low-frequency pulsation, the liquid meniscus pulsates between a sharp and relaxed conic shape with a large amplitude. As such, small and large droplets are generated alternatively, and the resultant droplets have a broad size distribution. In the high-frequency pulsation, the cone-jet pulsates between different cone angles periodically with a small amplitude, generating small droplets with a narrow size distribution. Moreover, by increasing this intrinsic pulsating frequency, we can tune the average droplet size to achieve control over the resultant emulsions. Our results provide guidelines for generating droplets with degree of controlled over their size and distributions in microfluidic-electrospray platform.

Results
We fabricated the capillary microfluidic device by aligning two tapered round capillaries, an injection and a collection, in a square capillary 18 , as shown schematically in Fig. 1a. The diameters of the injection and collection capillaries were denoted as d 1 and d 2 respectively. Deionized water was used as the inner phase that flowed through the injection capillary at a flow rate of Q 1 driven by a syringe pump (Longer Pump). We used dielectric oils, including paraffin, silicone oil or squalene as the outer phase. Surfactants, span 80 (Sigma) or ABIL EM 90 (Evonik), was added in the outer phase to modulate the interfacial tension and to stabilize the generated droplets. The inner aqueous phase was charged positively by a direct-current (DC) high voltage supply through an inserted electrode in the injection capillary. The outlet of the device was connected to ground through a metal capillary, as shown schematically in Fig. 1a. The DC voltage was applied between the injection and metal capillaries to create an electric field that induced an electrohydrodynamic flow. The resultant electric field strength E was estimated as E = U/L, with U being the potential and L being the distance between the water tip and the ground electrode. We focused on the dynamic behaviors of the charged liquid meniscus under a DC-applied voltage. The charged liquid were visualized using a microscope (Motic AE2000) coupled with a high-speed camera (Phantom M110). Due to the tiny size of the generated droplets in electro-microfluidics, measurement of the their diameter through high-speed images has little accuracy. Given the fact that the water tip would pulsate after emitting each droplet, we therefore characterize the generation of droplets by characterizing the pulsation of the water tip. The length of the water tip l as well as the pulsating frequency f were measured from the high-speed images.
Without the applied voltage, the tip of the inner phase is hemispherical and the generated droplets are uniform in dripping regime. When a voltage is applied, the inner phase is charged and the meniscus is stretched into a conical shape (Fig. 1b). At the end of the cone, a thin jet emits and breaks up into tiny droplets of sub-micron sizes. However, this process only maintains for a certain period of time, and the sharp cone would gradually relax back to a hemispherical one which emit much larger droplets (Fig. 1b). Afterwards, the hemispherical interface is recharged and becomes cone-shaped again, following which submicron droplets are produced. The transition between the cone and the hemispherical shapes of water tip is periodic, as shown in Fig. 1c. During the transition between these two states, droplets with intermediate sizes are generated (Video S1).
In microfluidic-electrospray, the meniscus is mainly subjected to three stresses: the electrostatic stress exerted on the meniscus surface, the shear stress from the surrounding liquid phase, and the surface tension. The former two promote an elongated jet while the latter tries to maintain a hemispherical shape. As the sum of ε E exceeds the capillary pressure 4γ/d 1 , the sharp cone forms, where μ 2 are the viscosity of the surrounding oil phase; γ is the interfacial tension between the water and oil; ε 0 is the permittivity of the free space. As a result, a higher Q 2 or μ 2 leads to a lower applied E to form a cone-shaped jet (Fig. 2a,b). At a sufficiently large Q 2 and μ 2 , the tip is conical without any applied electric field (Fig. 2c). This requires a high pumping power that could be a technical problem for less-robust microfluidic devices. The charged jet pulsates periodically in two distinctive modes with a low and high frequency, ~1 Hz and ~10 2 Hz, respectively 34,35 . In the low-frequency mode, the cone-shaped jet sprays for approximately 1 second, and then relaxes to generate large droplets for also 1 second. Subsequently the hemispherical tip becomes conical and a new cycle begins. The pulsating amplitude, represented by the tip length l of the meniscus, at low-frequency mode is at the same scale of the nozzle diameter d 1 (Fig. 3a). The droplets collected in this mode have a large polydispersity since both small and large droplets are produced alternatively.  The low-frequency pulsation occurs when the imposed electric stress is not comparable to the shear stress by the outer fluid. The large shear stress leads to the droplet detachment from the injection nozzle. After the droplet detaching, the cone volume becomes small and thus the curvature is large (Fig. 3a, inset). The increased curvature increases the capillary pressure to dominate over the shear stresses, therefore the meniscus could keep a hemispherical shape. Gradually with the imposing flow rate, the volume builds up and the curvature decreases to a point that the capillary pressure is overcame again. Then the conical tip forms and emits tiny droplets until a new cycle. As a result, the low-frequency pulsation can be suppressed by decreasing the velocity difference between the inner and outer fluids. Indeed, as we increase Q 1 , the conical tip lasts for tens of minutes during our observation period, as demonstrated in Fig. 3b and Video S2. This indicates that a delicate balance between charge and mass transportation must be provided for a stable droplet generation.
As the shear stress is comparable to the applied electric stress, the high-frequency pulsation starts where the conical tip oscillates between different angles (Fig. 3b, inset plot). The droplets collected in this mode have a much narrower size distribution (Fig. 4) than that in low-frequency mode. The size distribution is Gaussian and has an average droplet size of 2.25 µm and a width of 1.2 µm, as shown in the inset of Fig. 4. According to mass conservation, under constant volumetric flow rate, the faster droplets are generated, the finer they should be. Thus, the average droplet size can be influenced if the intrinsic pulsating frequency can be tuned. The pulsating frequency reported for electrospray-in-air has a magnitude around 1 kHz, while that in flow-focusing microfluidic-electrospray is on the order of ~10 2 Hz (Fig. 3b and Fig. 5a,b). This suggests that the intrinsic pulsating frequency is closely related to the interfacial tension. Moreover, we found that the nozzle diameter d 1 , the flow rates, and the applied E also affect the frequency. One hypothesis is that the intrinsic pulsating frequency relates with the capillary wave on the charged liquid interface. To test our hypothesis, we have the following from the capillary wave equation 34,35 : Where f is the intrinsic pulsating frequency, ρ is the liquid density, and r is the radius of the emitted jet. The eq.
(1) is supported by the interfacial tension data, where γ ow ∼ 1-4 mN/m in our system, at least 18 times lower than γ w ∼ 72 mN/m in electrospray-in-air. Furthermore, we vary different controlling parameters such as d 1 , Q 1 , Q 2 and E to verify the scaling relationship between the radius of emitted jet, r, and the intrinsic frequency, f. Indeed, the data collapses onto a dash line on a log-log plot with a scaling exponent of −1.5, in consistence with eq. (1) (Fig. 5c). These experimental evidence supports the capillary wave explanation. Therefore, we can tune the average size of the resultant droplets through changing the intrinsic pulsating frequency, using approaches such as increasing electrostatic and shear stress to vary the emitted jet radius. The results described here are potentially important in fabricating sub-micron emulsions and particulate delivery systems.

Discussion
Emulsion droplets of fine size are ubiquitous in our daily life, in industrial products, and are essential for emerging photo-acoustic therapies. Current emulsification either generates nano-sized emulsions with litter control over the characteristics of droplets, or precisely-controlled beautifully-uniform droplets that are too large for therapeutic purposes. We explored the microfluidic-electrospray technique by characterizing its operation modes and underlying mechanism. We found that a low-frequency pulsating mode, where the charge and fluid transportation are unbalanced, is responsible for droplets with a broad size distribution. By adjusting the imposing flow rate, an intrinsic high-frequency pulsating is pronounced, and through which the average droplet size can be manipulated. Our results could be beneficial to emulsion-based applications including food, cosmetics and pharmaceutics.

Methods
Fabrication of capillary microfluidic device. We fabricated capillary microfluidic device by aligning two tapered round capillaries into a square one 16, 17, 19-23, 28, 33 (Fig. 1a). The inner and outer diameter of the round capillaries are 0.58 mm and 1 mm respectively; those of the square one are 1 mm and 1.05 mm, respectively. The tip of the round capillaries was tapered to sizes between 20 µm and 580 µm. One or multiple liquids were injected using syringe pumps (Longer Pump) and soft micro-tubings (Scientific Commodities). The inner phase flowed through the injection capillary (Fig. 1a); an outer liquid phase flowed via the gap between the injection and square capillaries, then into the collection capillary. The outer liquid phase completely wetted the glass wall that was hydrophobitized by trimethoxysilane (Sigma).
Integration of the electrospray in a capillary microfluidic device. A metal wire was inserted into the injection capillary, and it was connected to the positive electrode of a direct current (DC) high voltage power supply. The device was grounded by connecting a metal tube wrapping the collection capillary to the negative end of the power supply. The direction of the electric field generated was the same as the flow direction of the inner liquid. The injected liquid phase was charged through the injection nozzle. The applied electric field intensity was controlled by adjusting the potential value of the power supply, U, while the distance between electrodes were kept constant. The applied electric field intensity typically ranged from 0 kV/cm to 6 kV/cm. The pulsating modes of the charged liquid jets were visualized and recorded using a high speed camera (Phantom M110) coupled with an inverted microscope (Motic AE2000).
Composition of the liquid phases. The inner liquid was deionized water; the outer liquids were dielectric oils, including paraffin, silicone oil or squalene, with viscosities of 40 mPa.s, 10 mPa.s and 27.8 mPa.s respectively. The electrical conductivity of the liquid affects the operation modes that could occur for charged liquid meniscus. We measured the conductivity of the water phase in our experiment to be 2.34 µS/cm, which can be classified into leaky dielectrics; while the electrical conductivity of the oil phases is on the order of 10 −9 µS/cm, thus the potential was mainly fall on the water phase. To tune the interfacial tensions, we added surfactants, such as span 80 (Sigma) or ABIL EM 90 (Evonik) to the outer phase. The concentration of span 80 and ABIL EM 90 were both 5 wt% that are higher than their critical micelle concentrations. The interfacial tension between paraffin, silicone oil, squalene with high concentration of surfactants and water, respectively, were measured to 3.1 mN/m, 2.8 mN/m, 2.5 mN/m. Due to the small size (0.02~1 mm) of the device, the corresponding Reynolds number was on the order of 10 −3 or below, thus we neglected the inertia of the inner phase.
Image analyzing. The pulsating frequency, jet radius and tip length of meniscus were obtained after processing and analyzing the high-speed images and videos using an open-source image-processing software, Image J (version: 1.48 v). The frame rates of the camera used for experiments were 400 frames·s −1 and 1000 frames·s −1 . We counted the frames during the pulsating cycles and calculated the corresponding frequency. Each frequency was based on measurements from at least five different cycles while each jet radius was measured using at least five high-speed images.