3.1. Effect of Vibration Frequency on Droplet Generation Frequency
To investigate the droplet generation process with external mechanical vibration, the effects of vibration frequency (fP) and vibration amplitude (am) on the generation frequency (fG) are first studied. The effect of vibration frequency is studied by varying the frequency of external mechanical vibration in the range of 0–500 Hz while the maximum acceleration is held at 60 m/s2. To study the effect of vibration amplitude, the external vibration frequency is kept constant at a certain frequency and the vibration amplitude varies through the control of acceleration.
When the flow rates of continuous phase (
Qc) and dispersed phase (
Qd) are 90 and 60 μL/h, respectively, the droplet generation frequencies at different vibration frequencies are shown in
Figure 3. The droplet generation frequency without external vibration (0 Hz), named as the natural generation frequency (
fN), is 44 Hz. As shown in the figure, it is obvious that the vibration in the dispersed phase plays an important role on the droplet generation frequency. When the external vibration frequency increases from 40 to 500 Hz, the generation frequency of discrete droplet fluctuates in the range of 40–170 Hz.
Promoting the vibration frequency from 40 to 80 Hz, the droplet generation frequency is consistent with the external vibration frequency. However, corresponding to the vibration frequencies of 90 and 100 Hz, the generation frequencies of droplet are 45 and 50 Hz, respectively, which are only half of the vibration frequencies applied. Continuously increasing the vibration frequency to the range of 110–500 Hz, it is interesting that the droplet generation frequency becomes consistent with the vibration frequency again in the range of 110–130 Hz, whereas the droplet generation frequency decreases sharply to 53.5 Hz as the vibration frequency reaches to 160 Hz. Then the generation frequency soars to 170 Hz which is in accordance with the external vibration frequency, thereafter, the generation frequency of dispersed droplet maintains around 50 Hz, as the vibration frequency varies in the range of 200–500 Hz.
The relation between the droplet generation frequency and the external vibration frequency is given in
Figure 4. As shown in the figure, linear correlation can be obviously observed, thus the droplet generation frequency can be expressed as follow:
where
k = 1 means the generation frequency of dispersed droplet is synchronized with the external mechanical vibration frequency, that is one external vibration can produce one droplet (such as the vibration frequency of 40 Hz). While
k = 1/2 indicates the droplet generation frequency is only half of the external vibration frequency, in other words, it needs two external vibrations in the dispersed flow to generate one droplet (such as vibration frequency of 90 Hz). Furthermore, relationships of
k = 1/3, ¼, and 1/5 are also observed in our experiments, as shown in
Figure 3 and
Figure 4.
Although the linear correlation between droplet generation frequency and vibration frequency hasn’t been mentioned in previous studies on the active droplet generation with mechanical vibration, it is found that Equation (2) is also applicable to the experimental results carried out by Zhu et al. [
11] on the droplet generation with external mechanical vibration in a co-flowing microfluidic device. The relevant values of droplet generation frequency and mechanical vibration frequency in reference [
11] are cited and shown in
Figure 5. Apparently, the relations of
k = 1, 1/3 and 1/4 can be observed. However, the relations of
k = 1/2 and 1/5 are not found, this may be related to the differences in device geometry and vibration condition.
3.2. Effect of Vibration Amplitude on Droplet Generation Frequency
Figure 6 shows the variation of droplet generation frequency with the increasing vibration amplitude when the vibration frequency is held at 170 Hz. The flow rates of continuous phase and dispersed phase are both 60 μL/h, correspondingly, and the natural generation frequency of dispersed droplet is 32 Hz. It is clear that the droplet generation in the flow-focusing device is greatly affected by the increase of vibration amplitude, as the external vibration amplitude increases from 0 m/s
2 (without vibration) to 136.3 m/s
2, the generation frequency of dispersed droplet increases monotonously in the range of 32–170 Hz, and the volume of generated droplet decreases correspondingly. When imposing external vibration on the dispersed phase and increasing the vibration amplitude, the droplet generation frequency maintains at the natural generation frequency of 32 Hz at first, till the vibration amplitude reaches to 10.6 m/s
2, the frequency of generated droplet jumps to 34 Hz which is one fifth of the vibration frequency (170 Hz). Continuously promoting vibration amplitude, the droplet generation frequency keeps at 34 Hz before the amplitude reaches to 19.1 m/s
2, and then the generation frequency skips to one quarter of the vibration frequency (43 Hz). Similarly, after held at 43 Hz, the droplet generation frequency arrives one third of the vibration frequency (58 Hz), corresponding to the vibration amplitude of 30.6 m/s
2. When the vibration amplitude gets to 39.9 m/s
2, the generation frequency jumps to 85 Hz. Finally, the droplet generation frequency reaches to 170 Hz, synchronizing with external vibration, as the vibration amplitude is greater than or equal to 136.3 m/s
2. Obviously, the relation between the droplet generation frequency and external vibration frequency under different vibration amplitudes also can be expressed by Equation (2). In other words, the step changes happen in droplet generation frequency with the increases of vibration amplitude in the range of 0–136.3 m/s
2.
The relation between the droplet generation frequency and the external vibration amplitude is shown in
Figure 7. It can be observed that the droplet generation frequency generally increases with the rising vibration amplitude when the external vibration frequency is constant. Moreover, there is a critical vibration amplitude corresponding to the imposing vibration frequency, and the droplet generation frequency will be synchronized with the vibration frequency if the vibration amplitude is equal to or greater than the critical amplitude. It also can be indicated in
Figure 7 that the minimal droplet generation frequency obtained with the imposing vibration amplitude less than the critical vibration amplitude is natural generation frequency.
In addition, the critical amplitudes at various vibration frequency are measured under the flow conditions of
Qc = 90 μL/h and
Qd = 60 μL/h (as shown in
Figure 8). No obvious functional relationship between the critical amplitude and the imposing vibration frequency could be deduced from the experimental data, since the critical vibration amplitude fluctuates with the increasing vibration frequency. However, it can be found in
Figure 8 that the critical amplitudes corresponding to the vibration frequencies in the ranges of 85–105 Hz and 135–160 Hz are greater than 60 m/s
2. Therefore, this is the reason why the droplet generation frequency is lower than the vibration frequency in some cases when the vibration amplitude is held at 60 m/s
2 (as presented in
Section 3.1 above).
Through the combination of effects of vibration frequency and vibration amplitude on droplet generation frequency, it can be indicated that the droplet generation frequency with external mechanical vibration is affected by the natural generation frequency, vibration frequency, and vibration amplitude. Since the natural generation frequency is determined by the flow condition in a certain microfluidic device, the droplet generation frequency with external vibration will vary from the natural generation frequency to the imposed vibration frequency at different vibration conditions.
3.3. Dynamics of Droplet Generation
Two typical processes of droplet generation in the flow-focusing device are illustrated in
Figure 9, with and without the external vibration. The flow rates of continuous phase and dispersed phase are both 60 μL/h, the natural droplet generation frequency at this flow condition is 32 Hz (see
Figure 9a), while the external vibration with the frequency of 170 Hz and the acceleration amplitude of 40 m/s
2 is applied on the dispersed phase, the droplet generation frequency at the same flow condition is 170 Hz.
Without vibration: as the dispersed phase thread breaks to form a droplet, a new generation cycle starts (defined as 0 ms). At the beginning, the fluid thread of dispersed phase retracts in the axial direction while expands in the radial direction due to the effects of surface tension and dispersed phase (around 0–4 ms). Then, the dispersed phase thread grows in both axial and radial directions, and the thread tip is shaped like a bullet (see
Figure 9a, 8.0 and 12.0 ms). As the expansion continues, the dispersed phase thread reaches the aperture and plugs into the outlet channel (see
Figure 9a, 16.0 ms). Later, the radial thread of dispersed phase is thinned by the continuous phase, thus a neck appears in the intersection region and the dispersed thread begins to collapse. Since the dispersed phase thread grows and moves downstream continuously, the thread in the outlet channel expands progressively to block the channel, however, the thread neck thins gradually. Lastly, the thread neck is pinched off, and a dispersed droplet is generated. The droplet generation without vibration in our study is similar to the droplet formation in the dripping regime reported by Fu et al. [
29], as the droplet generation processes go through three distinct stages: retraction, expansion, and collapse. However, this is quite different with the experimental work presented by Wu et al. [
30] where no retraction was observed in the ferrofluid droplet formation process in the flow-focusing device. Since the retraction of dispersed phase is resulted from the surface tension [
30], the much larger surface tension in our experiments could be the main reason cause the differences.
With vibration: the pinch-off moment of the dispersed phase thread is also defined as the beginning of a new droplet formation cycle. It can be obviously observed that the droplet generation process with external vibration is of great differences with the process without vibration. As the dispersed phase thread breaks in the vicinity of the aperture, firstly, it expands in both axial and radial directions and plugs into the outlet channel. The dispersed thread grows rapidly in the intersection and outlet channel, and its volume reaches the maximum at 2.3 ms. As a result, the last droplet deforms heavily when moving downstream. Secondly, the dispersed phase thread shrinks and the previously generated droplets move upstream, which are caused by the pressure drop in the dispersed phase. Thirdly, the thread thins in the intersection, thus a neck is present and shrinks gradually. Meanwhile, the thread volume in the outlet channel decreases and reaches the minimum at 5.3 ms, and then, the dispersed phase thread turns to expand again while the thread neck thins continuously. Finally, the dispersed phase thread is pinched off to generate a new droplet.
Figure 9b shows an example of droplet generation with vibration when the droplet generation frequency is synchronized with vibration frequency. Apparently, the process of droplet generation with vibration in this case can be divided into three stages: expansion, shrinkage, and collapse. The pressure fluctuations in the dispersed phase caused by the external mechanical vibration greatly contribute to the expansion and shrinkage of dispersed phase thread, affecting the droplet generation process significantly.
When the vibration is imposed on the dispersed phase, no retraction happens, however distinct expansion and shrinkage are observed which represent the main differences resulting from droplet generation without vibration. The volume variations of thread head during droplet generation process introduced above are presented in
Figure 10. The dispersed phase thread between the edge of the inlet 1 channel and the thread tip is defined as the thread head, and its volume (
Vt) is obtained by using image J software. Without vibration, the head volume of dispersed phase (
Vt) increases monotonously during the whole droplet generation cycle (
Figure 10a), since the dispersed phase is continuously pushed into the channel by the syringe pump. While the droplet generation frequency is synchronized with vibration frequency (170 Hz, in
Figure 10b), the
Vt first increases quickly and reaches the maximum volume at 2.3 ms, then decreases to a minimum volume at 5.0 ms, later the
Vt increases again, finally the dispersed phase thread breaks at 5.9 ms to form a new droplet. The processes of expansion, shrinkage and re-expansion are evidently revealed in
Figure 10b.
As discussed in
Section 3.1 and
Section 3.2, the droplet generation frequency can be controlled by the external vibration. Thus, the processes of droplet generation under different vibration conditions are also investigated, and
Figure 11 shows the volume variations of thread head at different vibration amplitudes (the vibration conditions are consistent with the experimental conditions in
Figure 6). Because the relationship between the droplet generation frequency and the external vibration frequency can be expressed by Equation (2), the corresponding values of coefficient
k for
Figure 11 are 1/5 (34 Hz), 1/4 (43 Hz), 1/3 (57 Hz), 1/2 (85 Hz), and 1 (170 Hz), respectively. It’s interesting that the head volume (
Vt) presents diverse peaks during droplet generation process once the external vibration is employed, and the number of peaks is equal to the reciprocal of coefficient
k. Moreover, one peak of the head volume indicates the expansion–shrinkage process of the dispersed phase thread. For example, when the droplet generation frequency is 34 Hz (
k = 1/5), the head volume of dispersed phase thread presents five peaks during the whole droplet generation cycle, and the expansion–shrinkage process appears five times before the breakup of the dispersed phase thread. That is to say, it needs five times of the external vibration to produce a new droplet. In addition to the droplet generation frequency increases with the rising vibration amplitude, when the vibration frequency is kept constant (
Figure 6), it can be revealed that peak value of
Vt in each expansion–shrinkage process also increases with the rising amplitude (
Figure 11), due to the increase of vibrational energy at the larger amplitude. While the
Vt at breakup moment decreases with the rising amplitude, which is obviously resulted from the increasing droplet generation frequency at the fixed flow condition.