# Monitoring the Capillary Jet Breakage by Vibration Using a Fast-Video Camera
## 4 Results and Discussion  
### Selection of the Optimum Vibration Frequency  
Several authors declare that droplet size could be controlled by changing the frequency. However, this fact contradicts Equation (9), which states that the jet diameter directly defines the droplet size, generally assimilated to the internal nozzle diameters. Moreover, doubling the frequency would only increase the diameter by a factor of 1.26, and the frequency will not be at its optimum value.  
Equation (4) shows that the liquid properties may affect the optimum wavelength (or frequency). Often, the liquid properties are not well known and could even vary during experiments if, for example, the liquid temperature increases. Therefore, the recommendations from the equipment suppliers (Figure 1D) may be considered as approximate values.  
Fortunately, most equipment based on resonance technology is equipped with LED flashing at the same frequency that the vibration applied to the liquid. Figure 3 represents the droplet observations using the camera while varying the frequency around its optimum value. The series of images correspond to the time interval, simulating the LED flashes. If the breakage and the applied vibration (then the LED flashes or the image framing) are synchronized, the droplets will look stationary (stroboscopic effect). The jet tends to break at the natural frequency, even if the vibration is applied to the jet. If natural and applied breakage frequencies do not correspond, it is then a competition between the two breakage processes, leading to intermediate mean droplet size and larger size distribution. If so, the droplets will look like they are moving to the front of the flashing LED.  
The optimum value for this experiment was approximately 500 Hz. It may be observed that if the frequency is too low, the droplets seem to move up. At the optimum frequency, they seem immobile (Figure 3b), while, at an overly high frequency, they seem to move down. In agreement with Equation (3), altering the optimum frequency (300 to 600 Hz) still allows obtaining relatively homogenous beads. However, if the frequency is too distant from the optimum, i.e., 700 Hz, the jet breakage is erratic, and coalescence between droplets is observed. Figure 3 shows that low size dispersion may be maintained while the optimum and applied vibration frequencies differ up to 20 %. The range of droplets having a narrow size distribution is \(\pm\)20% in volume but \(\pm\)6% in diameter. Moreover, filaments between droplets may break into smaller satellite droplets. It is then recommended to work near to the optimum frequency. Under these circumstances, the size is primarily defined by the nozzle size.  
The previous observations allowed us to easily define the optimum frequency by varying the frequency at a fixed flow rate or varying the flow rate at a fixed frequency (depending on the equipment). However, the situation is not that simple. Images displayed in Figure 3 were obtained with an image recording duration of 0.2 ms, while LED flashes have slightly less than 1 ms.  
The image displayed in Figure 3e simulates the direct observation of the jet without using a fast camera with a 0.7 ms recording duration. The image simulates the direct observation of the jet using the Encapsulator without the help of a fast camera. The image is blurred due to the fact that the droplets move during the flash length. While producing large beads and then using low frequency, the image remains relatively straightforward, but the optimum frequency determination requires some experience for the small bead production and then high frequency.  
Figure 3: Observation of the droplet production by varying the vibration frequency (alginate solution 18 g/L, nozzle 800 \(\upmu\)m, flow rate 38.5 mL/min) with recording duration of 0.2 ms. In this figure: (**a**) 300 Hz, (**b**) 500 Hz, (**c**) 600 Hz, (**d**) 700 Hz, (**e**) simulation of recording with 0.7 ms duration.