Micro-droplet deposition and growth on a glass slide driven by acoustic agglomeration

Abstract

Sound waves can be applied on fog elimination due to the acoustic agglomeration phenomena. However, existing studies have different understanding of the effective sound wave frequency and sound intensity for the acoustic agglomeration effect of micro-droplets. This study designs a novel microscopic experiment to visually present the growth process of droplets under the action of sound waves. A group of indexes are also proposed to quantitatively analyze the growing process of micro-droplets under the action of sound waves, such as area-weighted average particle size, relative growth rate of droplets, and relative growth factor of droplets. In addition, a series of experiments with different sound waves are also conducted to explore the impact law of sound frequency and sound intensity on droplet agglomeration. The results verify the acoustic agglomeration effect of micro-droplets by visible processes at microscopic scale and indicate that within the studied sound pressure level (SPL) and frequency range, the droplets’ deposition is faster under the action of sound waves of higher SPL and lower frequency. Most importantly, the critical values of sound wave characteristics for obvious acoustic agglomeration of droplets are presented, providing guidance for choosing effective sound waves in the actual application of acoustic fog elimination.

Graphical abstract

Appendices

Appendix 1

Flow chart and detailed operational procedures of the designed experiment

Detailed operational procedures of the designed experiment See Fig. 14

Fig. 14

Flow chart of the designed experiment

• (1) Before starting the experiment, use the air conditioner to adjust the laboratory temperature, which is measured by an indoor thermometer; use the handheld infrared thermometer to measure the temperature at the microscope stage. Both the laboratory temperature and the temperature at the microscope stage are controlled at 25 ± 1 °C.

• (2) Turn off the air conditioner after the temperature reaches the requirement and maintain a windless environment in the laboratory.

• (3) Soak the glass slides in 95% alcohol solution for 5 min to dissolve the surface grease.

• (4) Remove the glass slide from the alcohol solution and soak it in distilled water for 5 min to clean the surface alcohol.

• (5) Remove the glass slide from the distilled water with tweezers, let the distilled water on the surface flow down naturally until no surface water flow can be formed and then wipe the glass slide in one direction with a soft cotton towel; after there are no obvious water droplets on the surface of the glass slide, use an air pump to blow air on the surface of the slide for 1 min to ensure that the surface of the slide is dry.

• (6) Place the processed glass slide on the microscope stage.

• (7) Turn on the digital microscope, adjust the focal length of the microscope, so that the edge of the image under the microscope is clear.

• (8) Set the interval of taking photographs in the microscopic digital measurement analysis system to be 10 s.

• (9) Carry out preliminary experiments to select the appropriate spray flow rate of the humidifier, with which under the action of no sound wave, the droplet increases obviously, but the speed is relatively slow within 120 s. The suitable spray flow rate selected in the pre-experiment is set to be the standard flow rate and remains constant for different experiments.

• (10) Turn on the speaker and use MATLAB to generate the sound wave of the required frequency; use a handheld acoustic analyzer for monitoring; and use the speaker or computer volume control to adjust the sound wave to the required SPL.

• (11) Turn on the micro-droplet generator to keep it in the standard flow state and turn on the photograph and video buttons in the microscopic digital measurement and analysis system simultaneously.

• (12) After 120 s, turn off the button of the microscopic digital measurement and analysis system and save the images and then turn off the speaker and humidifier to end the experiment.

• (13) Put the used glass slides in the alcohol solution for soaking treatment.

• (14) Use an air pump to pump air into the rectification chamber for 2 min to ensure that the droplets remaining in the chamber are completely discharged to avoid affecting the next experiment.

• (15) Wipe the droplets on the surface of the stage with a cotton soft towel and blow them dry with an air pump;

• (16) Repeat the above steps for the next experiment.

Appendix 2

Derivation of the end-of-fall velocity of a droplet

The falling speed of a droplet is determined by three forces, namely gravity, air buoyancy and air resistance. The gravity on the droplet is shown in Eq. (13):

$$ F_{G} = \frac{4}{3}{\pi r}^{3} g\rho_{\omega } $$

(13)

$$ F_{f} = \frac{4}{3}{\pi r}^{3} g\rho_{a} $$

(14)

The air resistance of the droplet is shown in Eq. (15):

$$F_{R} = \frac{\pi }{2}r^{2} u^{2} \rho _{a} C_{D} = 6\pi \mu ru\left( {\frac{{C_{D} N_{{\text{Re} }} }}{{24}}} \right)$$

(15)

In the falling process, the gravity and the buoyancy and resistance of the air of the droplet quickly reach equilibrium, so that the droplet drops at a uniform speed, when the droplet has the end-of-fall velocity as shown in Eq. (16):

$$\frac{4}{3}\pi r^{3} g\left( {\rho _{\omega } - \rho _{a} } \right) = 6\pi \mu ru\left( {\frac{{C_{D} N_{{\text{Re} }} }}{{24}}} \right)$$

(16)

For a spherical droplet falling through the air, $\rho_{\omega } > > \rho_{a}$, so Eq. (16) can be approximated to Eq. (17):

$$\frac{4}{3}\pi r^{3} g\rho _{\omega } = 6\pi \mu ru\left( {\frac{{C_{D} N_{{\text{Re} }} }}{{24}}} \right)$$

(17)

where

$$ u = \frac{2}{9}\frac{{r^{2} g\rho_{\omega } }}{{\mu \frac{{C_{D} N_{{{\text{Re}}}} }}{24}}} $$

(18)

When the Reynolds number is small (the radius is about 0.5–50 μm):

$$ C_{D} = \frac{24}{{N_{{{\text{Re}}}} }} $$

(19)

At this time, the formula for the end-of-fall velocity can be simplified as in Eq. (A8):

$$ u = \frac{2}{9}\frac{{r^{2} g\rho_{\omega } }}{\mu } = K_{1} r^{2} $$

(20)

where $r$ is the droplet radius; $\rho_{\omega }$ is the droplet density; $\rho_{a}$ is the air density; $C_{D}$ is the characteristic drag coefficient of the liquid; $\mu$ is the dynamic viscosity coefficient; $N_{{{\text{Re}}}}$ is the Reynolds number; $u$ is the end-of-fall velocity; and $K_{1} \approx 1.19 \times 10^{6}$.