Investigation of Droplet Dynamics Under Shear Flow

The dynamics of droplet under shear flow was investigated in normal gravity and microgravity. Drop under shear flow has many applications in aerospace such as aircraft de-icing and environmental control and life support system in space station. Shape analysis of the droplet showed that drop in microgravity have a greater contact angle and height, but a smaller contact radius, than that in normal gravity. The difference between advancing and receding contact angle θa-θr is greater in microgravity than that in normal gravity under the same wind speed. The effect of airflow on the droplet is mainly dependent on the We number and the dimensionless number k′, which characterizes the ratio of wind force and adhesion force. the k’ in microgravity is larger than that in normal gravity. The droplet exposed to airflow from static to motion state can be divided into three regimes.


Introduction
Droplets exposed to the shear flow has wide application such as enhancing the efficiency of heat exchanger [1], aircraft de-icing [2].In addition to its application in the ground, it also has an important application in the field of microgravity such as environmental control and life support system (ECLSS) in space station.In order to recycle water, droplets need to be removed from the condensing plate [3].Usually, it can utilize gravity to make drops shed from the surface in ground.However, this is not feasible in the microgravity [4]because of the lack of gravity.An effective way is that using the airflow to make the droplet shed from the surface.
Droplet shedding caused by wind force is a complex problem because of the unsteadiness of the wind field.When a droplet exposed to the wind, the wind deforms the droplet causing the increase of advancing contact angle, θa and decrease of θr until the θa and θr reaches their threshold that is θA and θR.This θA and θR characterizes the drop shedding behavior.Many researchers have performed studies about the dynamics of drop exposed to wind.Durbin [5]used numerical methods to solve the integrodifferential equation describing the drop shape and found that the critical wind speed is characterized by a critical Weber number.Milne and Amirfazli [6]performed an experiment to study the shedding behavior of sessile droplets on superhydrophobic surface by the wind and found that the critical wind velocity is proportional (Lb/A) 1/2 .Recently Hooshanginejad and Lee [7]investigated the dynamics of drop under wind and gravity, they found that the critical wind speed can be scaled as Ucr~V-1/6 and with the increase of droplet size.
Few studies research on the dynamic of droplets in microgravity.Brutin and Zhu et.al [8] experimentally investigate the sessile drop creation in microgravity, they found that the behavior of contact angle is determined by the drop diameter and gravity.Diana et.al [9] described the shape of the water and ethanol droplets on aluminum placed on the and PTFE substrates in normal and reduced gravity.Recently Shakeri Bonab and Minetti et.al [10]performed an experiment to study the behavior of droplet shedding by shearing airflow in microgravity, they found that the critical wind velocity is lower in microgravity than that in normal gravity.
The purpose of this study is to investigate the dynamic behaviors of droplet exposed to airflow in microgravity, specially to establish a relationship between θa-θr and velocity of airflow which can be used to predict the critical speed and to study the evaporation characteristics of drop exposed to airflow in microgravity.

Experimental facility
To study the dynamic of evaporation droplets under shear flow, A small wind tunnel experimental equipment was designed.
The primary component of the experimental apparatus is an annular wind tunnel whose airflow wind speed (0-30 m/s), temperature (0-50°C), and relative humidity can be controlled.The microgravity environment was generated by parabolic flight (PF) which was implemented by the European Space Agency (ESA) 75th PF campaign in April 2021.The weightlessness time of a single flight curve is roughly 22 seconds.The level of gravitational acceleration is around 10 -3 g. Figure 1 [10] shows the actual experimental facility and schematic diagram.The length of experimental section was 150 mm with 2500(50×50) mm 2 square cross-section and droplets are generated on the aluminium substrate.On the bottom surface is a cartridge-like subsystem that can quickly change the substrate.The substrates were designed to fit the grooves of cartridge [10].A rail was designed to fix the bottom of the test section in the subsystem.We use aluminium substrate in experiment and the working medium is water.

Figure 1. Actual and schematic experimental facility
The temperature and humidity control system was used to make the experimental environmental reach the stable set value before the experiment.The temperature control system consists of a thermoelectric temperature controller (TC-48-20) and a temperature sensor (MP-3193), which can achieve the set temperature through the PID algorithm, and the vast majority of experiments in this paper were carried out in an environment of 25±0.1°C.In the humidity control system, the humidity controller (Auber HSR-HD 200) was used to measure the humidity.The humidity controller collected the humidity signal from the humidity sensor (Auber HD-220), and the feedback control ultrasonic atomizer (SD02_JSQ) was started and stopped to accomplish the humidity control capability of ambient humidity 99%± 4% relative humidity.After the temperature and humidity values are stabilized, Droplets were injected into the designated experimental area through the liquid injection system, followed by the start of the optical system and the wind speed control system.During the experiment, the optical system collects the droplet shape and obtains the droplet shape information by computer; the optical system consists of top-view and side-view CCD cameras (M1280, Genie Nano) with a field of view of 75 mm and a resolution of 1280×1080; the wind speed control system controls and measures the wind speed of the shear flow in the experiment with an accuracy of ±0.2 m/s, which is controlled by a fan ( MM1865 Series, Mechatronics Inc.), and a thermal anemometer (EE75, E+E Elektronik GmbH).

Influence of gravity on droplet morphology
When the droplet is in microgravity, the contact angle and contact line will change, altering the dynamic characteristics of the droplet.Hence, it is essential to analyze the shape of droplet in microgravity.
Figure 2 shows the profile of the 25μL droplet placed on the aluminum substrate in normal and microgravity gravity.It can be concluded from Figure 3 that the radius of the droplet in microgravity is shorter than that in normal gravity whereas the height and contact angle in microgravity is greater than that in normal microgravity.For the 25μL droplet, the height in microgravity is 5% higher than that in normal gravity, the contact radius is 2% smaller than that in microgravity and the contact angle is 4% greater than that in normal gravity.

Effect of gravity on droplet contact angle in microgravity
When the airflow imposed, the contact angle hysteresis both happen in the normal gravity and microgravity.
Figure 3 shows the 18μL droplet under 10.29m/s wind in normal gravity and microgravity.It can be found in Figure 3 that the difference between advanced and rear contact angle θa-θr in microgravity is larger than that in normal gravity.For the 18μL droplet, the difference in microgravity is 54% larger than that in normal gravity.If a droplet is in equilibrium state, the adhesion force is equal to the wind force.That is: The adhesion and wind force can be expressed as follows: Substitute equation (2) into equation ( 1) we can get that Where Figure 4 shows the relationship between the dimensionless number cosθa-cosθr and the Weber number in normal and microgravity.It can be found from Figure 4 that the cosθa-cosθr and Weber number We are linearly related which means k' in Eq (4) is independent of Weber number and keeps constant when the Weber number changes.The k' in microgravity is greater than that in microgravity, For 18µL droplet, the k' in microgravity for 18µL droplet is 16.2% greater than that in normal gravity.It can be found from the definition of k' that k' can represent the magnitude ratio of the wind force and the adhesion force.Hence, the effect of wind force relative to adhesion force is more significant in microgravity compared to the normal gravity which results in the larger difference of advancing and rear contact angle in microgravity.

Figure 4. cosθa-cosθr vs. We
Use the sum-difference product formula for the left end of Eq (3), We get: Where θ0 is the initial contact angle of the droplet.Figure 5 shows the sin(θa-θr)/2 using Eq (5) comparing to the experiment.It can be found from Figure 5 that Eq (5) is in good agreement with the experimental results in microgravity, but in normal gravity the agreement is not well.This is due to the influence of gravity on the shape of the droplet.5) and experimental data It can also be concluded from Eq (5), When the droplet reaches its shedding state, It should have the relationship as follow: Where the θA and θR is the maximum advancing contact angle and minimum contact angle, Ucr is the critical airflow velocity.

The dynamic characteristics of droplet from static to motion
Figure 6 depicts the contact angle and contact radius of a droplet as it transitions from a static state to a motion state as the airflow velocity increases from 0 to 12.6m/s.It can be found from figure 6 that the shedding process can be divided into three different regimes: static, transition, and kinetic regime when the droplet exposed to the wind in microgravity.In the static regime the advancing contact angle increases and receding angle decreases respectively with the increase of the airflow velocity, whereas the contact radius remains constant at first and begins to increase after about 2s, the θa-θr reach the maximum value of approximately 23° after about 4s meanwhile the contact radius also reaches the maximum.In the transition regime, the advanced contact angle decreased and the rear contact angle increased, while the contact radius begins to shrink and motion occurs.In the kinetic regime, the droplet sheds from the surface and the θa-θr and contact radius remains constant.7 shows R(cosθa-cosθr) vs. time from static to motion.Because the adhesion is proportional to R(cosθa-cosθr) Hence, R(cosθa-cosθr) can represent the trend of the adhesion.It can be found from Figure 7 that the adhesion can also be divided in three regimes.In the static regime, the adhesion increases with the increase of wind velocity to balance the wind force.In the transition regime, the adhesion reaches maximum and the motion happens, after that the adhesion begins to decrease.In kinetic regime, the adhesion remains constant and is smaller than the maximum static adhesion force.

Conclusion
An experiment was developed to investigate the droplet dynamic under shear flow.Shape analysis was conducted to study the effect of wind and gravity on the droplet.In microgravity, for the same wind velocity and droplet volume, θa-θr is larger than that in normal gravity.The effect of airflow on the droplet is mainly dependent on the Weber number and the dimensionless number k', which characterizes the ratio of wind force and adhesion force, the k' in microgravity is larger than that in normal gravity.The droplet exposed to airflow from static to motion can be divided into three regimes in microgravity: static, transition, and kinetic regime.

Figure 2 .
Figure 2. Profile of droplet in normal gravity and microgravity

Figure 6 .
Figure 6.Contact angle and radius vs. time

Figure
Figure7shows R(cosθa-cosθr) vs. time from static to motion.Because the adhesion is proportional to R(cosθa-cosθr) Hence, R(cosθa-cosθr) can represent the trend of the adhesion.It can be found from Figure7that the adhesion can also be divided in three regimes.In the static regime, the adhesion increases with the increase of wind velocity to balance the wind force.In the transition regime, the adhesion reaches maximum and the motion happens, after that the adhesion begins to decrease.In kinetic regime, the adhesion remains constant and is smaller than the maximum static adhesion force.