Effects of Liquid Viscosity on Agricultural Nozzle Droplet Parameters

To discuss the effects of pesticide viscosity on the atomisation characteristics of an agricultural nozzle, glycerite with different mass fractions was prepared to replace the pesticide. First, the atomisation region of the nozzle was meshed and sized. Second, the speed and kinetic energy of the droplets at different positions in the atomisation region were measured by Phase Doppler Anemometry. The results demonstrated that the Sauter mean diameter, volume mean diameter and arithmetic mean diameter of droplets first decreased and then increased gradually in the axial direction of the atomisation region. Surface waves of a certain pattern were formed on the liquid surface, which was ejected by the disturbance of external air resistance. As the distance increased, the amplitude increased and the wave crest was broken into small droplets. These droplets then collided and agglomerated into large droplets under the effect of gravity. Droplets had an approximately symmetric distribution on the radial direction of the atomisation region, and the droplets were small in the middle and large at the two ends. The droplet size was positively related to the radial distance. Compared with the droplet speed at the two ends, the droplet speed at the axis was higher and the droplet size was smaller. Moreover, the kinetic energy of the droplets along the axial direction decreased sharply and then increased slowly. Droplets with high viscosity at the near end of the nozzle had small kinetic energy, and the effects of liquid viscosity on the atomisation characteristics of a nozzle could not be neglected. The droplet kinetic energy slightly increased at the far end.


Introduction
One major standard of high-efficiency pesticide application technology is that pesticide deposition on the target is far higher than that for other target objects or regions. This increased deposition increases the utilisation of pesticides to a maximum extent and is an important way to eliminate damages of pesticides on operators and relieve environmental pollution [1] [2] [3]. Nowadays, China mainly depends on the mechanical spraying of pesticides. Because of the backward machinery and poor scientific application techniques, the utilisation of pesticides is only about 30%. Consequently, pesticides are underused and cause serious pollution to the ecological environment, leading to pesticide residue in crops exceeding safety guidelines [4] [5].
Pesticide atomisation is a process where pesticide disperses into the atmosphere as droplets to form a mist dispersion system. This method realises significant amplification of a specific surface of atomised droplets under external forces [6] [7] [8]. A nozzle is needed to transfer the pesticide to the target plant [9]. The atomisation degree of the pesticide directly influences the drift distance and effective deposition utilisation. The atomised droplet size distribution is the main detection index of the atomisation degree of pesticide [10] [11]. Large droplets can maintain momentum over a long period, and they arrive at the target quickly, accompanied by small drift. However, excessive large droplets can easily decrease the coverage of the pesticide and cause poor target adhesiveness and pesticide loss [12] [13] [14]. In contrast, small droplets with small mass are greatly affected by air resistance and have inadequate momentum to reach the target [15]. However, small droplets help increase pesticide coverage, droplet coverage uniformity and liquid penetrability of the crop canopy [16] [17] [18] [19].
The spraying quality of the nozzle is directly related to the droplet diameter [20] [21] [22] [23]. If the chosen droplet size is appropriate, the minimum pesticide quantity shall be used to realise maximum control of plant diseases and insect pests at minimum environmental pollution cost. If the actual droplet is larger than the required droplet, the wasted pesticide may increase the cubic rate of the droplet diameter [24].
Liquid viscosity influences the atomisation performance of the nozzle [25] [26] [27] [28]. In the present study, the atomised liquid viscosity effect on the droplet size of the agricultural nozzle was studied by preparing different viscosities of droplet liquid solution. Research results provide theoretical support and experimental references to improve pesticide spraying technological and mechanical performances.

Test Materials
There are dozens of pesticides for citrus pest control. Because of the multiple va-L. Zhang  Glycerinum is a type of sticky and in-toxic liquid, and it can mix with water at any proportions. In the present study, different viscosities of spraying solutions were prepared using glycerinum and water for a contrast analysis.
In the experiment, the solid cone nozzle of the Dongguan Shaou Spraying System Co., Ltd. was applied. The diameter of the nozzle was 0.8 mm and its internal structure is shown in Figure 1. This nozzle is a pressure centrifugal type. Under liquid pressure, the spraying solution enters the rotating chamber through two liquid phases, rotates and is then ejected by the nozzle.

Experimental Apparatus
In the present study, the main experimental apparatus included: 1) Phase Doppler Anemometry (PDA) from DANTEC Company (Denmark) that has a particle measuring range of 1 -10,000 μm and a measuring error of 1%; 2) NDJ-8T digital rotating viscosity meter from Shanghai Fangrui Instrument Co., Ltd., which has a measuring range of 1 -2 million, measuring error of ±1% and a repetitive error of ±0.5%. All instruments meet the measurement requirements of relevant parameters.

Test Platform
The test platform of the droplet parameters of the nozzle is shown in Figure 2.   Given a certain pressure, the nozzle atomises and produces a testing atomisation region. Two beams of different lights were produced by the optical splitter of particle dynamic analysis and intersected at the testing region through the transmitting probe laser beam. The receiving probe received data and transmitted to the PDA processer. Lastly, the droplet parameters of the nozzle were gained via PC processing.

Definition of Droplet Parameters
Here, the following three index parameters of droplets were measured and analysed: D 10 : Arithmetic mean diameter refers to the ratio between the sum of diameters of sampling droplet groups and the number of droplet groups:

Experiments
Generally, there is a strong negative correlation between the viscosity of liquid and temperature. Here, the viscosity of spraying solution was tested under the ambient temperature of 25˚C ± 0.5˚C.

Viscosity Range Test of Four Pesticides for Phylloxera Control
To reflect the effects of viscosity of pesticide on droplet parameters of the nozzle, four common pesticides used in citrus control were prepared according to the mixing ratio in the instructions. During the experiment, viscosities were measured with a viscosity meter every 2 min. One viscosity value was read and the mean of three reading data was chosen as the final viscosity. Results are shown in Table 1. Acetamiprid had the minimum viscosity (1.25 cp) among the four pesticides, whereas pyridaben showed the maximum viscosity (1.80 cp).

Preparation of Glycerinum Solutions with Different Viscosities
Because glycerinum and water can mix at any proportion and the viscosity of pure glycerinum is relatively high, four glycerinum solutions with different mass fractions were prepared by mixing glycerinum and water. The results are shown in Table 2. The viscosity of the solution increased as the mass fraction of glycerinum increased. Therefore, the viscosity range covered the viscosities of the common pesticides.

Setting of Sampling Points of Droplet Parameters
Experiments of the effects of viscosity of the spraying solution on the atomisation performance of the nozzle were divided into tests of axial and radial (given fixed height along the axial direction) droplet parameters of the nozzle under different viscosities of spraying solutions. In atomisation experiments, spraying solutions with different viscosities were prepared by glycerinum, and the nozzle was perpendicular to the ground along the axial direction. The spraying pressure was 0.9 Mpa. The spraying cone angle of the nozzle under a spraying pressure of 1.0 Mpa was measured 44.14˚ in early experiments for setting appropriate sampling points in the atomisation region. Hence, the boundary positions of the atomisation region can be determined according to the tangent of the spraying cone angle which is measured in the pre-test, thus enabling the range of the sampling points of droplets to be determined.
When the axial position (z-direction) is fixed, the position of the radial distance (x-direction) can be calculated according to the tangent of the spraying cone angle. However, because of the effect of gravity on the droplets, the actual spraying boundary is smaller than the theoretically calculated boundary. Appropriate sampling points in the atomisation region are determined according to pre-experimental results.
Droplet sampling points along the axial direction were determined as follows.
Axial droplet parameters were measured from z = 0 cm of the atomisation re-   According to previous studies, many factors can influence the uniformity of spraying fogs. An ideal spraying height is related to the working pressure of the nozzle and the fog distribution characteristics of the nozzle. The environmental wind force is smaller than 3 levels, and the spraying height is adjustable within 35 cm -80 cm [29]. Hence, the sampling range of droplets was chosen within 40 cm of the spraying height.

Spraying Test and Droplet Parameter Test
Spraying test and droplet parameter test are introduced as follows: 1) Open water valve of PDA and start the laser and preheat it for 15 min. 2) The laser power is increased to 0.330 W after stabilising the laser to achieve

Axial Distribution Characteristics of Droplet Size
Axial droplet distribution of nozzle is measured every 2 cm from the nozzle ( Table 3).
The variation curve of droplet parameters with viscosity along the axial direction of the nozzle was drawn according to test data to intuitively understand the         amplitude of the liquid surface may rapidly increase when the liquid has a high flow rate. Lastly, the wave crest was removed and large droplets were formed.
As the jetting distance increased, the wave amplitude of such surface wave gradually increased to split the liquid into large droplets. When the droplet diameter exceeded a certain threshold, the droplets were further broken into smaller liquid droplets under surrounding air shearing stress. Hence, the wave amplitude declined gradually in the 1 cm -6 cm range.
Rayleigh theory outputs the maximum instability ratio of the viscous jet. In other words, there is a minimum disturbance wavelength λ min , and the jet might be separated into the disturbance wavelength of liquid drops (λ opt ). When the initial disturbance close to the nozzle outlet is smaller than λ min , the jet disturbance where, u l is the liquid viscosity, ρ l is the liquid density, σ l is the liquid surface tension, and d is the jet diameter. Hence, the λ min of the viscous fluid is the same as that of non-viscous fluid, but the λ opt of viscous fluid is significantly higher than that of non-viscous fluid.
Experiments showed that given the same atomisation conditions, the density This relationship was mainly because it is more difficult to atomise a spraying solution with a higher viscosity and because the atomisation needs more atomising energy under the same jet pressure. Hence, a spraying solution with high viscosity forms large droplets rather than small droplets. In the 8 cm -40 cm interval, droplet size under differential axial distances increased gradually from the near position to the far position. Because of the dominant controlling of droplets by gravity and air resistance along the axial direction of the nozzle, droplets may drop at an accelerating speed, during which droplets agglomerate and collide to increase droplet size gradually and form big droplets.

Distribution of Axial Droplet Speed
The droplet speed is one of the barriers against effective utilisation. Droplets may collide at the target and then splash if the droplet speed is too high, thus resulting in pesticide waste. In contrast, droplets cannot effectively arrive at the target if the droplet speed is too low. To further analyse the moving laws of droplets under different viscosities, the axial droplet speed under different viscosities was tested (Table 4).
Variation curves of droplet speed with axial distance under different viscosities were drawn for an intuitive understanding of the relationship between droplet speed from an agricultural nozzle and viscosity of droplets ( Figure 10).   2) At the same position (z = 30 cm in Figure 10), the droplet speed was negatively correlated with the viscosity of the spraying solution. Table 3 shows that the droplet size was larger when the viscosity of the spraying solution was high and when atomising it was more difficult. Because of the same injection pressure, liquid with a high viscosity consumed more energy.
To further understand the relationship between the droplet speed and size, the droplet speed vector map (for the convenient analysis, data when viscosity is 1.63 cp are exhibited) along the axial direction (z-direction) was drawn with BSA ( Figure 11). The arrow direction represents the moving direction of the droplets. The arrow length on dots reflects the droplet size, and the size of dots reflects the volume mean diameter of the droplets.

Droplet Spectral Analysis
To further analyse the distribution of droplet size in droplet groups under different viscosities, the droplet spectrum at z = 20 cm was analysed ( Figure 12). In

Radial Droplet Size Distribution
The droplet sizes along the radial direction (y-direction) under different viscosities  Table 5 and Table 6, respectively. The variation law of droplet size with radial distance at the same axis position is discussed based on the results in Table 5 and Table 6.
The variation curves of the volume mean diameter of the droplets (D 30 ) with radial distance were drawn ( Figure 13 and Figure 14) to understand the viscosity effects of the spraying solution on the radial droplet size (for convenient analysis, z = 30 cm). In Figure 13, radial droplet size changed with distance. In addition, the variation curve of D 30 with viscosity at z = 30 cm was drawn ( Figure 14). Ohnesorg indicated that droplet size after jet breaking was mainly determined by the nozzle diameter and density, viscous force and surface tension of the liquid. Such relations were described by a dimensionless number Z [30]. Z is related to density, viscosity force and surface tension of the liquid to some extent: where, u l is the liquid viscosity, ρ l is the liquid density, σ l is the surface tension, and d 0 is the initial diameter of the jet.
Under the same experimental conditions, the density, surface tension and jet flow diameter of the spraying solution with different viscosities changed slightly.
Hence, the liquid viscosity was the main cause of the liquid breaking in atomisation. Viscosity served as damp during the increase of disturbance wave of the jet surface. Figure 14 shows that Z declined as the viscosity decreased indirectly through the reduction of resistance. Consequently, the droplet size was smaller.

Radical Droplet Speed Distribution
Moving speeds of droplets at different radial positions under different viscosities at z = 30 cm are listed in Table 7. Radial droplet D 30 and speed vector maps (for convenience of analysis, the viscosity of spraying solution was 1.63 cp, z = 30 cm and y = −8 cm -8 cm) were drawn with the PDA system to analyse the radial droplet speed distribution ( Figure 15). The dot size shows the volume mean diameter of droplets at the position and the arrow length shows the speed. The xoy plane cannot express speed along the z-direction. Specifically, the arrow direction shows that the droplet speed is perpendicular to the inward of the xoy plane. Figure 15 shows that there was a high droplet speed in the middle that gradually decreased as the radial distance increases. The volume mean diameter of the droplet was small in the middle and increased as the radial distance increased.
This can be explained as follows. Because of the high droplet speed at axis, droplets are broken completely under high-speed airflow, showing good atomisation

Kinetic Energy Analysis of Droplets
To further analyse the effects of viscosity on axial moving characteristics of droplets, test data of droplet speed and droplet size were used. According to the definition of kinetic energy: where, ρ is the spraying solution density, r is half the volume mean diameter of the droplet, and v is the droplet speed.
The kinetic energy of the droplets along the axial direction is shown in Table 8.
The variation curves of the kinetic energy of droplets along the axial direction are shown in Figure 16. The kinetic energy of droplets declined dramatically in the 0 cm -6 cm interval. Because of the atomisation of droplets at the near end In the z = 6 cm -40 cm interval, the kinetic energy of the droplets with different viscosities increased gradually. The measurement results of droplet speed (Table 4) showed that droplet speed in this interval declined gradually, indicating that mass in this interval was a major factor influencing the droplet kinetic energy. Moreover, the droplet mass increased while falling, and the gravitational potential energy of droplets was transformed into kinetic energy, increasing the droplet kinetic energy.

Discussion
In the experimental environment, temperature can affect the viscosity of the solution to some extent. In viscosity liquid measurements, environmental temperature changes dynamically. Therefore, the environmental temperature was measured many times before each experiment to assure the reliability of the experimental results. A NDJ-8Tdigital rotating viscometer was used to test viscosity. Before each experiment, the test results of the same sample were basically the same, assuring the stability of the results measured.
Droplet size measurement was performed under the hypothesis that droplets were spherical. However, droplets may not be standard spheres. Therefore, the theoretical value of the kinetic energy of droplets was slightly higher than the value measured.
The kinetic energy of the droplet at the target may influence the effective ad-

Conclusions
In the present study, variation laws of size, speed and kinetic energy of droplets along perpendicular (axial) and horizontal (radial) directions in the atomisation region under different viscosities were studied using PDA as the test platform.
Some conclusions could be drawn: 1) The droplet size from the nozzle was positively related to the viscosity of the spraying solution. As the viscosity increased, the droplet size along the axial direction first increased and then decreased. The high viscosity of the spraying solution resulted in it being more difficult to atomise droplets. The droplet size at the radial boundaries in the atomisation region was higher than the internal droplet size.
2) Droplet speed at the near end of the nozzle decreased at an accelerating speed because of inertial force. The droplet speed increased and droplets were formed as a response to disturbance of the external air resistance.
3) The kinetic energy of droplets dropped quickly in the beginning and then increased slowly along the axial direction. The fast breaking of droplets under the influence of shear stress was the main influencing factor of kinetic energy changes at the near end of the nozzle. However, the droplet mass determined the kinetic energy of droplets at the far end of the nozzle. 4) Adding different concentrations of glycerite significantly affected the droplet size. The spraying solution with different viscosities had different effects. The appropriate mixing ratio should be chosen based on the actual condition of spraying, thus decreasing the drift of pesticide droplets and increasing the penetrability of droplets. 5) According to the test results, droplets in the atomisation region from the solid cone nozzle belonged to mist droplets. In addition, the droplet size outside the fog cone was higher than that inside the fog cone.