Pulse Width Modulation on the Droplet Spectrum and Velocity of Spray Nozzles

Abstract

Pulse width modulation (PWM) allows for the real-time flow rate adjustment of spray nozzles without changing system pressure, indicating that PWM is a promising technology for improving the quality of pesticide applications. However, its effect on the droplet formation process is not yet fully understood. In this study, the effects of a PWM system on the droplet spectrum and velocity generated by different flat fan hydraulic nozzles were evaluated. The experiment was conducted via a spray simulator to test the impact of PWM technology under various operational conditions and flat fan nozzle types (standard, pre-orifice, and air inclusion). With the aid of a real-time particle analyzer and high-resolution imaging, the following variables were analyzed: volume median diameter (VMD), relative span, droplet velocity, and the percentage of volume composed of droplets with a diameter smaller than 100 µm. Four simulated working speeds (1.1, 1.7, 2.8, and 3.9 m s⁻¹), which were equivalent to four PWM valve duty cycles (35%, 42%, 71%, and 100%), respectively, were evaluated. The PWM system altered the droplet size, generally reducing the VMD in comparison to the conventional system. The relative span was not influenced by the PWM system’s duty cycle, although system activation increased droplet size heterogeneity in some nozzle types. The droplet velocity was generally slower using the PWM system in comparison with the conventional system, but higher duty cycles increased this parameter. Overall, the results of this study suggest that spray patterns are altered by PWM activation, and the traits of this behaviour depend on the spray nozzle type.

1. Introduction

The application of agrochemicals plays a key role in modern agriculture by mitigating the damage caused by weeds, pests, and diseases, contributing to increased crop health and yield. Nevertheless, challenges concerning the efficiency of spraying and the mitigation of environmental impact remain significant, underscoring the need for the ongoing development of increasingly precise and sustainable technologies [1].

The control of droplet size and distribution is a major factor that affects spraying efficiency [2]. The droplet spectrum affects the coverage, drift, and runoff, thereby directly impacting the efficacy of agrochemical treatments and environmental safety [3]. In general, the formation of droplets results from the passage of liquid under pressure through small-diameter orifices, resulting in an unstable liquid sheet that fragments into droplets with diameters varying from micrometres to hundreds of micrometres [4].

Conventional applications, which are usually performed at a constant application rate (L ha⁻¹), tend to be less efficient because they do not consider various factors such as the presence of weeds, vegetation density, or topographic conditions [5]. In addition, errors during maneuvers, such as in curves or uneven terrain, can cause under- or overapplication, compromising agrochemical efficacy, promoting pest resistance, and increasing environmental risk [6,7].

In this context, the use of variable rate application technologies guided by real-time detection sensors (such as infrared, LIDAR, and ultrasound sensors) has shown promise for reducing losses and improving spraying efficiency [8,9,10]. To meet the operational requirements of high speed and wide booms, flow control systems have also emerged in order to allow dynamic adjustments, such as the pulse width modulation (PWM) system.

A PWM system controls flow via the rapid pulsation of solenoid valves located in the nozzle holders, typically operating at frequencies between 10 and 50 Hz [6,11]. The final flow rate is determined by the proportion of the duty cycle, allowing adjustments in real time without changing the pressure, unlike conventional systems based on pressure variation [12]. Thus, in theory, aspects such as working pressure and droplet size can be maintained constant, even during working speed changes or field maneuvers [13].

Recent studies have shown that PWM technology can significantly reduce the applied spray volume and improve distribution accuracy [14]. However, gaps remain regarding the real impact of PWM on the generated droplet spectrum, especially when combined with different spray nozzle types, such as pre-orifice and air-inclusion flat fan nozzles [15]. The proper selection and use of nozzles are crucial for mitigating drift and enhancing coverage; consequently, their interaction with the PWM system still warrants further investigation [16].

Therefore, elucidating the effects of the PWM system on droplet size and velocity across different spray nozzles under simulated field conditions is essential for optimizing sprayer performance and enhancing both agronomic effectiveness and environmental sustainability [17].

In this context, the objective of this study was to analyze the influence of the operation of a PWM valve modulated at different duty cycles on the spectrum and velocity of droplets generated by different flat fan nozzle types under operating conditions similar to those observed in the field.

2. Materials and Methods

2.1. Research Station and Test Object

The experiment was conducted in 2023 at the Laboratory of Application Technology of Máquinas Agrícolas Jacto S/A, located in the city of Pompéia-SP, Brazil. The measurements were performed on a spray bench (Figure 1), consisting of a 500 L reservoir, a piston pump (JP 45, Máquinas Agrícolas Jacto S/A, Pompéia, Brazil) with a nominal flow rate of 45 L min⁻¹, a pressure gauge (Wika Alexander Wiegand SE & Co., Klingenberg, Germany) with a scale of 413 kPa (60 PSI), a manual two-way lever pressure regulator (Máquinas Agrícolas Jacto S/A, Pompéia, Brazil) with return flow control, and a nozzle holder in which the PWM valve and nozzle were mounted (Figure 1a). The PWM system consisted of a solenoid valve (Figure 1b), a spray module, and a monitor (Figure 1c) where the operating parameters were configured.

2.2. Experimental Evaluation

The PWM system was evaluated in terms of the spectrum of droplets generated when coupled to different nozzles. The measurements were performed via a real-time particle analyser based on high-resolution images (Model VisiSize P15, Oxford Lasers, Inc., Didcot, UK) (Figure 2). This system is equipped with a camera that captures images of spray particles in an air trajectory and is capable of measuring droplets with diameters above 10 µm, in addition to measuring the distribution of the particle diameter and velocity in real time. To obtain the mean values, 5000 droplets were counted in each replicate. To maintain a fixed height, the nozzles were attached to a spray boom positioned 30 cm above and centred in relation to the light beam.

During the evaluations, mobile equipment was mounted such that the entire sprayed jet passed transversally at a speed of 2 mm s⁻¹ through the light beam of the analyser, which allowed the average droplet spectrum to be obtained for each desired condition. The tests were performed using only water and in a controlled environment (air temperature below 28 °C, relative humidity above 60% and absence of wind).

The tests were performed with the PWM system on and off (conventional system), using flat fan nozzles with a nominal flow rate of 0.757 L min⁻¹ (0.2 US gallon min⁻¹ at 276 kPa pressure), simulating a fixed application rate of 90 L ha⁻¹ and working speeds of 1.1, 1.7, 2.8, and 3.9 m s⁻¹ (which results in speeds of 4, 6, 10, and 14 km h⁻¹), which correspond to flow rates of 0.210, 0.315, 0.525, and 0.735 L min⁻¹, respectively, considering a nozzle spacing of 0.35 m. With the PWM system on, four duty cycle settings were evaluated: 35%, 42%, 71%, and 100% to obtain the corresponding flow rates at the simulated working speeds of 1.1, 1.7, 2.8, and 3.9 m s⁻¹, respectively. The duty cycle represents the percentage of time during which the valve is open. A working pressure of 262 kPa (38 PSI) was used for speeds of 1.7, 2.8, and 3.9 m s⁻¹. Since the minimum duty cycle is 35%, it was necessary to adjust the working pressure to 179 kPa (26 PSI) to obtain 0.210 L min⁻¹ when simulating a working speed of 1.1 m s⁻¹. The PWM system was configured to work at 30 Hz in the simulations of working speeds above 1.9 m s⁻¹ and 20 Hz for speeds below 1.9 m s⁻¹, according to the manufacturer’s recommendations. With the PWM system off, a working pressure of 90 kPa (13 PSI) was used for 1.1 and 1.7 m s⁻¹ speeds, and 138 kPa (20 PSI) was used for 2.7 m s⁻¹ and 262 kPa (38 PSI) for 3.9 m s⁻¹. The same pressure was adopted for speeds of 1.1 and 1.7 m s⁻¹ because the minimum system velocity was set at 1.7 m s⁻¹, so that the pressure was not lower than 90 kPa (13 PSI).

The tests were performed via a single-nozzle configuration and were repeated three times.

2.3. Spray Nozzles

The spray nozzle types evaluated in this study, along with their respective characteristics, are described in detail by Jacto [18] and summarized in

Table 1. Spray nozzles.

Model	Nominal Flow * (L min−1)	Fan Shape/Material
AXI 11002	0.757	Flat fan/Ceramic
ADI 11002	0.757	Flat fan (pre-orifice)/Ceramic
CVI 11002	0.757	Flat fan (air-inclusion)/Polymer
JAI 12002	0.757	Flat fan (air-inclusion)/Polymer
J3D 10002	0.757	Flat fan (angled)/Polymer
JTT 11002	0.757	Flat fan (deflector)/Polymer
JGC 12002	0.757	Flat fan (angled pre-orifice/Polymer
JAP 11002	0.757	Flat fan (air-inclusion)/Polymer

* At a pressure of 276 kPa (40 PSI).

. The main differences between CVI, JAI, and JAP are their design and pressure range: CVI operates between 138 and 414 kPa (20–60 PSI), JAI between 103 and 827 kPa (15–120 PSI), and JAP between 207 and 827 kPa (30–120 PSI).

2.4. Evaluated Characteristics

The parameters of interest were as follows: droplet velocity (DV), Dv0.5 (droplet diameter such that 50% of the volume of the sprayed liquid consists of droplets smaller than this value, also known as volume median diameter (VMD)), volume percentage of droplets smaller than 100 μm (% < 100) and relative span (RS), expressed by the following equation (Equation (1)):

RS = (Dv0.9 − Dv0.1)/Dv0.5

(1)

where RS is the relative span; Dv0.1 is the droplet diameter such that 10% of the volume sprayed is in droplets smaller than this value; Dv0.9 is the droplet diameter such that 90% of the volume sprayed is in droplets smaller than this value.

2.5. Statistical Analysis

To clearly present the experimental setup, the constants, variables, and measured outputs are listed below:

• Constants:

  ○

  Nozzle type: AXI, ADI, CVI, JAI, J3D, JTT, JGC, and JAP;

  ○

  Nozzle flow: 0.757 L min⁻¹;

  ○

  Spray height: 30 cm.

• Variables:

  ○

  Spraying systems: PWM valve on and off;

  ○

  Work speeds: 3.9, 2.8, 1.7, and 1.1 m s⁻¹, which correspond to duty cycles of 100%, 71%, 42% and 35%, respectively.

• Outputs:

  ○

  Droplet size (Dv0.5);

  ○

  Percentage of the volume composed of droplets < 100 µm;

  ○

  Droplet velocity;

  ○

  Relative span.

The experimental design adopted was completely randomized, with three replicates, in a 2 × 3 + 1 factorial design: two spraying systems (PWM system on and off), three simulated working speeds (1.1, 1.7, and 2.8 m s⁻¹, which correspond to duty cycles of 35%, 42%, and 71%, respectively), and an additional treatment simulating speed of 3.9 m s⁻¹ and a duty cycle of 100%. This last treatment was considered additional because there was no difference between treatments with 100% duty cycles with the PWM system on and off.

All the data were first subjected to the Shapiro–Wilk test for normality of residuals and the Oneill–Mathews test for homogeneity of variance, both at 0.05 significance level. In cases where the assumptions were not achieved, the data were transformed into √ (x + 0.5) and subjected to a new analysis. Only when the transformation corrected at least one of the assumptions, without harming the others, were the transformed data used for analysis of variance. Otherwise, the original data were used [19].

After the assumptions were analyzed, the data were subjected to analysis of variance via the statistical programme R Studio version 4.4 (Foundation for Statistical Computing, Vienna, Austria) [20]. When relevant, the treatments were compared with each other using Tukey’s test and with the additional treatment using Dunnett’s test at 0.05 significance level.

3. Results and Discussion

Table 2. Volume median diameter (VMD) and relative span (RS) of droplets sprayed through standard flat fan nozzles with the PWM system on (ON) and off (OFF) at four working speeds (v).

AXI 11002
v (m s−1)		VMD (μm)			RS
	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	126 bA	175 aA	151	1.09 ns	1.08 ns	1.08 A
1.7	42	112 bB ns	175 aA	146	1.36	1.08 ns	1.22 A
2.8	71	121 bA ns	137 aB	129	1.38	0.95 ns	1.16 A
3.9	100	111			0.72
Mean		120	162		1.28 a	1.03 b
CV (%)		3.29			21.06
J3D 10002
		VMD (μm)			RS
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	194 bA	282 aA	238	2.20 ns	1.17 ns	1.69 A
1.7	42	154 bB ns	282 aA	218	2.11 ns	1.17 ns	1.64 A
2.8	71	164 aB ns	180 aB	172	2.46 ns	1.36 ns	1.91 A
3.9	100	149			1.45
Mean		171	248		2.26 a	1.23 b
CV (%)		5.95			32.53
JTT 11002
		VMD (μm)			RS
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	404 ns	488	446 A	1.52 ns	1.40 ns	1.46 A
1.7	42	364 ns	488	426 A	1.74 ns	1.40 ns	1.57 A
2.8	71	388 ns	425 ns	406 A	1.36 ns	1.42 ns	1.39 A
3.9	100	374			1.39
Mean		385 b	467 a		1.54 a	1.41 a
CV (%)		7.93			10.74

Means followed by distinct uppercase letters in the columns and lowercase letters in the rows differ from each other, according to Tukey’s test, at 0.05 significance; ^ns: There was no difference between the mean and the additional treatment by Dunnett’s test; CV: Coefficient of variation.

shows the VMD and RS results for the AXI, J3D, and JTT standard flat fan nozzles. For the VMD, the interaction between factors (PWM system and working speed) was significant for the AXI and J3D nozzles. The interaction between the factors was not significant for the JTT nozzle. For RS, the interaction between the factors was not significant for the three nozzles.

Under most of the tested conditions, the PWM system resulted in the production of smaller droplets than did the conventional system, with the PWM system off. This behaviour was especially evident in the AXI and JTT nozzles, in which the VMD showed reductions of up to 49 μm (for example, 175 µm at OFF mode to 126 µm at ON mode for the AXI at 35% cycle). The observed reduction in droplet size can be attributed to the flow resistance introduced by the solenoid valve in the PWM system, which creates a pulsating flow regime that favours the formation of smaller droplets even at high duty cycles. In addition, the duty cycle influenced the VMD, except for the JTT nozzle, where the droplet diameter remained stable across duty cycles. The observed outcome is likely due to the JTT nozzle design. Although being a flat fan nozzle, droplets are generated as the spray passes through the orifice and strikes a deflector, unlike other nozzle types. For the J3D nozzle, there was a change in the VMD from 154 µm to 164 µm when the duty cycle was increased from 42% to 71%.

A comparison of the VMDs with the additional treatment, 100% duty cycle, revealed that there was a distinct behaviour between the nozzles, although the lowest VMDs were always found with the 100% duty cycle. This is explained by the fact that the highest working pressure, 262 kPa, was used under these conditions. With the PWM valve on and operating with a cycle equal to or above 42%, there was no difference in the VMD in relation to the cycle condition at 100%, which represents a positive characteristic regarding the operation of the system. This finding corroborates the argument of Butts et al. [6], who recommend that applications in sprayers with PWM systems should be performed in cycles of 40% or more.

Theoretically, one of the advantages of PWM systems compared with conventional systems is that they allow the flow rate to be changed without changing the working pressure, which results in the maintenance of the size of the droplets produced [21]. However, it is clear from the analysis that, for some nozzle models, there is a change in the droplet size when the duty cycle of the valves is altered. Even in the case of flat fan nozzles without drift reduction technology, there was a difference in behaviour between them.

With the PWM system off, the speed simulation was performed by changing the pressure. Therefore, it was expected that, in these cases, the increase in speed would lead to an increase in the working pressure and, consequently, to a decrease in the droplet size. This behaviour was observed for the AXI and J3D nozzles, but did not occur for the JTT. A high proportion of fine droplets increases the risk of drift, especially under high temperatures and low humidity, when their lifespan is short. However, fine droplets can also improve plant surface coverage without increasing the risk of runoff.

Butts et al. [6] reported that the use of a solenoid valve in the spray line caused a reduction in droplet size when a 100% duty cycle was used compared with a system without a solenoid valve using non-air-inclusion nozzles. However, this does not fully explain the reduction in droplet size at a duty cycle lower than 100%. In these cases, the nozzles operate with intermittent and pulsating apertures, which can influence the atomization pattern in a more complex way, involving rapid variations in jet dynamics and flow instabilities. However, further investigations are needed to clarify the mechanisms underlying this phenomenon, considering aspects such as the interaction between the pulsation frequency, valve response time, and behaviour of the liquid at the nozzle exit during the opening and closing cycles.

In this context, the use of PWM may be advantageous because, even with smaller droplets, it tends to promote better coverage of the target surface because of the greater number of droplets per unit area. Maintaining stable working pressure contributes to more uniform deposition, especially when associated with nozzles suitable for drift reduction, such as those with air inclusion. Thus, it is necessary to consider not only the risk of drift but also the positive impact of the technology on the quality of application, especially with respect to the coverage and deposition of agrochemicals.

Giles and Comino [22] described a significant effect of the duty cycle on Dv0.1 and Dv0.5 for flat fan nozzles, with an increase in droplet size as the duty cycle decreased, similar to that reported in the present study. In this regard, Butts et al. [6] reported that the droplet size generally increases, which reduces the percentage of driftable fines as the duty cycle decreases, both for Venturi and non-Venturi nozzles.

Wei et al. [23] compared two PWM systems from different brands and found notable differences between them. These results indicate that hydraulic behaviour can vary between solenoid valves, directly affecting atomization. The authors emphasized the importance of carefully selecting the nozzle based on the specific characteristics of the PWM valve used, in order to ensure consistency in droplet size and spray performance. In addition, it is essential to distinguish variable rate spraying with speed control from spraying in which there is a real change in the applied dose per unit area because the behaviour of the system may vary in each situation. Thus, the appropriate combination of valve, nozzle, and application strategies is essential to ensure the efficiency, coverage, and safety of the application.

Table 2 also shows the results of the relative span, which is an essential parameter for evaluating the quality of a spray because its analysis provides information on the homogeneity of the droplet spectrum [24]. The ideal scenario would involve RS values tending to zero because the greater the relative span, the more uneven the droplet spectrum. The duty cycle impaired the homogeneity of the droplets produced by the AXI and J3D nozzles when the PWM system was on. For the PWM system off, the change in working speed, and consequently the working pressure, did not affect the results.

Comparing the RS results from the additional treatment (100% duty cycle), it was observed that, in general, the duty cycle did not affect this characteristic. For this variable, a higher coefficient of variation was observed, indicating heterogeneity in the dataset in relation to the mean, which also helps explain the lack of significant differences.

Table 3. Volume median diameter (VMD) and relative span (RS) of droplets sprayed through pre-orifice and air-inclusion flat fan nozzles with the PWM system on (ON) and off (OFF) at four working speeds (v).

ADI 11002
		VMD * (μm)			RS
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	182 bA	375 aA	278	1.49	1.19	1.33 A
1.7	42	140 bB ns	375 aA	257	1.53	1.17	1.35 A
2.8	71	147 bB ns	211 aB	179	1.40	1.17	1.30 A
3.9	100	140			0.97
Mean		156	320		1.47 a	1.18 b
CV (%)		5.67			8.45
CVI 11002
		VMD (μm)			RS
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	624 aA	731 aA	678	2.11 ns	1.34 ns	1.73 A
1.7	42	321 bB ns	731 aA	526	1.75 ns	1.34 ns	1.55 A
2.8	71	373 aB ns	497 aB	435	2.44 ns	1.38 ns	1.91 A
3.9	100	266			1.60
Mean		439	653		2.10 a	1.36 b
CV (%)		15.87			20.89
JGC 12002
		VMD (μm)			RS
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	310 aA	325 aA	317	2.07 ns	1.55 ns	1.81 A
1.7	42	293 bA	325 aA	309	1.96 ns	1.55 ns	1.76 A
2.8	71	289 aA	264 bB	277	2.35 ns	1.24 ns	1.80 A
3.9	100	227			1.42
Mean		297	305		2.13 a	1.45 b
CV (%)		4.44			30.30
JAI 12002
		VMD (μm)			RS
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	394 bA ns	529 aA	461	1.39 ns	1.12 ns	1.26 A
1.7	42	340 bB ns	529 aA	434	1.29 ns	1.12 ns	1.21 A
2.8	71	369 bA ns	436 aB	403	1.44 ns	1.28 ns	1.36 A
3.9	100	378			1.31
Mean		368	498		1.37 a	1.18 a
CV (%)		4.45			16.87
JAP 11002
		VMD (μm)			RS
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	402 bA	485 aA	444	2.04 ns	1.51 ns	1.77 A
1.7	42	331 bB ns	485 aA	408	1.79 ns	1.51 ns	1.65 A
2.8	71	334 bB ns	429 aB	382	1.83 ns	1.46 ns	1.64 A
3.9	100	318			1.34
Mean		356	466		1.89 a	1.49 b
CV (%)		5.38			19.64

Means followed by distinct uppercase letters in the columns and lowercase letters in the rows differ from each other, according to Tukey’s test, at 0.05 significance; * Root-transformed data (x + 0.5); ^ns: There was no difference between the mean and the additional treatment by Dunnett’s test; CV: Coefficient of variation.

shows the VMD and RS results for the nozzles with drift reduction systems (ADI, CVI, JGC, JAI, and JAP) under different operating conditions. For the VMD, the interaction between both factors was significant, whereas for the RS, the interaction between the factors was not significant, for all nozzle types.

In general, there was a reduction in VMD of the droplets when the PWM system was on in comparison to the PWM system off across nozzle types. This trend was more evident for nozzles such as the ADI nozzle, whose average VMD decreased from 320 µm with PWM off to 156 µm with PWM on, representing a reduction of 51%, which implies greater formation of fine droplets and thus a greater potential risk of drift. For the CVI nozzle, the mean VMD with the PWM on was 439 µm, whereas it was 653 µm with the PWM off, a reduction of approximately 33%.

Although in many cases there was no significant difference (^ns), the trend of VMD reduction with the use of the PWM system is consistent, especially at lower duty cycles and speeds. Regarding the RS, the means were greater with the PWM system on for all nozzles, indicating less uniform spraying with greater variation in droplet size. This difference was significant in most cases, as evidenced by the distinct letters in the columns. Therefore, the use of the PWM system, despite contributing to the generation of smaller droplets, can also compromise spraying uniformity, requiring attention to nozzle selection and operational adjustments to mitigate agronomic and environmental risks.

Except for the JGC and JAI nozzles, the diameter of the droplets increased as the duty cycle decreased. Similar findings were also reported by Butts et al. [6]. This effect is achieved through a restriction in the solenoid valve, which reduces the pressure at the nozzle while the gauge pressure remains stable.

The ADI and JGC nozzles have a pre-orifice that creates an internal chamber with the objective of promoting an increase in the size of the droplets and allowing smaller droplets to group together, which results in larger droplets and reduces the risk of drift in conventional systems. Generally, they produce droplets of intermediate size between the standard flat fan and air-inclusion nozzles [25]. A considerable reduction in the droplet size was observed when the PWM system was switched from off to on for the ADI nozzle, which shows a more pronounced effect of the solenoid valve on the drift reduction nozzle through pressure control. However, there was little effect of the number of duty cycles on the spraying, and thus, there were no significant results according to Dunnett’s test at the ADI nozzle, except for the 35% cycle, in which a slight increase in the droplet size was observed, as a function of pressure reduction, compared with the 100% cycle.

The CVI, JAI, and JAP nozzles work with air inclusion through the Venturi effect, in which coarser droplets are generated, and are widely used in applications of systemic products. The Venturi effect introduces air into the liquid, which consequently generates coarse to very coarse droplets and reduces the risk of drift [26]. Similarly to the ADI nozzle, a reduction in the droplet size was observed for the JAI and JAP nozzles with the activation of the PWM system. For the CVI nozzle, this trend did not occur under the conditions tested, except at 1.7 m s⁻¹ working speed. For the JAI nozzle, there was no difference in VMD when the PWM system was on compared with the 100% duty cycle; however, for the CVI and JAP nozzles, there was a difference in the shorter duty cycle, demonstrating that the behaviour may be different even between air-inclusion nozzles. With the exception of the JGC nozzle, there was no difference in VMD between 100%, 71% and 42% duty cycles, indicating that preference should be given to the use of duty cycles equal to or greater than 42% to avoid variations in droplet size, which is in accordance with the recommendations presented by Butts et al. [6]. Some valves malfunction at low percentages [27]. Below 40%, there may be a significant delay in the valve response, or it may not open in a controllable manner. This is due to the internal mechanical and electromagnetic forces that must be overcome for proper operation.

Table 3 also shows the relative span data. The duty cycle did not affect the homogeneity of the droplet spectrum. However, the PWM system increased the RS of the droplet spectrum produced by all nozzles, except for the JAI. Comparing the results of RS with the additional treatment, it was noticed that the PWM system, on or off, did not affect this variable, except for the ADI nozzle. The outcome for the ADI nozzle may be explained by its lower coefficient of variation (CV) of relative span (8.45 vs. 20.89, 30.30, 16.87, and 19.64; Table 3), which likely enabled statistical differences to be detected between the PWM treatments and the 100% duty cycle. A higher coefficient of variation indicates heterogeneity in the dataset, which may explain the absence of significant results.

The results of the evaluations of the volume percentage of droplets smaller than 100 µm and velocity of the droplets produced through the AXI, J3D, and JTT flat fan nozzles are presented in

Table 4. Volume percentage of droplets smaller than 100 μm (% < 100) and droplet velocity (DV) generated by standard flat fan nozzles with the PWM system on (ON) and off (OFF) at four working speeds (v).

AXI 11002
		% < 100 *			DV (m s−1)
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	28.77 aB	11.03 bB	19.90	1.42 bB	1.96 aA ns	1.69
1.7	42	39.20 aA ns	11.03 bB	25.12	1.63 bA	1.96 aA ns	1.80
2.8	71	29.77 aB	20.07 bA	24.92	1.77 bA	1.95 aA ns	1.86
3.9	100	37.30			1.98
Mean		32.58	14.04		1.61	1.96
CV (%)		12.05			3.91
J3D 10002
		% < 100			DV (m s−1)
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	14.60 aB	5.52 bB	10.06	1.77 bC	2.51 aB	2.14
1.7	42	24.13 aA ns	5.52 bB	14.82	2.16 bB	2.51 aB	2.33
2.8	71	19.87 aA ns	15.00 aA	17.43	2.61 bA	2.82 aA	2.71
3.9	100	23.80			3.18
Mean		19.53	8.68		2.18	2.61
CV (%)		19.81			3.46
JTT 11002
		% < 100			DV (m s−1)
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	5.87 aAB ns	2.47 bB	4.17	1.67 bC	1.94 aB	1.80
1.7	42	7.10 aA	2.47 bB	4.78	2.21 aB	1.94 bB	2.07
2.8	71	5.67 aB ns	3.47 bA	4.57	2.69 aA	2.36 bA	2.52
3.9	100	5.43			3.30
Mean		6.21	2.80		2.19	2.08
CV (%)		12.73			2.61

Means followed by distinct uppercase letters in the columns and lowercase letters in the rows differ from each other, according to Tukey’s test, at 0.05 significance; * Root-transformed data (x + 0.5); ^ns: There was no difference between the mean and the additional treatment by Dunnett’s test; CV: Coefficient of variation.

. For % < 100 and DV, the interactions between the factors were significant for all nozzles.

Following the trend presented for the VMD, the change from off mode to on mode of the PWM system reduced the droplet size, which increased the % < 100. For the AXI nozzle, for example, the average percentage of 14.04% increased to 32.58%, which characterizes a 2.3-fold greater risk of drift when using the PWM system. Regarding the duty cycles with the PWM system on, the behaviour was dependent on the nozzle model. A greater % < 100 was observed at 42% duty cycle than at 71% duty cycle for the AXI and JTT nozzles, but similar for the J3D nozzle.

According to Cunha et al. [28], there is no ideal or permissible value for the risk of drift, and values lower than 15% of % < 100 are typically recommended for safe applications. Butts et al. [6] reported that fine droplets from standard nozzles were reduced as the duty cycle decreased from 100% to 40%, thus demonstrating that pulsation in a PWM system can decrease the risk of drift. However, this trend was not always observed in the present study, which was conditional on the type of nozzle evaluated. At the J3D nozzle, for example, there was a reduction in the risk of drift with a decrease in the duty cycles.

With the PWM system off, faster simulated working speeds led, in general, to an increase in the risk of drift, as there was an increase in pressure and, consequently, a reduction in the size of the droplets. For the additional treatment, the pressure used was the highest, thus contributing to the increased risk of drift. According to Camara et al. [29], the droplet size is directly proportional to the operating pressure, i.e., as the pressure increases, the droplet size decreases. The DV results, in general, also changed when the PWM system was activated. Under most of the tested conditions, the PWM system led to a reduction in DV (AXI and J3D nozzles) compared with the PWM system off.

Droplets, when moving away from the nozzle, face the influence of gravity and air resistance. This resistance softens the DV, which may even fragment it into smaller droplets. Small droplets slow down faster than coarse droplets, fall down more slowly, and are more susceptible to being carried away by the wind, promoting drift. According to Farooq et al. [30], near the nozzle, smaller droplets move at a lower speed than larger droplets. When moving away from the nozzle, small droplets may even have a negative velocity, suggesting their upwards movement.

Thus, the fine droplets remain suspended in the air for a longer time, which increases the probability of being carried by the wind, especially when spraying is performed under unfavourable weather conditions, such as temperatures above 30 °C, relative humidity lower than 55%, and winds above 10 km h⁻¹. In these situations, there is a greater risk of losses by evaporation and drift, making spraying inefficient. This terminal velocity is important because the smaller the droplet size is, the longer it will take to deposit on the target; thus, during this period, it is subject to the action of evaporation and wind drag out of the target area [25].

When comparing the treatments with different duty cycles (PWM on), increasing the valve opening time promoted an increase in the DV produced by the J3D and JTT nozzle. With the PWM off, the increase in the simulated speed from 1.1 to 2.8 m s⁻¹ also led to an increase in DV produced by the J3D and JTT nozzles. For the AXI nozzle, no differences were observed for this parameter.

When comparing the PWM connected with the additional treatment, it was observed that the DV with a 100% duty cycle was always higher than when the valve worked in shorter cycles. With the PWM off, the increase in pressure also led to an increase in DV, except for the AXI nozzle.

Table 5. Volume percentage of droplets smaller than 100 μm (% < 100) and droplet velocity (DV) generated by pre-orifice and air-inclusion flat fan nozzles with the PWM system on (ON) and off (OFF) at four working speeds (v).

ADI 11002
		% < 100 *			DV (m s−1)
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	18.13 aB ns	2.93 bB	10.53	1.51 bC ns	2.07 aA ns	1.79
1.7	42	25.17 aA	2.93 bB	14.05	1.71 bB ns	2.07 aA ns	1.89
2.8	71	20.93 aB ns	9.83 bA	15.38	2.07 aA ns	2.12 aA ns	2.09
3.9	100	19.70			2.22
Mean		21.41	5.23		1.76	2.09
CV (%)		10.73			1.76
CVI 11002
		% < 100 *			DV (m s−1)
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	2.90 aB ns	0.83 bA	1.87	1.29 bC	1.45 aB	1.37
1.7	42	6.40 aA ns	0.83 bA	3.62	1.43 aB	1.45 aB	1.43
2.8	71	3.63 aB ns	1.63 bA	2.63	1.64 aA	1.62 aA	1.63
3.9	100	4.43			1.85
Mean		4.31	1.10		1.45	1.50
CV (%)		31.45			3.06
JGC 12002
		% < 100			DV (m s−1)
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	8.47 aA	5.13 bB	6.80	1.79 bC	2.13 aB	1.96
1.7	42	10.03 aA ns	5.13 bB	7.58	2.48 aB	2.13 bB	2.30
2.8	71	8.43 aA	7.57 aA	8.00	2.96 aA	2.59 bA	2.77
3.9	100	11.97			3.55
Mean		8.98	5.94		2.41	2.28
CV (%)		12.88			4.36
JAI 12002
		% < 100 *			DV (m s−1)
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	3.20 aB	0.78 bA	2.00	1.47 bC	1.76 aA	1.61
1.7	42	5.67 aA	0.78 bA	3.23	1.78 aB	1.76 aA	1.77
2.8	71	2.90 aB	1.03 bA	1.97	2.07 aA ns	1.75 bA	1.91
3.9	100	1.93			2.26
Mean		3.92	0.86		1.77	1.76
CV (%)		17.27			4.91
JAP 11002
		% < 100			DV (m s−1)
v (m s−1)	Cycle (%)	ON	OFF	Mean	ON	OFF	Mean
1.1	35	5.70 aB ns	1.67 bB	3.68	1.49 bC	2.01 aB	1.75
1.7	42	7.27 aA	1.67 bB	4.47	1.93 bB	2.01 aB	1.97
2.8	71	6.23 aB ns	2.80 bA	4.51	2.35 aA	2.28 bA	2.31
3.9	100	6.13			2.83
Mean		6.40	2.04		1.92	2.10
CV (%)		10.56			1.73

Means followed by distinct uppercase letters in the columns and lowercase letters in the rows differ from each other, according to Tukey’s test, at 0.05 significance; * Root-transformed data (x + 0.5); ^ns: There was no difference between the mean and the additional treatment by Dunnett’s test; CV: Coefficient of variation.

shows the results of % < 100 and DV for the ADI, CVI, JGC, JAI, and JAP nozzles. The interaction between the factors was significant for all nozzles.

Similar behaviour observed in Table 4 can be observed for the nozzles in Table 5, where there was a considerable increase in the population of droplets smaller than 100 μm with the PWM system on. For the ADI nozzle, for example, the average percentage of 5% increased to 21%, which represents an increase of 320%. The effects of the different duty cycles, in general, were dependent on the nozzle type; however, the highest potential risk of drift was noticed at 42% duty cycle for all the nozzles evaluated, although there was no significant difference for the JGC nozzle.

It was not possible to establish a common linear relationship for the nozzles evaluated between the duty cycle and the risk of drift. In fact, there are conflicting results in the literature for this relationship. Grela et al. [5] reported an increase in % < 100 as the duty cycle decreased from 100% to 30%, indicating a physical effect on the generation of smaller droplets. In contrast, Butts et al. [6] reported that as the duty cycle was reduced, the percentage of droplets prone to drift decreased, whether for Venturi or non-Venturi nozzles, which demonstrates that this complex process still requires further study.

According to Adegas and Gazziero [31], the change in working pressure directly affects the droplet size, producing larger or smaller droplets as the pressure is reduced or increased, regardless of the state-of-the-art technology used. Compared with the additional treatment at 100% duty cycle, greater values of % < 100 were observed at 42% duty cycle for the ADI, JAI, and JAP nozzles, which indicates greater drift potential. For the ADI nozzle, for example, the % < 100 increased from 19.7% at 100% duty cycle to 25.17% at 42% duty cycle and up to 18.13% at 35% duty cycle, reinforcing the increased risk of fine droplet formation in smaller cycles. These results show that although the additional treatment generally results in a lower proportion of fine droplets, intermediate cycles, such as 42%, may represent the greatest risk of drift, especially in air-inclusion or pre-orifice nozzles. Therefore, the selection of the ideal duty cycle should consider not only the flow control but also the nozzle type and the impacts on the droplet spectrum.

According to Butts et al. [21], sprayers with PWM systems allow more efficient applications through the automation of opening and closing individual nozzles. With the activation of the PWM system, the DV was affected in most conditions tested (Table 5). The effect of the working speed with the PWM system always resulted in higher droplet velocities with higher duty cycles.

An analysis of the PWM system at different duty cycles compared with the additional treatment, 100% cycle, revealed that the DV of the CVI, JGC, and JAP nozzles was significantly greater at 100% duty cycle than at lower cycles. For example, for the ADI nozzle, the DV was 2.22 m s⁻¹ at 100% duty cycle, whereas at 35%, 42%, and 71% the DVs were 1.51, 1.71, and 2.07 m s⁻¹, respectively, representing an increase of up to 47% in the maximum cycle. Similarly, for the JGC nozzle, the DV reached 3.55 m s⁻¹ at 100% duty cycle, whereas it reached 1.79, 2.48, and 2.96 m s⁻¹ at lower cycles, indicating an increase of almost 98% between the extremes. For the JAP nozzle, the DV at 100% cycle was 2.83 m s⁻¹, whereas at 35%, 42%, and 71% the values were 1.49, 1.93, and 2.35 m s⁻¹, respectively, which indicates an increase of 89.9% in the DV between the 35% and 100% duty cycles.

Oppositely, when the PWM system was off, an increase in DV was also observed with increasing working pressure, which simulates an increase in working speed. For the CVI nozzle, for example, the DV increased from 1.45 m s⁻¹ at the lowest duty cycle to 1.62 m s⁻¹ at the highest duty cycle. A similar situation was observed for the JGC nozzle, whose DV increased from 2.13 m s⁻¹ to 2.59 m s⁻¹; and for JAP nozzle, from 2.01 m s⁻¹ to 2.28 m s⁻¹. Directly comparing the PWM system on and off in the same duty cycle, for example, at 71% duty cycle, it is noted that, in general, the DV was slightly lower with the system on. For the JAP nozzle, the DV was 2.35 m s⁻¹ with the PWM on and 2.28 m s⁻¹ with the PWM off, a difference of only 3%. However, for the JGC nozzle, this difference was greater: 2.96 m s⁻¹ with PWM on versus 2.59 m s⁻¹ with the PWM off, indicating that PWM technology can, under certain conditions, contribute to increases in droplet velocities, especially in higher duty cycles. These data reinforce that DV is influenced both by the duty cycle and configuration of the system, and it is essential to consider the interaction between these factors to obtain effective and safe spraying.

4. Conclusions

The activation of the PWM system, characterized by a change from the off mode to the on mode, resulted in droplet size changes, with a tendency to decrease the VMD for most of the tested nozzles. However, this variation was lower than that observed with the conventional system, in which pressure changes more markedly influenced the droplet size.

The RS of the droplet spectrum was not significantly influenced by the duty cycle, although PWM activation increased the droplet size heterogeneity for some nozzle types. For the conventional system, the change in pressure did not substantially change the homogeneity of the droplets.

An increase in the potential risk of drift was observed with the use of the PWM system in some duty cycles, especially for nozzles that do not use drift reduction technology. The DV was reduced with the PWM system under most conditions tested, but increased with higher duty cycles.

Although some studies do not indicate the use of air-inclusion nozzles with PWM systems, this is due to the specificities of each study and the nozzles used. In the present study, it was observed that it is possible to use some air-inclusion nozzles with the PWM system.

Finally, it is possible to conclude that the PWM system is a viable alternative to variable rate spraying. The proper selection of nozzle and duty cycle is essential to ensure efficiency and safety in the application. The use of duty cycles above 40% and extra attention to the selection of nozzles is recommended, especially for air-inclusion nozzle types. More studies are needed to fully understand the interaction between the PWM valve, nozzle type, droplet spectrum, and spray coverage under different operating conditions, as well as to assess whether these results are maintained when surfactants are added to the spray mixture.