trigger sprayer characterization of large droplets … t4-b-1.pdftrigger sprayer characterization of...

Trigger Sprayer Characterization of Large Droplets by Pneumatic Separation and Spray Deposition

J. A. Stamper* and J. P. Hecht

Process Technologies, Procter & Gamble 8256 Union Centre Blvd.

West Chester, OH 45069 USA

D. K. Giles Department of Biological & Agricultural Engineering

University of California, Davis Davis, CA 95616 USA

Abstract A pneumatic spray separation and deposition technique was developed to characterize large droplets produced by consumer trigger sprayers. These large droplets (~ >1000µm) are few in number and sparse in the spray, so they are difficult to detect accurately with conventional droplet-sizing techniques. The pneumatic separation technique automatically actuates the trigger and sprays in to a high velocity horizontal air source (~20m/sec). The air separates and classifies droplets by size; smaller droplets are carried away by the air and larger ones fall to the ground a closer distance to the nozzle. The larger droplets in the spray are measured by allowing the droplets to deposit onto one of eleven substrate sections spanning ~2.4m from the air source. Each substrate section was weighed before and after spraying to determine mass deposition. Four liquid samples and two nozzle designs were tested; 30%-70% of the total sprayed mass was collected. The sample masses and sampling distances were used along with a simple mathematical model to differentiate between the nozzles and the fluids. The mass deposition data agreed fairly well against the predictions of the mathematical model. This technique may be used to screen trigger sprayer designs for certain droplet size limits or may be used as a quality assurance method to determine batch-to-batch variations for a given product design.

*Corresponding author

ILASS Americas, 21st Annual Conference on Liquid Atomization and Spray Systems, Orlando, Florida, May 18-21 2008

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Introduction and Motivation Several industries including consumer goods, agriculture, pest control, et cetera utilize hand-actuated trigger sprayers. In most applications, the purpose of the trigger sprayer is to deposit droplets onto a surface. In some instances it is desirable to have extremely large droplets and in other instances it is desirable to have extremely small droplets. Due to the large numbers of extremely small droplets produced, they can be easily detected and measured with traditional sizing techniques (laser diffraction or digital photography). Large droplets from trigger sprayers prove more difficult to detect and measure with traditional sizing techniques. There are several reasons that lead to this conclusion: 1. The spray characteristics are a function of time during each spray event and are not spatially uniform. 2. Droplet size distributions are wide, with very few large droplets. 3. Traditional techniques have a small measurement volume, so given the low spatial density of large droplets, the probability of detecting them is low. Trigger sprays have lifetime of about 10,000 pulls; this is insufficient to give statistically-relevant data on large droplets. Given these considerations, a simple and robust technique is needed to accurately characterize the large droplets generated with these sprayer types. The main idea presented in this paper is that a high-velocity fan is used to pneumatically separate the droplets by size, so the deposition of each droplet size occurs at a different distance from the sprayer. Small droplets will be carried farther away by the air, while larger droplets will fall to the ground closer to the nozzle. Objectives The objective of this study was to develop a technique to better characterize the extremely large droplets generated using hand-actuated trigger sprayers. Specifically, the goals were to:

1. Develop, validate, and compare a simple two dimensional mathematical

model to predict droplet drift in an air flow.

2. Construct a simple and inexpensive device to screen hand actuated trigger sprayers and compare the test results for model fluids of varying viscosity.

Mathematical Model Model Formulation A two-dimensional mathematical model was constructed using a force balance on a single droplet in both the horizontal and vertical directions. The force balance assumed weight forces and drag forces while neglecting buoyancy forces and air turbulence. The model also neglects the effects of droplet drying and the potential for secondary atomization. The formulations for both the horizontal (Equation 1) and vertical (Equation 2) components can be seen below: Horizontal component: (1) Vertical component: (2) (3) (4) Model Inputs The mathematical model requires several key inputs from the physical system. These include pre-defined inputs and user defined inputs. Pre-Defined Inputs: These include any input into the model that is used to describe the physical system and would not be normally changed from run to run. These include:

1. Air Velocity Profiles 2. Drag Coefficient 3. Air Density 4. Air Viscosity

Horizontal and vertical air velocity profiles were experimentally measured and inputted into the

( )2

22,2

2air

xxD RuCdt

xdm

ρπ ⋅⋅⋅−=

( )2

22,2

2air

zzD RuCmgdt

zdm

ρπ ⋅⋅⋅−=

dtdx

ux =

dtdz

uz =


3

model. The drag coefficients were also inputted into the model in the form of an empirical fit for experimental data of free falling water droplets [1], see Figure 1. Empirical fits for the air density and air viscosity have also been incorporated into the model but the air temperature is required to determine these values. User-Defined Inputs: These include any input into the model that the user would change on a per case basis. These include:

1. Droplet Size 2. Droplet Fluid Density 3. Initial Droplet Velocity and Orientation 4. Air Temperature

The droplet size is required to calculate the droplet mass and the drag coefficient. The fluid density is also needed to calculate droplet mass. The initial droplet velocity and orientation are required to determine the initial state of the droplet. The model also requires the air temperature to correct for the air density and the air viscosity. Model Validation and Comparison The two-dimensional mathematical model was validated with experimentally measured data and validated against another similar droplet motion model. Validation Experiments: The model was experimentally validated using a simple procedure. A micropipette was used to generate numerous dye droplets of various sizes ranging from ~1,400µm to 2,500µm. The droplets were discharged into the air flow field. Each droplet was tracked and labeled after making contact with plotter paper. After each droplet size series was complete, the droplet drift distances were measured, see Figure 2. The run conditions were then input into the model to compare the model predictions to the experimentally measured values. These data are summarized in Figure 3. The experimentally measured data and the model predictions were found to be comparable. Model Comparison: Model predictions were compared to another droplet drift model, DriftSim [2], see Figure 4 [3], to further ensure accuracy. The DriftSim model was developed by The Ohio State University (OSU) and is a database of

Computation Fluid Dynamics (CFD) model results. The DriftSim model interpolates between the CFD results based on the user input and assumes 20% turbulence. Comparisons between the two models can be seen in Figure 5. There is very good agreement between these two models, especially in the large droplet range, droplets greater than 500µm. Discussion of Model Assumptions Several assumptions were made within the model. These include the following:

1. Droplet Drying 2. Secondary Atomization

Droplet Drying: Droplet drying is important to consider as any change in droplet size while the droplet is in flight will affect the trajectory. To ensure that droplet drying could be neglected for large droplets, the Ranz-Marshall Correlation [4] was used. The two limiting cases were imposed on droplets of various sizes, a droplet in stagnant air and a droplet moving at terminal velocity. These cases can be seen in Figure 6. Based on these results, and assuming that typical flight times are less than 0.5 seconds, it is reasonable assume that droplet drying in air does not affect large droplets. Secondary Atomization: Secondary atomization is also important to consider. For a liquid, break-up is achieved when the aerodynamic drag is equal to the surface tension forces [5], see Figure 7. (5) Equation 5 can be rearranged in terms of a Weber Number, We. (6) The critical Weber Number, Wecrit, for free falling droplets is 22 and Wecrit for droplets in a high velocity air stream is 13 [5]. Calculated values of We for limiting cases of water and a surfactant system can be seen in Tables 1 and 2.

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C R2

A

2

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Table 1: Weber Numbers for Water Surface Tension, σ: 0.072 N/m

10.0 15.0 20.050 0.1 0.2 0.3

100 0.2 0.4 0.6500 0.8 1.8 3.2

1000 1.6 3.6 6.42000 3.2 7.3 12.95000 8.1 18.1 32.2

size, µmRelative Velocity, m/sec

Table 2: Weber Numbers for Surfactant Surface Tension, σ: 0.032 N/m

10.0 15.0 20.050 0.2 0.4 0.7

100 0.4 0.8 1.5500 1.8 4.1 7.3

1000 3.6 8.2 14.52000 7.3 16.3 29.05000 18.1 40.8 72.5

size, µmRelative Velocity, m/sec

Based on this analysis, secondary atomization is possible for extremely large droplets, liquids with very low surface tension, and high droplet to air relative velocities. It is important to note that the relative velocity between the droplet and the air flow is only of concern during the initial stages of droplet acceleration. Experimental Apparatus and Procedure Apparatus Trigger Sprayers: Two disposable, commercially available hand-actuated trigger sprayers were used for this series of tests, as seen in Figure 8 [6]. The sprayers consisted of a hand-actuated piston pump, which supplied liquid to the discharge nozzle. The sprayers were not adjustable and not altered from their original design; the spray nozzle was rotated to the “on” position. Both sprayers used in this study were from the same series, TS-800 (MeadWestvaco/Calmar, Winfield, KS) and the sprayers included the TS-800-1 and the TS-800-2H. The TS-800-1 and the TS-800-2H dispensed ~0.94ml and ~0.85ml per stroke respectively. Test Fluids: The two materials used in this study were de-ionized municipal water and glycerine (Moon NK Glycerine, Food Grade, 99.7%, P&G Chemicals). These materials were selected because they are simple, inexpensive, non-toxic, and have been studied extensively. The physical

properties of the glycerine/water mixes used in this study are listed in Table 3. Table 3: Physical Properties of Test Fluids

Glycerine Concentration

Viscosity, Pa·s

Surface Tension, mN/m

Density, g/cm3

0.0% 0.001 70.9 1.00 44.0% 0.005 68.8 1.11 57.0% 0.010 67.7 1.14 63.0% 0.015 67.0 1.16 67.0% 0.020 66.6 1.18

Trigger Actuator: The trigger actuator unit consists of a logic controlled stepper motor, trigger depression arm, reservoir support base, and control unit. To assemble the unit, the reservoir is attached to the support frame and the trigger is attached a threaded base. The trigger unit is position to contact the trigger depression arm. To operate the unit, the stepper motor rotates the trigger depression arm to engage the trigger. The motor was preset to rotate the trigger depression arm at 120°/sec for a total stroke arc of 40°. At these settings the trigger is depressed for ~0.33 seconds. This leads to a nominal average flow rate for the TS-800-1 and the TS-800-2H of 2.82 ml/sec and 2.55 ml/sec respectively. It is important to note that due to the transient nature of the spray cycle, the instantaneous flow rate in constantly changing. Air Source: The air flow used in this study was provided by a centripetal blower (Model #: 4C592B, Grainger). This blower was attached to an extruded aluminum frame. A chute from the blower exit was constructed to reduce air dispersion prior to the delivery of a spray. No further actions were taken in attempts to create a more uniform air flow. Air velocity measurements for the blower were made at various distances and heights away from the blower. These data can be seen in Figures 9 and 10. Collection Panels: Collection panels for each test consisted of 11 absorbent pads ~210mm X 420mm in dimension. The absorbent pads were positioned end-to-end extending from the blower base outward spanning a distance of ~2.4m. The absorbent pads were attached to a base (to prevent flapping) with three Velcro strips. Analytical Balance:


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An analytical balance is used to pre-weigh and post-weight the collection panels. For this study a Mettler Toledo PR1231 balance was used. A sketch of the assembled apparatus can be seen in Figure 11. Procedure The test procedure consisted of the following: 1. Fill reservoir with test fluid and attach to

support frame 2. Attach trigger sprayer to support frame 3. Pre-weigh and label collection panels 4. Affix collection panels to base 5. Engage blower motor 6. Allow for blower to reach a steady state 7. Engage the automatic trigger actuator 8. Disengage blower once trigger actuator

has completed one cycle (10 sprays) 9. Remove collection panels and re-weigh 10. Process sample weight distribution Results The mathematical model is used to correlate drift distance with droplet size, see Figure 12. This correlation is then used in tandem with the sample weight distribution to tabulate a droplet size distribution (% Mass vs. Droplet Size). A summary of the results can be seen in Figures 13. A replicate of each test was completed and the data presented in Figure 13 represent the average of both runs for each test fluid and nozzle pairing. Conclusion A technique has been developed that employs pneumatic separation and droplet deposition to characterize hand actuated trigger sprayers. The technique is able to show consistent differences in sprayer nozzles; this is most evident in the high viscosity case, as shown in Figure 14. This technique also shows the sensitivity of a trigger sprayer to small changes in viscosity as seen in Figure 15. Discussion A benefit of this technique is the sample size that is measured. Traditional techniques only measure a small portion of an entire spray. On average with this technique ~50% of the sprayed sample mass was accounted for, far exceeding 1 The analytical balance was calibrated by a technician in January 2008.

the measured sample volumes of traditional techniques. While this technique may not yield exact droplet counts, an assumed count can be made for large droplets. Assuming an average droplet size of 1,000µm, this technique indicates that ~10,000 droplets have been counted. This calculation can be seen in Table 4. Table 4: Droplet Number Calculation Droplet Diameter 0.001 mWater Density 1000 kg/m3

Mass/Drop 5.24E-07 kg/dropNumber of Drops 9,875 dropsTotal Collected Mass 0.0052 kgTotal Collected Mass 5.20 g Nomenclature Cd Drag Coefficient, unitless D Droplet Diameter, m g Acceleration Due to Gravity, m/s2 m Mass, kg R Droplet Radius, m t Time, s UR Relative Velocity, m/sec We Weber Number, untiless x Horizontal Position, m z Vertical Position, m µ Viscosity, Pa·s π 3.14159 ρ Density, g/cm3

σ Surface Tension, mN/m Acknowledgment The authors would like to thank Tom Crowe of Procter & Gamble for developing the automatic trigger actuator device for the sprayers. References 1. Gunn, R. and Kinzer, G. D., J. Meteorology 6, 243-248 (1949) 2. Zhu, H., et al, Applied Engineering in Agriculture 11(3), 365-369 (1995) 3. Zhu, H., et al, DRIFTSIM version 1.12.04 4. Marshall, W. R., Atomization and Spray Drying 50, 81-92 (1986) 5. Lefebvre, A. H., Atomization and Sprays, 29-34 (1989) 6. Saint-Gobain/Calmar, TS-800 Bi-Injected Trigger, 03/30/2006, from Calmar website: http://www.calmar.com/library.aspx?sort=*&prod=ts800&file=*


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Drag Coefficient vs. Reynolds Number

0.01

0.1

1

10

100

1000

1.00E-02 1.00E+00 1.00E+02 1.00E+04 1.00E+06 1.00E+08

Reynolds Number, Re

Dra

g C

oeffi

cien

t, C

dSolid SpheresWater DropletsCircular Disks

Figure 1: Drag Coefficients

Droplet Size vs. Drift Distance

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1000 1200 1400 1600 1800 2000 2200 2400 2600

Droplet Size, µµµµm

Dri

ft D

ista

nce,

m

1388 microns1569 microns1615 microns1655 microns1768 microns2087 microns2290 microns2497 microns

Figure 2: Experimentally Collected Model Validation Data


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Model vs. Experimental Data

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1000 1200 1400 1600 1800 2000 2200 2400 2600Droplet Size, µµµµm

Flig

ht D

ista

nce,

m

Collected Data

Model Predictions, with Drop Cd

Figure 3: Experimental Data and Model Prediction Comparison

Figure 4: DriftSim User Interface. Taken from [3]


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Model Comparisons

0

2

4

6

8

10

12

0 500 1000 1500 2000 2500Droplet Size, µµµµm

Flig

ht D

ista

nce,

m

JAS Model

OSU DriftSim Model

Figure 5: DriftSim and JAS Model Comparison

Droplet Evaporation with and without Air Flow

0.1

1

10

100

1000

10000

0.001 0.01 0.1 1 10 100 1000 10000 100000

Evaporation Time, Sec

Dro

plet

Dia

met

er, µµ µµ

m

At Terminal Velocity

Stagnant Air

Figure 6: Ranz-Marshall Correlation for Droplet Evaporation


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Figure 7: Mechanisms for Secondary Atomization. Taken from [4]

Figure 8: Diagram of Hand-Actuated Trigger Sprayer. Taken from [6]


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Air Velocity Profiles

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

Air Velocity, x-direction, m/sec

Hei

ght

, m0.000m0.356m0.762m1.321m

Figure 9: Experimentally Measured X-Direction Air Velocity Profiles

Air Velocity Profiles

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.1 0.2 0.3 0.4 0.5 0.6

Height, m

Air

Vel

ocity

, z-d

ir, m

/sec 0.000m

0.356m0.762m

1.321m

Figure 10: Experimentally Measured Z-Direction Air Velocity Profiles


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Figure 11: Sketch of Air Separation Unit

Droplet Size vs. Drift Distance

0

500

1,000

1,500

2,000

2,500

0 2,000 4,000 6,000 8,000 10,000 12,000

Droplet Size, microns

Dri

ft D

ista

nce,

cm

Figure 12: Example of Droplet Size to Drift Distance Correlation


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% Mass Collected vs. Droplet Size

0%

5%

10%

15%

20%

25%

30%

35%

0 500 1000 1500 2000 2500 3000


% M

ass

Col

lect

ed67% Glycerine TS-800-1-167% Glycerine TS-800-2H-157% Glycerine TS-800-1-157% Glycerine TS-800-2H-144% Glycerine TS-800-1-144% Glycerine TS-800-2H-10% Glycerine TS-800-1-10% Glycerine TS-800-2H-1

Figure 13: Summary of Collected Droplet Size Distributions


0%

5%

10%

15%

20%

25%

30%

35%

0 500 1000 1500 2000 2500


% M

ass

Col

lect

ed

67% Glycerine TS-800-1-1

67% Glycerine TS-800-2H-1

Figure 14: Trigger Sprayer Differences at High Viscosity


13


0%

5%

10%

15%

20%

25%

30%

35%

0 500 1000 1500 2000 2500 3000


% M

ass

Col

lect

ed67% Glycerine TS-800-2H-1




Figure 15: Trigger Sprayer Sensitivity to Increasing Viscosity

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