Advanced Powder Technology 25 (2014) 795–800

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Advanced Powder Technology

journal homepage: www.elsevier .com/locate /apt

Original Research Paper

Influence of water pressure and apex angle on prediction of particle sizefor atomization of copper powder

0921-8831/$ - see front matter � 2013 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rightshttp://dx.doi.org/10.1016/j.apt.2013.11.014

⇑ Corresponding author. Tel.: +91 020 25507262; fax: +91 020 25507299.E-mail address: nbdhokey@yahoo.co.in (N.B. Dhokey).

N.B. Dhokey ⇑, M.G. Walunj, U.C. ChaudhariDepartment of Metallurgy and Material Science, College of Engineering, Pune 411005, India

a r t i c l e i n f o

Article history:Received 31 May 2013Received in revised form 1 November 2013Accepted 27 November 2013Available online 21 December 2013

Keywords:Water atomizerWater jet pressureApex angleParticle size

a b s t r a c t

Water atomization can be used to produce wide range of particle size, shape and particle size distributionof metal powder efficiently by varying operating variables which include design parameters, processparameters and thermophysical properties of metal and water. Liquid copper was water atomized in alaboratory fabricated atomizer. Few experiments were conducted to produce copper powder by varyingwater jet pressure. In the present work, mathematical model was formulated to propose a relationshipbetween particle size of copper powder and operating variables. Proposed mathematical model is devel-oped to predict particle size affected by different parameters and validated with experimental results. 3-D surface response was analyzed by varying water pressure and apex angle.� 2013 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder

Technology Japan. All rights reserved.

1. Introduction

In water atomization process, a number of operation variablesare to be considered in order to properly control the process. Thevariables include geometry parameters, process parameters andthermophysical properties of metal and water. Each design andconfiguration of atomization unit is unique and thus only somespecific operation conditions may be employed and many of thesevariables are interrelated [1]. Therefore, there may exist more thanone set of optimum variable combinations for a given atomizationunit. Several studies have shown that the pressure of the atomizingwater has significant effect on the atomized particle size, as re-ported by Persson et al. wherein water pressure from 8 to17.5 MPa during atomization of Fe–C alloy in a laboratory atomizerdecreased particle size by 45–50% [2]. Effect of increasing apex an-gle on decreasing particle size is also observed. Yenwiset et al.showed that high heat temperature level of liquid metal, flow rateof liquid metal and water pressure directly affected average sizesof produced copper powder particles [3]. Rajgure has designedand developed an atomizer using closed V-jet type nozzles [4].The existing mathematical models derived for prediction of parti-cle size in powder atomizer are limited and those are comprisedof two to nine variables [5–12]. However in the present researchwork, a mathematical model is proposed for prediction of powdersize which comprise of thirteen parameters affecting particle sizeduring water atomization.

2. Experimental work and procedure

In the present work, a laboratory fabricated water atomizer wasused for atomization of copper powder. Only water pressure andwater flow rate were varied by keeping other parameters un-changed such as superheat temperature (150 �C), melt flow rate(7.832 � 10�6 m3/s), apex angle (45�). Water jet system was de-signed and attached to an atomizer chamber as shown below inFig. 1. A closed V-jet type nozzle assembly was used in this atom-izer chamber, directing the water jets at a concentric point alongthe axis of metal stream (freely falling under gravity). In order tovary pressure of water jet, a small control system consisting ofpressure gauge and control valve were attached to the water pipeline. Copper metal was superheated by 150 �C above melting point(1506 K) in induction furnace (25 KW). The liquid copper was thenpoured into hot crucible (800 �C) closely fitted on the top of thenozzle assembly. The liquid metal makes a stream falling throughthe 3 mm bottom nozzle provided to the crucible. Stream of liquidmetals passes through a high impact zone created by water jetsthrough nozzles mounted at an angle of 45�. The water pressurewas varied from 10 psi to 40 psi at an equal interval. After theatomization wet powder was dried in a furnace at 120 �C. Then itwas characterized by sieve size analysis using sieves of differentmesh to get powder particle size distribution.

3. Formulation of dimensionless particle size model (DPSM)

In the present work, it was postulated that copper powder par-ticle size is affected by the various process parameters as described

reserved.

Fig. 1. Schematic sketch of laboratory fabricated water atomizer.

Fig. 2. Relationship of apex angle with length of interaction.

796 N.B. Dhokey et al. / Advanced Powder Technology 25 (2014) 795–800

in Table 1 and its relationship was expressed by Eq. (1). This can besolved by using Buckingham’s Pi theorem. It is stated that dimen-sionally homogeneous equation involving ‘n’ variables in ‘m’ pri-mary or fundamental dimensions can be reduced to a singlerelationship among n–m independent dimensionless products[13]. The final form of the model is given by Eq. (2) and detailingof the steps is given in Appendix A.

D ¼ f ðP;Q w;Q m;qw;qm;qp; Tmp; Tsuperheat;gm;hf ;Cp; LÞ ð1Þ

The corresponding DPSM equation is

DL¼ ;

L13 � Qm � qw � qp � Tmp � gm � hf � CP

q4m

� P

Q8w

" #A

ð2Þ

Y ¼ ;XA ð3Þ

3.1. Terminology

Dimensionless particle size parameter (Y) is the ratio of diameterof the particle (D) to the length of interaction (L). Thus length ofinteraction is a function of apex angle and distance between theprinciple axis of the liquid metal stream and the position of the

Table 1Abbreviations of symbols and their dimensional forms.

Sr. no. Description of parameters

1 Average particle sizea

2 Pressure of water3 Flow rate of water4 Flow rate of melt5 Density of water6 Density of melt7 Density of powder particle8 Melting temperature of metal9 Superheat temperature of melt

10 Viscosity of melt11 Heat of fusion of melt12 Heat capacity of melt13 Length of interaction14 Actual particle size15 Predicted particle size

a D ¼PðW�MÞPðWÞ , where W = weight of powder retained on particular sieve size, M = mid

nozzle. The schematic explanation of the parameters involved isshown in Fig. 2 and their inter-relationship is given by Eq. (4).

L ¼ Htana

ð4Þ

Dimensionless process parameter (X) is defined by Eq. (5) consistsof number of variables affecting the particle size while atomizationof liquid metal. It is a combined interactive process parameter. Anyinteraction amongst the variables configured in X is reflected interms of exponent A.

X ¼L13 � Q m � qw � qp � Tmp � gm � hf � Cp

q4m

� p

Q 8w

ð5Þ

Symbols Units Dimensional form

D m [M0L1T0h0]P N/m2 [M1L-1T-2h0]Qw m3/s [M0L3T-1h0]Qm m3/s [M0L3T-1h0]qw kg/m3 [M1L-3T0h0]qm kg/m3 [M1L-3T0h0]qp kg/m3 [M1L-3T0h0]Tmp K [M0L0T0h1]Tsuperheat K [M0L0T0h1]gm kg/ms [M1L-1T-1h0]hf J/kg [M0L2T-2h0]Cp J/kg.K [M0L2T-2h-1]L m [M0L1T0h0]DA m [M0L1T0h0]DP m [M0L1T0h0]

value of class interval of sieve size.

Table 2Sieve size analysis of water atomized copper powder for different experiments.

Experiment no. 1 2 3 4

Sr. no. ASTM Mesh no. (lm) P, (psi)

10 20 30 40

Distribution of weight of powder retained on sieve (gm)

1 Coarse Particle 139.933 221.879 258.104 1412 +35 (500 lm) 168.55 389.548 344.555 4803 +85 (180 lm) 66.03 145.183 181.599 330.6194 +100 (152 lm) 2.787 11.62 11.128 22.8885 +120 (125 lm) 0.908 4.417 4.227 10.9476 +150(106 lm) 1.439 6.399 7.86 14.9547 +170 (90 lm) 1.133 6.682 13.947 15.9

Total Input metal (gm) 980 900 970 1100

Total output powder (gm) 380.78 785.728 821.42 1016.308

%Yield 38.86% 87.30% 84.68% 92.39%

0.01087192

0.01102642

0.0108

0.011

0.0112

N.B. Dhokey et al. / Advanced Powder Technology 25 (2014) 795–800 797

There are two dimensionless constants of the model (Eq. (2))emerged as U and A which can be called as characteristics constantand it depends on the type of liquid metal and other operatingparameters. These constant can be obtained by conducting exper-iments and solving Eq. (2) at constant values of parameters usingAppendix B [14].

0.00989392

0.010310794

0.0098

0.01

0.0102

0.0104

0.0106Y

Y= 0.0042954 X0.0305

4. Results and discussions

Few set of experiments for water atomization of copper wascarried out for varying water pressure. Sieve size analysis of pow-ders was conducted to categorize particle distribution as reportedin Table 2. Particle size distribution data given in Table 2 is used tocalculate average particle size (D) for different water pressure (P)

Table 3Summary of the parameters varied for atomization of copper powder.

Exp.no.

P(psi)

Qw (m3/s) D (lm) X Y

1 40 0.25 � 10�3 499.6961 1.606 � 1012 9.993 � 10�3

2 30 0.23 � 10�3 515.5397 2.357 � 1012 10.31 � 10�3

3 20 0.192 � 10�3 543.596 6.669 � 1012 10.871 � 10�3

4 10 0.14 � 10�3 551.321 41.727 � 1012 11.0264 � 10�3

551.3211

543.596

515.5397

494.6961

490

500

510

520

530

540

550

560

0 10 20 30 40 50

D, (

μ m)

P, (psi)

Fig. 3. Relationship water pressure and average particle size obtained inexperimentation.

0.00E+00 2.00E+13 4.00E+13 6.00E+13

X

Fig. 4. Power law relationship of dimensionless particle size model.

as given in Table 3. Fig. 3 is plotted to give influence of water pres-sure on particle size obtained from experimental trials. A plot ob-tained between Y and X as shown in Fig. 4 gives rise to power lawrelationship with characteristics constant emerging are U = 0.0043and exponent A = 0.0305.

4.1. Variation of pressure on prediction of particle size

Using the already derived constants U = 0.0043 and A = 0.0305of DPSM represented by Eq. (6) and simply varying water pressurewith corresponding flow rate with keeping remaining parametersconstant at particular values given in Appendix B it may be possi-ble to predict the particle size using Eq. (6) and those are men-tioned in Table 4. A plot of predicted and actual particle size asindicated in Fig. 5 gives result in close agreement. Thus it validatesthe dimensionless particle size model.

Y ¼ 4:2954� 10�3½X�0:0305 ð6Þ

Eq. 6 can be expressed by Eq. (7) in order to calculate predicted par-ticle size which is function of pressure and water flow rate.

Dp ¼ 4:2954� 10�3½X�0:0305 � L ð7Þ

The existing models derived for prediction of particle size arelimited and those are comprised of two to nine variables [9–16].Persson et al. [2] showed model proposed by Bergquist [11] in gen-eral the best agreement with the current experimental results. But

Table 6Predicted particle size by Equation-8 for different apex angle for 40 psi pressure.

Exp. no. a (�) X Y DP (lm)

1 30 3.03 � 1015 0.013 11032 35 2.47 � 1014 0.012 8433 40 2.35 � 1013 0.011 8554 45 2.40 � 1012 0.010 5125 50 2.45 � 1011 0.009 4016 55 2.33 � 1010 0.0089 3117 60 1.90 � 109 0.0082 238

1103.27

842.78

654.58

512.35

401.01

311.49237.9

200

300

400

500

600

700

800

900

1000

1100

1200

20 30 40 50 60 70

DP

(µm

)

α (Degree)

40 psi

Fig. 6. Effect of apex angle on particle size.

Table 4Comparison between predicted particle size and actual particle size.

Exp. no. P (psi) X Y DP (lm) DA (lm)

1 40 1.606 � 1012 10.124 � 10�3 506 4992 30 2.357 � 1012 10.242 � 10�3 512 5153 20 6.669 � 1012 10.598 � 10�3 530 5434 10 41.727 � 1012 11.179 � 10�3 564 551

Fig. 5. Relationship of predicted and actual particle size with change in pressure.

798 N.B. Dhokey et al. / Advanced Powder Technology 25 (2014) 795–800

some parameters such as density of melt, density of water, super-heat temperature of melt, heat of fusion of melt, heat capacity ofmelt, and length of interaction are not included to predict the par-ticle size. Experimental results are applied to Bergquist [11] modeland particle size predicted using Bergquist [11] model comparedwith predicted particle size obtained using proposed mathematicalmodel, it shows in Table 5 that percentage true error is more forBergquist [11] model than that for proposed model .Hence superi-ority of the proposed mathematical model is more than the previ-ously proposed model with nine parameters.

4.2. Variation of apex angle on prediction of particle size

The apex angle (a) is expressed in terms of the length of inter-action (L) by Eq. (4). It may be possible to predict particle size byvarying apex angle for the range of 30–60� at particular water pres-sure (40 psi) using the constant U = 0.0043 and A = 0.0305 of DPSMas determined experimentally and given in Eq. (6). It may be pos-sible to predict the particle size using Eq. (8) and those are men-tioned in the Table 6. Obviously Eq. (8) as plotted in Fig. 6 showsthat predicted powder particle size (DP) estimated at constantwater pressure (40 psi) is inversely proportional to the apex angle(a). It means that finer particle size is obtained for larger apex an-gle. However it is seen that apex angle cannot be increased beyond60�, because of possibility of freezing of liquid metal at end of noz-zle tip [1,2].

Table 5Comparison of predicted particle size obtained from Bergquist [11] model and proposed m

Pressure(psi)

Pressure(Pa)

Water flowrate (m3/s)

Actual particlesize (lm) (A)

Particle size by Proposedmathematical model (lm

40 275790.28 2.50 � 10�04 499 50630 206842.71 2.30 � 10�04 515 51220 137895.14 1.92 � 10�04 543 53010 68947.57 1.40 � 10�04 551 564

* Bergquist et al. [11] model d ¼ k c0:8M lM

P0:8W sin a

mWmM

� ��0:043.

Dp ¼ 4:2954� 10�3½X�0:0305 � L� Htana

ð8Þ

Particle size is influenced by the apex angle between the axis ofthe water jet nozzle and the liquid metal stream. As apex angle in-creases the horizontal velocity component normal to the metalstream increases. Maximum kinetic energy of water jet is impartedto melt stream with high rate of transfer of momentum which re-sults in the shearing action of melt stream gives fine size particle.This similar observation is noted in elsewhere [1]. Fig. 6 shows thatparticle size decreases with increasing apex angle.

4.3. Combined effect of pressure and apex angle on prediction ofparticle size

Using the constants of the model (U = 4.2954 � 10�3,A = 0.0305), a mathematical model relationship representing inter-action between pressure and apex angle can be elaborated in thefollowing manner. Using DPSM given by Eq. (6) and their corre-sponding characteristics constants, it is possible to predict the par-ticle size from Eq. (6) by theoretically varying pressure and apex

athematical model.

) (B)Percentage true

error (%) ðA�BÞA � 100

Particle size by Bergquist[11] model (lm) (C)

Percentage true

error (%) ðA�CÞA � 100

�1.4028056 317 36.472940.5825242 422 18.058252.3941068 633 �16.57458�2.3593466 1264 �129.4010

Fig. 7. 3D plot showing combined effect of pressure and apex angle on predictedparticle size.

Fig. 8. Contour plot drawn from 3D plot showing iso-particle size lines influencedby the apex angle and water pressure in which experimentally obtained actualparticle size is superimposed.

Table 7Effect of varying pressure and apex angle on predicted particle size.

Exp. No. a P (psi) X Y DP (lm)

1 30� 10 7.27x1016 14.03 � 10�3 121615 4.15 � 1016 13.80 � 10�3 119520 2.34 � 1016 13.56 � 10�3 117425 1.35 � 1016 13.33 � 10�3 115530 7.95 � 1015 13.12 � 10�3 113635 4.84 � 1015 12.92 � 10�3 111940 3.03 � 1015 12.74 � 10�3 1103

2 35� 10 5.92 � 1015 13 � 10�3 92915 3.38 � 1015 12.78 � 10�3 91320 1.90 � 1015 12.56 � 10�3 89725 1.09 � 1015 12.35 � 10�3 88230 6.48 � 1014 12.15 � 10�3 86835 3.94 � 1014 11.97 � 10�3 85540 2.47 � 1014 11.80 � 10�3 843

3 40� 10 5.63 � 1014 12.10 � 10�3 72215 3.22 � 1014 11.89 � 10�3 70920 1.82 � 1014 11.69 � 10�3 69725 1.04 � 1014 11.49 � 10�3 68530 6.16 � 1013 11.31 � 10�3 67435 3.75 � 1013 11.14 � 10�3 66440 2.35 � 1013 10.98 � 10�3 655

4 45� 10 5.76 � 1013 11.29 � 10�3 56415 3.29 � 1013 11.09 � 10�3 55420 1.85 � 1013 10.90 � 10�3 54525 1.07 � 1013 10.72 � 10�3 53630 6.29 � 1012 10.55 � 10�3 52835 3.83 � 1012 10.39 � 10�3 52040 2.39 � 1012 10.24 � 10�3 512

5 50� 10 5.88 � 1012 10.53 � 10�3 44215 3.36 � 1012 10.35 � 10�3 43420 1.89 � 1012 10.17 � 10�3 42725 1.09 � 1012 10.03 � 10�3 42030 6.44 � 1011 9.84 � 10�3 41235 3.92 � 1011 9.69 � 10�3 40740 2.45 � 1011 9.55 � 10�3 401

6 55� 10 5.59 � 1011 9.80 � 10�3 34315 3.19 � 1011 9.63 � 10�3 33720 1.80 � 1011 9.46 � 10�3 33225 1.03 � 1011 9.31 � 10�3 32630 6.13 � 1010 9.16 � 10�3 32135 3.73 � 1010 9.02 � 10�3 31640 2.33 � 1010 8.89 � 10�3 312

7 60� 10 4.56 � 1010 9.08 � 10�3 26215 2.60 � 1010 8.92 � 10�3 25820 1.46 � 1010 8.77 � 10�3 25325 8.43 � 109 8.62 � 10�3 24930 4.98 � 109 8.42 � 10�3 24535 3.03 � 109 8.36 � 10�3 24140 1.90 � 109 8.24 � 10�3 238

N.B. Dhokey et al. / Advanced Powder Technology 25 (2014) 795–800 799

angle as given in Table 7. Then these data is plotted to get 3D sur-face response (Fig. 7) and 2D contour (Fig. 8). The actual particlesize obtained from experimentation as indicated in Table 3 issuperimposed for the fix apex angle 45� of the nozzle system inthe 2D contour map gives results in close agreement to the pre-dicted particle size range 500–600 lm and thus it validates themodel. This clearly indicates that the apex angle has profoundinfluence on the particle size.

5. Conclusions

A dimensionless particle size model (DPSM) has been obtained.The constants derived from this model can be conveniently used topredict particle size relationship with selected parameters such aspressure and apex angle. The following conclusions can be drawn:

1. A mathematical model for relationship between particle sizeand twelve parameters is proposed. It gives rise to characteris-tics constants for the given set of conditions employed.

2. A relationship between actual particle size and predicted parti-cle size is in close agreement with R2 value of 0.95.

3. From the analysis of model, it is found that the predicted parti-cle follows inverse relationship with water pressure and apexangle if varied independently.

4. Percentage true error is more for Bergquist [11] model than thatfor proposed mathematical model as part of the present work.

5. 2D contour obtained as a result of combined effect of apex angleand pressure is in close agreement when actual size of the par-ticles is superimposed on the 2D map for the fixed apexangle.

Appendix A

A.1. Derivation of dimensionless particle size model (DPSM)

D ¼ f ðP;Q w;Qm;qw;qm;qp; Tmp; Tsuperheat;gm;hf ;Cp; LÞ ðA:1Þ

f1ðD; P;Qw;Q m;qw;qm;qp; Tmp; Tsuperheat;gm; hf ;Cp; LÞ ¼ 0

Table B1Thermophysical properties of solidifying copper [14].

Sr.no.

Properties Symbols Value

1 Superheat temperature of melt Tsuperheat 1500 (K)2 Melting point of copper Tmp 1356 (K)3 Heat of fusion for copper ½DHf �Tmp

205 (J/kg)

4 Density of solid spherical particle qp 8993 (kg/m3)5 Density of liquid spherical particle qm 8001 (kg/m3)6 Heat capacity of solid spherical particle Cps 385 (J/kg K)7 Heat capacity of liquid spherical particle Cpl 480 (J/kg K)8 Thermal conductivity of copper particle Kd 401 (W/m k)9 Length of interaction L 0.05 (m)

10 Flow rate of melt Qm 7.832 � 10�6

m3/s12 Density of water qw 1000 (kg/m3)14 Viscosity of melt gm 4.0025 (N s/m2)17 Kinematic viscosity of fluid medium m 16.41 � 10�6

(m2/s)18 Thermal conductivity of fluid medium K 24.6 � 10�3

(W/m k)19 Apex angle a 45�20 Coefficient of heat transfer by convection hd 966.819 W/m2 K21 Heat content in copper melt when

superheatedDH 461.770 kJ/kg

800 N.B. Dhokey et al. / Advanced Powder Technology 25 (2014) 795–800

Total no. of variables n = 13.Total no. of fundamental dimensions m = 4.No. of dimensionless p terms = n �m = 13 � 4 = 9.Repeating variables (1) length of interaction (L), (2) flow rate ofwater (Qw), (3) density of melt (qm), (4) superheat temperatureof melt (Tsuperheat).

f1ðp1;p2;p3;p4;p5;p6;p7;p8;p9Þ ¼ 0

p1 – Term can be calculated as follows:

p1 ¼ LaQ bwqc

mTdsuperheatD ðA:2Þ

½M0L0T0h0� ¼ ½M0L1T0h0�a½M0L3T�1h0�b½M0L�3T0h0�c½M0L0T0h1�d

½M0L1T0h0�

For M; c ¼ 0

ForL; aþ 3b� 3c þ 1 ¼ 0 a ¼ �1

ForT; �b ¼ 0

Forh; d ¼ 0

p1 ¼ L�1Q0wq0

mT0superheatD

p1 ¼DL

ðA:3Þ

Similarly,

p2 ¼L4P

Q 2wqm

; p3 ¼Q m

Qw; p4 ¼

qw

qm; p5 ¼

qp

qm;

p6 ¼Tmp

Tsuperheat; p7 ¼

Lgm

Qwqm; p8 ¼

L4hf

Q2w

; p9 ¼L4CPTsuperheat

Q2w

f1DL;

L4P

Q 2wqm

;Q m

Q w;qw

qm;qp

qm;

Tmp

Tsuperheat;

Lgm

Qwqm;L4hf

Q 2w

;L4CPTsuperheat

Q 2w

!¼ 0

DL¼ ; L4P

Q 2wqm

;Qm

Q w;qw

qm;qp

qm;

Tmp

Tsuperheat;

Lgm

Q wqm;L4hf

Q2w

;L4CPTsuperheat

Q2w

!

DL¼ ; L4P

Q2wqm

� Qm

Qw� qw

qm�

qp

qm� Tmp

Tsuperheat� Lgm

Qwqm� L4hf

Q2w

� L4CPTsuperheat

Q2w

" #A

DL¼ ;

L13 � Qm � qw � qp � Tmp � gm � hf � Cp

q4m

� p

Q8w

" #A

ðA:4Þ

Appendix B

See Table B1.

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