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Electro hydrodynamic atomization in the cone-jet mode. A physical model of the liquid cone and jet.
Vol. 28, Suppl. I, pp. $527-$528, 1997 ©1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain PII:S0021-8502(97)00312-1 0021-8502/97 $17.1)0+0.00 J. Aerosol Sci.
Pergamon
ELECTRO HYDRODYNAMIC ATOMIZATION IN THE CONE-JET MODE. A PHYSICAL MODEL OF THE LIQUID CONE AND JET.
R.P.A. Hartman, J.C.M. Marijnissen, and B. Scarlett Delft University of Teclmology, Department of Chemical Fnginccring and Material science, Particle Technology Group, Julianalaan 136, 2628 BI., Delft, The Nclhcrlands.
KEYWORDS Electro Hydrodynamic Atomization; Cone Shape; Jet Shape; Current; Physical Model; ConeJet Mode; Electro Spray; Surface Charge; Electric Field Strength; Liquid Velocity Profile; If a liquid droplet is brought into a strong electric field, then this electric field induces a free charge and an electric stress in the liquid surface. This stress transforms the droplet shape into a conical shape. At the cone apex a liquid jet with a high charge density occurs. This jet breaks up into highly charged main droplets with a ,aarrow size distribution, and smaller satellite droplets. The produced droplet size mainly depends on the liquid flow rate Q and the liquid properties: density p, viscosity p, conductivity K, dielectric constant % and surface energy y. A physical numerical model has been developed to investigate the influence of these parameters on the cone shape, droplet size and droplet charge. The model calculates the current flowing through the cone, the surface charge, the electric fields inside and outside the cone, the cone shape, and the shape of the liquid jet that occurs at the cone apex. The shape of the liquid cone is calculated by solving the Navier-Stokes equation in one dimension, for a steady state situation. Ou. dr+ z
tj,.~g
dz
dr ~ 2(--~zS) -1
c3~t...+
P= dr 2 P Oz (_....Ldz) +1
__dV
3p---cgz dz +Eto) dr )2
1 +(
Y dz2
y dr
r+ ( 1+( ~
_ 2( r
X
2 i ) )5
1 (E2o_2e r E2+E2 &. 2 3 2 % • . $ ( I+(~) )5
~)
.
Where, p,z,q uz,Cp, O, are pressure, the axial coordinate for the cylindrical coordinate system, the radial distance of the liquid-air interface from the axis, the liquid velocity in the axial direction, a correction factor for the radial velocity profile inside the liquid, and surface charge. En, i , Ep, o, E t are the electric fields normal and tangential to the liquid-air surface, inside and outside the liquid. To be able to solve these equations, the electric field strengths, the surface charge and the radial velocity profile inside the liquid have to be known. Ira certain cone shape is assumed then the electric fields inside and outside the liquid are numerically calculated using Gauss' law. The surface charge follows then from the current c~( ,' it.,. o ) _ K r 1~, (1 + ( -ar, - ) 2 )~ balance at the liquid-air interface and fi'om ~2 " " dz the estimation of the liquid velocity at the liquid-air interface. 1
1 d du d(2PUz2) la 7-~_.(r-~__z) F O'F UF dz
p
du..~
-
- F, o +
dr
dr.,.
r :
$527
2
P u:(--d-if)
2(drs)2
-~-z-
- 4
_ d2r i1 It z s
drs 2
dz 2
1 + (-~z)
$528
Abstracts of the 1997 European Aerosol Conference
The one dimensional Navier-Stokes equation is then used to calculate a new cone-shape which is used as input for new electric field, and surface charge calculations. This process is repeated until input cone shape and output cone shape have converged. Currents were measured for ethylene glycol technical grade, and ethylene glycol chemical grade 99% purity. LiCI was used to enhance the conductivity. The following liquid properties, taken from literature, were used in the model: density l l09[kg m'S], viscosity 0.02 [Pa.s], surface energy 0.048 [N m'*], Dielectric constant 37. Figure 1 shows a comparison between the measured currents coming from the liquid cone and the calculated currents. The measured currents and the calculated current and jet radius were compared to the present scaling laws as described by Gaffe.n-Calve (1994) and Fernandez 250 de la Mora (1994). This was done with respect to Teehn. Pure 761~S/ml the influence of the liquid flow rate and the • conductivity on the current and jet radius. 200 +
LiC172 h.tS/ml
•
150
l,iC1186 htS'ml
r~
Model 69 It~Wml m Model 186 I~d';,'ml
100
50 0 1 2 3 Liquid Flow Rate IE-9 [m3/s]
Figure 1
Comparison of the currents measured and calculated by the model.
I - (-) "tt'
Liquid
r.1~t-= 0"o
l~K'~lx
conductivity [p.S m "t] Eth. GI. Techn.grade 76 Eth. GI. 99% +LiCI 72 Eth. GI. 99% +LiCI 186 Model 69 Scaling Law ace am Model 1 ramJet 0.705 0.538 Model 2.3 mm Jet 0.637 0.538 Scaling Law 0.333 0.500
"j,t ~ K ' ' ~
atQ 0.490 0.492 0.479 0.490 0.500 ae¢ -0.136 -0.333
CONCLUSIONS It is possible to model the electro hydrodynamic atomization in Cone-Jet mode by means of a completely physical model without any fitting parameters. With respect to the jet radius as function of the liquid flow rate and as function of the conductivity, the results of the Cone-Shape model seem to show a different result compared to the scaling laws. Two reasons could be found. First the model calculates the jet radius where the scaling law is fitted to the droplet size. Second, this fitting is done, using a dimensionless number ¢oQ/Kr3. The model indicates that using this dimensionless number is not valid. The Cone-Shape model gives the electric field strengths, the charge density, and the cone and jet shape. This allows further investigation of electrical discharges of the surrounding air, of the jet breaking up into droplets, of the movement of droplets in the electric field after production, and of the influence of electrode configurations. It gives more insight in the phenomena itself, which makes it possible to come to better scaling laws. We like to thank NWO/SON for funding this project REFERENCES Fern~mdez de ia Mora J., Loscertales I.G. (1994) ,I. F l u i d M e c h . 260, 155-184. Gafihn-Calvo A.M., Davila J., Barrero A., (I 994) Prec. 4th Int. Aerosol Conf. LA. 1, 44-45.
Pergamon
ELECTRO HYDRODYNAMIC ATOMIZATION IN THE CONE-JET MODE. A PHYSICAL MODEL OF THE LIQUID CONE AND JET.
R.P.A. Hartman, J.C.M. Marijnissen, and B. Scarlett Delft University of Teclmology, Department of Chemical Fnginccring and Material science, Particle Technology Group, Julianalaan 136, 2628 BI., Delft, The Nclhcrlands.
KEYWORDS Electro Hydrodynamic Atomization; Cone Shape; Jet Shape; Current; Physical Model; ConeJet Mode; Electro Spray; Surface Charge; Electric Field Strength; Liquid Velocity Profile; If a liquid droplet is brought into a strong electric field, then this electric field induces a free charge and an electric stress in the liquid surface. This stress transforms the droplet shape into a conical shape. At the cone apex a liquid jet with a high charge density occurs. This jet breaks up into highly charged main droplets with a ,aarrow size distribution, and smaller satellite droplets. The produced droplet size mainly depends on the liquid flow rate Q and the liquid properties: density p, viscosity p, conductivity K, dielectric constant % and surface energy y. A physical numerical model has been developed to investigate the influence of these parameters on the cone shape, droplet size and droplet charge. The model calculates the current flowing through the cone, the surface charge, the electric fields inside and outside the cone, the cone shape, and the shape of the liquid jet that occurs at the cone apex. The shape of the liquid cone is calculated by solving the Navier-Stokes equation in one dimension, for a steady state situation. Ou. dr+ z
tj,.~g
dz
dr ~ 2(--~zS) -1
c3~t...+
P= dr 2 P Oz (_....Ldz) +1
__dV
3p---cgz dz +Eto) dr )2
1 +(
Y dz2
y dr
r+ ( 1+( ~
_ 2( r
X
2 i ) )5
1 (E2o_2e r E2+E2 &. 2 3 2 % • . $ ( I+(~) )5
~)
.
Where, p,z,q uz,Cp, O, are pressure, the axial coordinate for the cylindrical coordinate system, the radial distance of the liquid-air interface from the axis, the liquid velocity in the axial direction, a correction factor for the radial velocity profile inside the liquid, and surface charge. En, i , Ep, o, E t are the electric fields normal and tangential to the liquid-air surface, inside and outside the liquid. To be able to solve these equations, the electric field strengths, the surface charge and the radial velocity profile inside the liquid have to be known. Ira certain cone shape is assumed then the electric fields inside and outside the liquid are numerically calculated using Gauss' law. The surface charge follows then from the current c~( ,' it.,. o ) _ K r 1~, (1 + ( -ar, - ) 2 )~ balance at the liquid-air interface and fi'om ~2 " " dz the estimation of the liquid velocity at the liquid-air interface. 1
1 d du d(2PUz2) la 7-~_.(r-~__z) F O'F UF dz
p
du..~
-
- F, o +
dr
dr.,.
r :
$527
2
P u:(--d-if)
2(drs)2
-~-z-
- 4
_ d2r i1 It z s
drs 2
dz 2
1 + (-~z)
$528
Abstracts of the 1997 European Aerosol Conference
The one dimensional Navier-Stokes equation is then used to calculate a new cone-shape which is used as input for new electric field, and surface charge calculations. This process is repeated until input cone shape and output cone shape have converged. Currents were measured for ethylene glycol technical grade, and ethylene glycol chemical grade 99% purity. LiCI was used to enhance the conductivity. The following liquid properties, taken from literature, were used in the model: density l l09[kg m'S], viscosity 0.02 [Pa.s], surface energy 0.048 [N m'*], Dielectric constant 37. Figure 1 shows a comparison between the measured currents coming from the liquid cone and the calculated currents. The measured currents and the calculated current and jet radius were compared to the present scaling laws as described by Gaffe.n-Calve (1994) and Fernandez 250 de la Mora (1994). This was done with respect to Teehn. Pure 761~S/ml the influence of the liquid flow rate and the • conductivity on the current and jet radius. 200 +
LiC172 h.tS/ml
•
150
l,iC1186 htS'ml
r~
Model 69 It~Wml m Model 186 I~d';,'ml
100
50 0 1 2 3 Liquid Flow Rate IE-9 [m3/s]
Figure 1
Comparison of the currents measured and calculated by the model.
I - (-) "tt'
Liquid
r.1~t-= 0"o
l~K'~lx
conductivity [p.S m "t] Eth. GI. Techn.grade 76 Eth. GI. 99% +LiCI 72 Eth. GI. 99% +LiCI 186 Model 69 Scaling Law ace am Model 1 ramJet 0.705 0.538 Model 2.3 mm Jet 0.637 0.538 Scaling Law 0.333 0.500
"j,t ~ K ' ' ~
atQ 0.490 0.492 0.479 0.490 0.500 ae¢ -0.136 -0.333
CONCLUSIONS It is possible to model the electro hydrodynamic atomization in Cone-Jet mode by means of a completely physical model without any fitting parameters. With respect to the jet radius as function of the liquid flow rate and as function of the conductivity, the results of the Cone-Shape model seem to show a different result compared to the scaling laws. Two reasons could be found. First the model calculates the jet radius where the scaling law is fitted to the droplet size. Second, this fitting is done, using a dimensionless number ¢oQ/Kr3. The model indicates that using this dimensionless number is not valid. The Cone-Shape model gives the electric field strengths, the charge density, and the cone and jet shape. This allows further investigation of electrical discharges of the surrounding air, of the jet breaking up into droplets, of the movement of droplets in the electric field after production, and of the influence of electrode configurations. It gives more insight in the phenomena itself, which makes it possible to come to better scaling laws. We like to thank NWO/SON for funding this project REFERENCES Fern~mdez de ia Mora J., Loscertales I.G. (1994) ,I. F l u i d M e c h . 260, 155-184. Gafihn-Calvo A.M., Davila J., Barrero A., (I 994) Prec. 4th Int. Aerosol Conf. LA. 1, 44-45.