Proceedings of the 22nd
National and 11th
International
ISHMT-ASME Heat and Mass Transfer Conference
December 28-31, 2013,...
Rayleigh–Taylor instability on the edges of the spreading
liquid film. Liu et al. [3] numerically studied the impact of a
...
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d
ll
lslsl gg
g
fffgg ρρρ
ρ
ρ
)1(,,1,1 −+===+=+
aird FF ρρρ )1( −+= ,
airdeff cFcFc )1( −+=
airdeff kFkFk )1( −+= wi...
Figure 2. SPREADING PATTERN OF CONTINUOUS
DROPLET DURING THE IMPACT PROCESS (SHOWN BY
CONTOUR OF VOF FOR LIQUID PHASE)
t =...
Figure 6. SPREADING PATTERN OF HOLLOW DROPLET
DURING THE IMPACT PROCESS (SHOWN BY CONTOUR
OF VOF FOR LIQUID PHASE)
t = 0.2...
6 for spreading, solidification, velocity and temperature at
different time.
From the velocity contour shown in Figure 7c ...
6 for spreading, solidification, velocity and temperature at
different time.
From the velocity contour shown in Figure 7c ...
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Splashing mechanism during impact of a hollow droplet on a substrate(156)doc

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Splashing mechanism during impact of a hollow droplet on a substrate(156)doc

  1. 1. Proceedings of the 22nd National and 11th International ISHMT-ASME Heat and Mass Transfer Conference December 28-31, 2013, IIT Kharagpur, India HMTC1300290 SPLASHING MECHANISM DURING IMPACT OF CONTINUOUS AND HOLLOW DROPLETS ON A SUBSTRATE Rajesh Kumar Shukla Indian institute of Technology Kanpur Kanpur, Uttar Pradesh, 208016 India shuklark@iitk.ac.in Arvind Kumar Indian Institute of Technology Kanpur Kanpur, Uttar Pradesh, 208016 India arvindkr@iitk.ac.in ABSTRACT In a thermal spray coating process the quality of the coating depends on the impingement process of the feedstock particles on the substrate in which the individual molten particles flatten and solidify on the substrate forming the individual splat. It has been reported that improved quality of coating can be obtained using hollow particles in comparison to the conventional continuous particles. In this paper the splashing behaviour of continuous and hollow molten droplet during its impact on a substrate has been numerically investigated and compared. The spherical hollow droplet used in this study consists of a liquid shell enclosing a gas (air) cavity immediately prior to droplet-substrate collision. Volume of fluid surface tracking method (VOF) coupled with the solidification model within a one-domain continuum formulation is used to model the transient flow during the droplet impact, subsequent spreading and solidification. The results show that splashing reduces significantly while using the hollow droplets. On the other hand, an analogous conventional continuous droplet shows significant splashing. We highlight that how a new phenomenon, formation of counter liquid jetting, with the hollow droplets is responsible for less splashing. NOMENCLATURE c Specific heat capacity C Constant related to Darcy source term D0 Initial droplet diameter d0 Initial void diameter fl Weight fraction of liquid fs Weight fraction of solid F Volume of fluid function Fvol Continuum surface tension force g  Acceleration due to gravity vector gl Volume fraction of liquid gs Volume fraction of solid k Thermal conductivity L Latent heat of fusion T Time T Temperature U0 Droplet's initial impact velocity u  Continuum velocity vector Greek symbols μ Dynamic viscosity ρ Density Subscript d Droplet subs Substrate air Air eff Effective l Liquid 0 Initial s Solid INTRODUCTION In a thermal spray coating process molten particles are projected towards the substrate where they flatten and solidify on the substrate forming the coating layer. However, splashing (break up into smaller satellite droplets known as impact splashing, and break up during flattening known as spreading splashing or fingering) occurs when molten droplets impact with high velocity on a solid substrate. Droplet splashing is undesirable since it reduces the deposition efficiency (the fraction of sprayed material which adheres to the surface) of the process. It not only results in wastage of material but also create environmental pollution and reduces the strength of the coating. Due to its practical importance many studies have been devoted to investigate the mechanism behind splashing of molten metal droplet just after the impact to solid surface. Fukumoto and Huang [1] observed that freezing along the bottom of an impinging droplet causes splashing: liquid flowing on top of the solid layer jets off and splashes. Delaying solidification, either by raising surface temperature or increasing thermal contact resistance at the droplet– substrate interface, is expected to suppress splashing. Allen [2] first put forward the hypothesis that splashing is caused by
  2. 2. Rayleigh–Taylor instability on the edges of the spreading liquid film. Liu et al. [3] numerically studied the impact of a droplet onto substrates with wavy surfaces; however, their two-dimensional axi-symmetric model did not include solidification. They found that for wavelengths of the surface larger than the droplet diameter, droplet spreading ended with break up. Bussman et al. [4] used a three-dimensional computational fluid dynamics code to model droplet impact and splashing. They initiated the growth of fingers in their simulations by introducing a sinusoidal perturbation into the velocity field immediately after impact. They speculated that in reality protrusions on the surface disturb liquid flow, with the amplitude of the perturbation proportional to the magnitude of surface roughness. Ahmed and Rangel [5] numerically studied the impingement and solidification of an aluminum droplet on uneven substrates, using a two- dimensional axi-symmetric model. Their results show that droplet impact onto an uneven substrate is almost always accompanied by splashing. However, the degree of splashing decreases with the increase in surface roughness height. Recently Mandre and Brenner [6] suggested that one possible mechanism of splashing just after the impact of droplet on a wall is due to the ejection of a liquid sheet launched into air immediately after contact. The overall mechanism occurs through two steps, first step involves the ejection of a thin liquid sheet before the droplet touches the surface, and the second stage of splashing requires this sheet to be deflected away from the solid surface. Lei et al. [7], observed that splashing can be suppressed by decreasing the pressure of the surrounding gas. It is worth to point out that most of the studies reported for splashing mechanism during droplet impact assume continuous shape of the droplets without any voids inside. New possibilities for thermal spraying of functional coatings formed by deposition of hollow melt droplets are discussed in the work by Solonenko et al. [8, 9]. The limited studies reported in this field suggest that the resulting coating from hollow melt droplets have improved coating characteristics as compared to the conventional continuous droplets. Recently, Kumar et al. [10, 11] reported that the impact of a hollow droplet onto the substrate and its spreading behaviour differ from an analogous continuous droplet. Likewise, the splashing behaviour of continuous and hollow droplets can also be different. The objective of this study is to discuss the fundamental difference between splashing mechanism of continuous and hollow droplets. The impact, flattening and solidification behaviour of the two droplets onto a solid substrate are numerically studied. We discuss how the flattening and solidification patterns in the two droplets govern the splashing mechanism. MODEL AND GOVERNING EQUATIONS We simulate the high velocity impact of ZrO2 droplet onto a solid surface with conditions typically found in a real thermal spray coating process. We consider two-dimensional axi-symmetric formulation (Figure 1), based on a previously validated model of Kamnis and Gu [12] for a continuous droplet. The impact of a spherical hollow droplet and an analogous (same mass) spherical continuous droplet is considered. The hollow droplet consists of a liquid shell enclosing a gas (air) cavity immediately prior to droplet- substrate collision (Fig. 1). The impact conditions are: the droplets at an initial uniform temperature of 2970 K impinge with a velocity U0 (150 m/s) onto the substrate kept at an initial temperature of 300 K. The thermophysical property data used in the simulations are shown in Table 1 [10]. The model used in the current study has been discussed in detail elsewhere [10]. Therefore, here we would only mention specific features of the model. In the droplet impingement model transient fluid flow dynamics during the impact, droplet spreading onto the substrate and solidification heat transfer are considered using the volume of fluid surface tracking method (VOF) coupled with a solidification model within a one-domain continuum approach based on the classical mixture theory [10-12]. For computational cells which are undergoing phase change (solidification), the solid-liquid interaction in the momentum conservation (Eq. 4) is considered using Darcy's model of viscous flow through a porous medium using the source term Su (Eq. 5) [12]. Momentum conservation equation (Eq. 4) also accounts for surface tension effects at the free surface, which is considered by a continuum surface force model [11]. The momentum and the energy conservation equations (Eqs. 4 and 6) are coupled. The source term Sh (Eq. 7), for handling the solidification phase change, appearing in the energy conservation (Eq. 6) is active only for the computational cells filled with molten droplet (F = 1). In the substrate only the conduction heat transfer is solved (Eq. 9). For the substrate thermal contact resistance a constant value of 1.8×10-6 m2 KW- 1 , corresponding to a stainless steel substrate roughness of 0.06 μm, is used [11]. VOF equation: 0=⋅∇+ ∂ ∂ Fu t F  (1) Mixture quantities definitions for a cell in the mushy state: Void (air) cavity Symmetry axis Atmosphere(air) g D0 = 50 µm, d0 = 25 µm U0 = 150 m/s Hollow droplet Substrate Symmetry axis Atmosphere(air) g D = 0.956.D0 U0 = 150 m/s Continuousdroplet Substrate (a) (b) Figure 1. SCHEMATIC OF (a) CONTINUOUS AND (b) HOLLOW DROPLET IMPACT ON A SUBSTRATE
  3. 3. sllld d ll lslsl gg g fffgg ρρρ ρ ρ )1(,,1,1 −+===+=+ aird FF ρρρ )1( −+= , airdeff cFcFc )1( −+= airdeff kFkFk )1( −+= with sllld kgkgk )1( −+= (2) Table 1. MATERIAL PROPERTIES DATA Material properties Values Impinging droplet material Zirconia (ZrO2) Substrate material Stainless steel (SS) Gas phase (the void and the droplet surrounding medium) Air (air) Droplet initial temperature 2970 K Substrate initial temperature 652 K Solidus temperature (ZrO2) 2949 K Liquidus temperature (ZrO2) 2951 K Thermal conductivity (liquid ZrO2) 2.00 W ∙ m-1 / K Thermal conductivity (solid ZrO2) 2.32 W ∙ m-1 / K Thermal conductivity (SS) 14.9 W ∙ m-1 / K Thermal conductivity (air) 0.0242 W ∙ m-1 / K Density (liquid ZrO2) 5700 kg/m3 Density (solid ZrO2) 5700 kg/m3 Density (SS) 7900 kg/m3 Density (air) 1.225 kg/m3 Droplet surface tension 0.43 N/m Contact angle 100° Viscosity (liquid ZrO2) 0.021 kg ∙ m-1 /s Viscosity (air) 1.7894×10-5 kg ∙ m-1 /s Specific heat capacity (solid and liquid ZrO2) 713 J ∙ kg-1 / K Specific heat capacity (SS) 477 J ∙ kg-1 / K Specific heat capacity (air) 1006.43 J ∙ kg-1 / K Latent heat of fusion 7.07x105 J/kg Continuity: 0)()( =⋅∇+ ∂ ∂ u t  ρρ (3) Momentum conservation: (4) 2 3 (1 ) 1 0 1 l l g C u F Su g F   − =  =     <   (5) Energy conservation: heffeffeff STkTcuTc t +∇⋅∇=⋅∇+ ∂ ∂ )()()(  ρρ (6)        < =      ∇+ ∂ ∂ − = 10 1).()( F Ffuf t L S ll h  ρρ (7) liquidussolidus liquidus solidus l liquidusl solidusl TTTif TT TT f TTiff TTiff << − − = ≥= ≤= 1 0 (8) Substrate heat transfer: )()( TkTc t subssubssubs ∇⋅∇= ∂ ∂ ρ (9) RESULTS AND DISCUSSION Continuous Droplet Flattening and spreading pattern of the continuous droplet at different time is shown in Figure 2. Splashing at the advancing edge of the spreading droplet can be noticed from the very beginning. This results in break up at the edge and finally creates a discontinuous splat. For better understanding of the physical mechanism we subsequently show in Figs. 3-5 the zoomed images in the rectangular portion marked in Fig. 2 for spreading, solidification, velocity and temperature at different time. It was noticed that just after the impact during the initial stage of spreading droplet flattens with very high velocity (450 m/s). Such high velocity creates instability at the advancing edge and some small satellite droplet get detached from the main spreading droplet material [2]. These detached droplets solidify at the substrate. This tendency can be seen from the maps of VOF, solidification, velocity and temperature shown in Fig. 3. Such behaviour leads to formation of discontinuous solidified layer at the substrate. From the spreading and solidification maps shown in Figs. 3-5 at different time a thin discontinuous layer of solidified splat develop at the substrate surface. Further flattening of droplet occurs over this thin discontinuous solidified layer which lead to further instability of the advancing droplet and its break up. This tendency is refer to as flattening splashing [4]. This splashing is formed because of very high flattening velocity and formation and solidification of detached satellite droplets over the substrate during the early stage of the spreading process. The solidified detached drops crates a barrier in the path of the spreading liquid leading to further instability and splashing in the spreading droplet known as flattening splashing.
  4. 4. Figure 2. SPREADING PATTERN OF CONTINUOUS DROPLET DURING THE IMPACT PROCESS (SHOWN BY CONTOUR OF VOF FOR LIQUID PHASE) t = 0.19 µsTemperature (K) Velocity (m/s) (a) (b) (c) (d) Figure 3. ZOOMED IMAGES OF (A) SPREADING (VOF OF LIQUID PHASE) (B) SOLIDIFICATION (LIQUID FRACTION) (C) VELOCITY (MAGNITUDE) AND (D) TEMPERATURE AT 0.19 µs IN RECTANGULAR PORTION MARKED IN FIG. 1 t = 0.25 µsTemperature (K) Velocity (m/s) (a) (b) (d) (c) Figure 4. ZOOMED IMAGES OF (a) SPREADING (VOF OF LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION) (c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT 0.25 µs IN RECTANGULAR PORTION MARKED IN FIG. 1 (a) t = 0.43 µsTemperature (K) Velocity (m/s) (b) (c) (d) Figure 5. ZOOMED IMAGES OF (a) SPREADING (VOF OF LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION) (c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT 0.43 µs IN RECTANGULAR PORTION MARKED IN FIG. 1 t = 0.14 µs t = 0.19 µs t = 0.25 µs t = 0.43 µs t = 0.51 µs t = 0.83 µs t = 2.19 µs
  5. 5. Figure 6. SPREADING PATTERN OF HOLLOW DROPLET DURING THE IMPACT PROCESS (SHOWN BY CONTOUR OF VOF FOR LIQUID PHASE) t = 0.20 µs Temperature (K) Velocity (m/s) (a) (c) (d) (b) Figure 7. ZOOMED IMAGES OF (a) SPREADING (VOF OF LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION) (c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT 0.20 µs IN RECTANGULAR PORTION MARKED IN FIG. 6 t = 0.35 µsTemperature (K) Velocity (m/s) (a) (b) (c) (c) (d) (a) (b) FIGURE 8. ZOOMED IMAGES OF (a) SPREADING (VOF OF LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION) (c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT 0.35 µs IN RECTANGULAR PORTIONS MARKED IN FIG. 6 t = 0.55 µsTemperature (K) Velocity (m/s) (a) (b) (c) (d) (c) Figure 9. ZOOMED IMAGES OF (a) SPREADING (VOF OF LIQUID PHASE) (b) SOLIDIFICATION (LIQUID FRACTION) (c) VELOCITY (MAGNITUDE) AND (d) TEMPERATURE AT 0.55 µs IN RECTANGULAR PORTIONS MARKED IN FIG. 6 Hollow Droplet Flattening and spreading pattern of the hollow droplet at different time is shown in Figure 6. Unlike the continuous droplet no splashing at the advancing edge of the spreading droplet is noticed at the beginning of the Further, a final continuous splat is observed [10]. However, in contrast to the continuous droplet a new phenomenon of counter liquid jetting can be clearly seen in this case. This formation of phenomenon is reported in [10]. Because of the formation of the upward moving counter jet large mass of liquid goes into this jet and only some mass of liquid is horizontally spreading along the substrate. This reduces the inertia of the horizontally spreading liquid and hence its flattening velocity. For better understanding of the physical mechanism we show in Figs. 7- 9 the zoomed images in the rectangular portion marked in Fig. t = 0.06 µs t = 0.12 µs t = 0.20 µs t = 0.23 µs t = 0.35 µs t = 0.55 µs t = 0.91 µs
  6. 6. 6 for spreading, solidification, velocity and temperature at different time. From the velocity contour shown in Figure 7c we can observe that the velocity of the advancing liquid during the initial spreading stage in the case of hollow droplet is very less (250 m/s) in comparison to that in the continuous droplet. Comparing Figs. 3-5 and Figs. 7-9 we can notice the same tendency in the magnitude of the advancing velocity. The lower advancing velocity reduces the instability at the advancing front and hence any formation of initial detached drops. The further spreading of the hollow droplet material does not experience any barrier, as observed for continuous droplet. This causes smooth flattening of the droplet along the substrate without any instability. We can clearly see in Figs. 7-9 that the solidification layer along the substrate is smooth and continuous (no break up) and the advancing velocity is also much lower. Since a 2D approach is used in the current study, more detailed 3D simulations and some quantitative comparison with the experiments on the hollow droplets are needed in order to develop further insights of the splashing phenomenon. Our future work will undertake a 3D simulation of hollow droplet impact. CONCLUSIONS This study contributes to the development of new techniques to increase the material deposition efficiency during thermal spray coating process. In the spraying using hollow particles it is likely that the impacting droplets will less break up after the impact, and hence splashing can be reduced which will enhance the efficiency. We studied the splashing behaviour of continuous and hollow droplets during their impact onto a solid substrate. The main conclusions are: • A new phenomenon, formation of counter liquid jetting, leads to less splashing in case of the hollow droplets. On the other hand, flattening mainly governed by inertia in case of the continuous droplet leads to significant splashing. • Continuous splats (no break up) obtained in case of the hollow droplet with absence of any flattening splashing imply improved efficiency and good bonding of the coating with the substrate. In this way, coating of precious metal using hollow particles can be a better substitute for dense particles. REFERENCES [1] Fukumoto, M., and Huang, Y., 1999. “Flattening Mechanism in Thermal Sprayed Ni Particles Impinging on Flat Substrate Surface”. Journal of Thermal Spray Technology, 8(3), pp. 427–432 [2] Allen, R.F., 1988. “The Mechanics of Splashing”. Journal of Colloid and Interface Science , 124(1), pp. 309–316. [3] Liu, H., Lavernia, E.J., and Rangel, R.H., 1995. “Modeling of Molten Droplet Impingement on a Non- Flat Surface”. Acta Metallurgica et Materialia, 43(5), pp-2053–2072. [4] Bussmann, M., Chandra, S., and Mostaghimi, J., 2000. “Modeling the Splash of a Droplet Impacting a Solid Surface”. Physics of Fluids, 12, pp. 3121–3132. [5] Ahmed, A.M., and Rangel, R.H., 2002. “Metal Droplet Deposition on Non-flat Surfaces: Effect of Substrate Morphology”. International Journal of Heat and Mass Transfer, 45, pp. 1077–1091. [6] Mandre, S., and Brenner, M.P., 2012. “The Mechanism of a Splash on a Dry Solid Surface”. Journal of Fluid Mechanics, 690, 148–172. [7] Xu, L., Zhang, W.W., and Nagel, S. R., 2005. “Drop Splashing on a Dry Smooth Surface”. Physical Review Letters, 94(18), pp. 505–516. [8] Solonenko, O.P., Smirnov, A.V., and Gulyaev, I.P., 2008. “Spreading and Solidification of Hollow Molten Droplet under its Impact onto Substrate: Computer Simulation and Experiment” in Tokuyama, M., Oppenheim, I., Nishiyama, H. (Eds.), AIP Conference Proceedings, Vol. 982. pp. 561–568. [9] Solonenko, O.P., Gulyaev, I.P., and Smirnov, and A.V., 2008. “Plasma Processing and Deposition of Powdered Metal Oxides consisting of Hollow Spherical Particles”. Technical Physics Letters, 34, pp. 1050–1052 [10] Kumar, A., Gu, S., Tabbara, H., and Kamnis, S., 2012. “Study of Impingement of Hollow ZrO2 Droplets onto a Substrate”. Surface and Coatings Technology, 220, pp. 164–169. [11]Kumar, A., Gu, S. and Kamnis, S., 2012. “Simulation of Impact of a Hollow Droplet on a Flat Surface”. Applied Physics A: Materials Science & Processing, 109, pp. 101–109. [12] Kamnis, S., and Gu, S., 2005. “Numerical Modelling of Droplet Impingement”. Journal of Physics D: Applied Physics, 38, pp. 3664–3673.
  7. 7. 6 for spreading, solidification, velocity and temperature at different time. From the velocity contour shown in Figure 7c we can observe that the velocity of the advancing liquid during the initial spreading stage in the case of hollow droplet is very less (250 m/s) in comparison to that in the continuous droplet. Comparing Figs. 3-5 and Figs. 7-9 we can notice the same tendency in the magnitude of the advancing velocity. The lower advancing velocity reduces the instability at the advancing front and hence any formation of initial detached drops. The further spreading of the hollow droplet material does not experience any barrier, as observed for continuous droplet. This causes smooth flattening of the droplet along the substrate without any instability. We can clearly see in Figs. 7-9 that the solidification layer along the substrate is smooth and continuous (no break up) and the advancing velocity is also much lower. Since a 2D approach is used in the current study, more detailed 3D simulations and some quantitative comparison with the experiments on the hollow droplets are needed in order to develop further insights of the splashing phenomenon. Our future work will undertake a 3D simulation of hollow droplet impact. CONCLUSIONS This study contributes to the development of new techniques to increase the material deposition efficiency during thermal spray coating process. In the spraying using hollow particles it is likely that the impacting droplets will less break up after the impact, and hence splashing can be reduced which will enhance the efficiency. We studied the splashing behaviour of continuous and hollow droplets during their impact onto a solid substrate. The main conclusions are: • A new phenomenon, formation of counter liquid jetting, leads to less splashing in case of the hollow droplets. On the other hand, flattening mainly governed by inertia in case of the continuous droplet leads to significant splashing. • Continuous splats (no break up) obtained in case of the hollow droplet with absence of any flattening splashing imply improved efficiency and good bonding of the coating with the substrate. In this way, coating of precious metal using hollow particles can be a better substitute for dense particles. REFERENCES [1] Fukumoto, M., and Huang, Y., 1999. “Flattening Mechanism in Thermal Sprayed Ni Particles Impinging on Flat Substrate Surface”. Journal of Thermal Spray Technology, 8(3), pp. 427–432 [2] Allen, R.F., 1988. “The Mechanics of Splashing”. Journal of Colloid and Interface Science , 124(1), pp. 309–316. [3] Liu, H., Lavernia, E.J., and Rangel, R.H., 1995. “Modeling of Molten Droplet Impingement on a Non- Flat Surface”. Acta Metallurgica et Materialia, 43(5), pp-2053–2072. [4] Bussmann, M., Chandra, S., and Mostaghimi, J., 2000. “Modeling the Splash of a Droplet Impacting a Solid Surface”. Physics of Fluids, 12, pp. 3121–3132. [5] Ahmed, A.M., and Rangel, R.H., 2002. “Metal Droplet Deposition on Non-flat Surfaces: Effect of Substrate Morphology”. International Journal of Heat and Mass Transfer, 45, pp. 1077–1091. [6] Mandre, S., and Brenner, M.P., 2012. “The Mechanism of a Splash on a Dry Solid Surface”. Journal of Fluid Mechanics, 690, 148–172. [7] Xu, L., Zhang, W.W., and Nagel, S. R., 2005. “Drop Splashing on a Dry Smooth Surface”. Physical Review Letters, 94(18), pp. 505–516. [8] Solonenko, O.P., Smirnov, A.V., and Gulyaev, I.P., 2008. “Spreading and Solidification of Hollow Molten Droplet under its Impact onto Substrate: Computer Simulation and Experiment” in Tokuyama, M., Oppenheim, I., Nishiyama, H. (Eds.), AIP Conference Proceedings, Vol. 982. pp. 561–568. [9] Solonenko, O.P., Gulyaev, I.P., and Smirnov, and A.V., 2008. “Plasma Processing and Deposition of Powdered Metal Oxides consisting of Hollow Spherical Particles”. Technical Physics Letters, 34, pp. 1050–1052 [10] Kumar, A., Gu, S., Tabbara, H., and Kamnis, S., 2012. “Study of Impingement of Hollow ZrO2 Droplets onto a Substrate”. Surface and Coatings Technology, 220, pp. 164–169. [11]Kumar, A., Gu, S. and Kamnis, S., 2012. “Simulation of Impact of a Hollow Droplet on a Flat Surface”. Applied Physics A: Materials Science & Processing, 109, pp. 101–109. [12] Kamnis, S., and Gu, S., 2005. “Numerical Modelling of Droplet Impingement”. Journal of Physics D: Applied Physics, 38, pp. 3664–3673.

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