- •Foreword
- •1. General Introduction
- •2. Processes and Techniques for Droplet Generation
- •2.1.0 Atomization of Normal Liquids
- •2.1.1 Pressure Jet Atomization
- •2.1.3 Fan Spray Atomization
- •2.1.4 Two-Fluid Atomization
- •2.1.5 Rotary Atomization
- •2.1.6 Effervescent Atomization
- •2.1.7 Electrostatic Atomization
- •2.1.8 Vibration Atomization
- •2.1.9 Whistle Atomization
- •2.1.10 Vaporization-Condensation Technique
- •2.1.11 Other Atomization Methods
- •2.2.0 Atomization of Melts
- •2.2.1 Gas Atomization
- •2.2.2 Water Atomization
- •2.2.3 Oil Atomization
- •2.2.4 Vacuum Atomization
- •2.2.5 Rotating Electrode Atomization
- •2.2.7 Electron Beam Rotating Disk Atomization
- •2.2.9 Centrifugal Shot Casting Atomization
- •2.2.10 Centrifugal Impact Atomization
- •2.2.11 Spinning Cup Atomization
- •2.2.12 Laser Spin Atomization
- •2.2.14 Vibrating Electrode Atomization
- •2.2.15 Ultrasonic Atomization
- •2.2.16 Steam Atomization
- •2.2.17 Other Atomization Methods
- •3.1.0 Droplet Formation
- •3.1.1 Droplet Formation in Atomization of Normal Liquids
- •3.1.2 Secondary Atomization
- •3.1.3 Droplet Formation in Atomization of Melts
- •3.2.0 Droplet Deformation on a Surface
- •3.2.3 Droplet Deformation and Solidification on a Cold Surface
- •3.2.4 Droplet Deformation and Evaporation on a Hot Surface
- •3.2.5 Interaction, Spreading and Splashing of Multiple Droplets on a Surface
- •3.2.6 Sessile Droplet Deformation on a Surface
- •3.2.7 Spreading and Splashing of Droplets into Shallow and Deep Pools
- •4.1.0 Concept and Definitions of Droplet Size Distribution
- •4.2.0 Correlations for Droplet Sizes of Normal Liquids
- •4.2.1 Pressure Jet Atomization
- •4.2.5 Rotary Atomization
- •4.2.6 Effervescent Atomization
- •4.2.7 Electrostatic Atomization
- •4.2.8 Ultrasonic Atomization
- •4.3.0 Correlations for Droplet Sizes of Melts
- •4.3.1 Gas Atomization
- •4.3.2 Water Atomization
- •4.3.3 Centrifugal Atomization
- •4.3.4 Solidification and Spheroidization
- •4.4.0 Correlations for Droplet Deformation Characteristics on a Surface
- •4.4.1 Viscous Dissipation Domain
- •4.4.2 Surface Tension Domain
- •4.4.3 Solidification Domain
- •4.4.4 Partial Solidification Prior to Impact
- •5.1.0 Energy Requirements and Efficiency
- •5.2.0 Modeling of Droplet Processes of Normal Liquids
- •5.2.1 Theoretical Analyses and Modeling of Liquid Jet and Sheet Breakup
- •5.2.2 Modeling of Droplet Formation, Breakup, Collision and Coalescence in Sprays
- •5.2.3 Theories and Analyses of Spray Structures and Flow Regimes
- •5.2.5 Modeling of Multiphase Flows and Heat and Mass Transfer in Sprays
- •5.3.0 Modeling of Droplet Processes of Melts
- •5.3.4 Modeling of Multiphase Flows and Heat Transfer in Sprays
- •5.4.0 Modeling of Droplet Deformation on a Surface
- •5.4.1 Modeling of Deformation of a Single Droplet on a Flat Surface
- •5.4.2 Modeling of Droplet Deformation and Solidification on a Cold Surface
- •6. Measurement Techniques for Droplet Properties and Intelligent Control of Droplet Processes
- •6.1.0 Measurement Techniques for Droplet Size
- •6.1.1 Mechanical Methods
- •6.1.2 Electrical Methods
- •6.1.3 Optical Methods
- •6.1.4 Other Methods
- •6.2.0 Measurement Techniques for Droplet Velocity
- •6.3.0 Measurement Techniques for Droplet Number Density
- •6.4.0 Measurement Techniques for Droplet Temperature
- •6.5.0 Measurement Techniques for Droplet Deformation on a Surface
- •6.6.0 Intelligent Control of Droplet Processes
- •Index
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Empirical and Analytical Correlations 295 |
Eq. (36) |
N teeth = 0.215(ρ Lω 2 d 3 /σ )0.417 ( ρ Lσd / μ L2 )0.167 |
In both the Direct Droplet and Ligament regimes, the mean droplet size is inversely proportional to the rotational speed ω and the square root of the electrode or disk diameter d:[5]
Eq. (37) |
MMD = Kω –1d –0.5 |
This approximate relationship is similar to those for centrifugal atomization of normal liquids in both Direct Droplet and Ligament regimes. However, it is uncertain how accurately the model for K developed for normal liquid atomization could be applied to the estimation of droplet sizes of liquid metals.[5] Tornberg[486] derived a semi-empirical correlation for rotating disk atomization or REP of liquid metals with the proportionality between the mean droplet size, rotational speed, and electrode or disk diameter similar to the above equation. Tornberg also presented the values of the constants in the correlation for some given operation conditions and material properties.
From these correlations, it is clear that the mean droplet size may be controlled by changing rotational speed, and/or disk diameter for a given liquid metal. In addition, the droplet size increases with increasing liquid viscosity and/or surface tension, and/or decreasing liquid density. However, the effect of liquid viscosity is inconclusive. A large disk diameter and/or a high rotational speed are required to obtain a high metal velocity and fine droplets. The technical limitations to spin a large disk at a high rotational speed along with the additional effect of viscosity make it very difficult to produce fine powders via centrifugal atomization.[486]
4.3.4Solidification and Spheroidization
In atomization of melts, the final droplet size also depends on the relative magnitude of the time tb for a droplet to undergo deformation prior to secondary breakup, and the time tsol required for
296 Science and Engineering of Droplets
cooling a superheated metal droplet to its melting temperature and for droplet solidification to complete. The latter time can be estimated using the following expression[319] for a small Biot number and negligible radiative heat transfer:
Eq. (38) |
tsol |
= |
Dρ L |
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6hc |
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where TD is the initial droplet temperature and hc is the heat transfer coefficient. Ranz-Marshall correlation[505] has been frequently used to determine the heat transfer coefficient:
Eq. (39) |
hc |
= |
kG |
(2 + 0.6 Re0.5 Pr 0.33 ) |
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D |
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where Pr is the Prandtl number. If the breakup time is less than the total solidification time, secondary breakup may occur.
The final droplet/particle shape is determined by the time required for a deformed droplet to convert to spherical shape under surface tension force. If a droplet solidifies before the surface tension force contracts it into a sphere, the final droplet shape will be irregular. Nichiporenko and Naida[488] proposed the following dimensionally correct expression for the estimation of the spheroidization time, tsph:
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3 π 2 |
μL æ |
1 ö4 |
4 |
4 |
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Eq. (40) |
tsph |
= |
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ç |
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÷ |
(Dend |
- Dinit ) |
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4 VDσ |
2 |
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ø |
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where VD is the droplet volume, Dinit is the smallest dimension of the initial, non-spherical droplet, and Dend is the final droplet diameter. A more detailed and general model for the estimation of the spheroidization of a droplet has been proposed by Rao and Tallmadge.[506] The model-predicted spheroidization times are not