Solidification and Spheroidization

In atomization of melts, the final droplet size also depends on the relative magnitude of the time th for a droplet to undergo deformation prior to secondary breakup, and the time tsol required for 

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[488l proposed the following dimensionally correct expression for the estimation of the spheroidization time, tsph  

For the deformation of droplets of normal liquids at low impact velocities on a horizontal plane surface without phase change, Tan et al)513 developed a physical-mathematical model with a droplet falling from a certain height under the influence of gravity. They derived quantitative relations for the dimensions of the deformed droplet, including the effects of initial droplet diameter, height of fall, and thermophysical properties of liquid. In this model, the behavior of droplet deformation was assumed to be governed by 

For the deformation of droplets of normal liquids on a heated, horizontal, flat surface with attendant phase change, i.e., evaporation, Chandra and Avedisian14111 derived the following equation based on a simplified model  

Several other special cases have also been analyzed numerically, leading to simplified formulations for the flattening ratio, as detailed below in each model group. 

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