Statistical Modeling for Oblique Collision of Nano and Micro Droplets in Plasma Spray Processes

Document Type : Research Paper


1 Department of Mathematics and Statistics, Lahijan branch, Islamic Azad University, Lahijan, Iran.

2 Department of Mechanical Engineering, Payame Noor University (PNU), P.O. Box: 19395-3697, Tehran, Iran.


  Spreading and coating of nano and micro droplets on solid surfaces is important in a wide variety of applications including plasma spray coating, ink jet printing, DNA synthesis and etc. In spraying processes, most of droplets collide obliquely to the surface. The purpose of this article is to study the distribution of nano and micro droplets spreading when droplets impact at an oblique angle. We introduce the generalized exponential distribution as a new alternative for spreading data. The generalized exponential distribution shares many physical properties of the Weibull distribution which is used frequently for engineering data. For shape parameter greater than one, the generalized exponential distribution offers increasing hazard function, which is in accordance with the inclined droplet impact in plasma coating processes. We apply a number of criteria and model selection tests to evaluate the suitability of the generalized exponential distribution to other rival models, such as the Weibull, inverse Weibull, Burr III, Burr X,  inverted exponentiated Rayleigh and exponentiated Pareto distributions. The analyses results indicate that the generalized exponential distribution shows better results than the other distributions for nano and micro droplets spreading data. Finally, graphical displays for informal checks on the appropriateness of the generalized exponential distribution in probabilistic assessment of inclined impact as well as formal goodness of tests are presented. An important implication of the present study is that the generalized exponential distribution, in contrast to other distributions, fits more appropriately in the spreading data.