Monosize droplet deposition as a means to investigate droplet behavior during spray deposition
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I. INTRODUCTION
THE widespread industrial application of spray deposition methods has illuminated the need for insight into the fundamental interactions that govern droplet-based materials processing. From thermal spraying (for coatings and thin films) to the spray forming of bulk materials and net-shaped components, droplet deposition processes share the intrinsic complexities of many-body systems. For instance, thermal interactions between the molten particles in a spray tend to convolute the straightforward correlation between temperature and solidification in the bulk deposit. Droplet interactions, direct and indirect, tend to obscure the driving forces behind spreading, adhesion, and porosity formation. In such cases, one must employ an appropriate approximation to correctly model the relationships between process parameters and the resulting material properties. A. Modeling Efforts To circumvent some of the difficulties of analyzing the multidroplet case, one may consider instead the behavior of a single droplet in isolation from its nearest neighbors. This approach provides only limited insight into droplet behavior in spray deposition processes, since droplet-droplet interactions are neglected. However, this modeling approach has been very fruitful and has allowed for the identification of important process mechanisms (e.g., the role of liquid-jet overflow in pore formation[1]). Indeed, a number of groups[2–9] have studied the effects of process parameters upon the heattransfer aspects and fluid dynamics of single droplets both in flight and at impact. For small, spherically symmetric droplets, the in-flight
S.Q. ARMSTER and ENRIQUE J. LAVERNIA, Professor, are with the Department of Chemical and Biochemical Engineering and Materials Science, University of California, Irvine, CA 92697-2575. J.-P. DELPLANQUE, Assistant Professor, is with the Engineering Division, Colorado School of Mines, Golden, CO 80401. W.-H.L. LAI, Associate Professor, is with the Institute of Aeronautics and Astronautics, National Chong Kung University, Taiwan, Republic of China. Manuscript submitted August 27, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS B
thermal characteristics can be predicted from single-dimensional models that include convective and radiative heatloss terms. From here, one can employ Fourier’s equation, T 2T 5a 2 t x
[1]
with appropriate boundary conditions: T(x, t 5 0) 5 T0;
T x
Z
5 0; x50
[2]
Tdrop Tair kdrop 2 kair 5 Jrad 1 Jconv x x (where k is the heat-transfer coefficient for the droplet and the surrounding air, and Jrad and Jconv are the portions of the heat flux due to radiation and convection, respectively) to develop a solution for the temperature field within the molten particle. When solidification occurs, a two-domain approach may be used, as described in Reference 10, to predict the droplet thermal state. For the most part, two different approaches are employed to simulate droplet impact and deformation: the finite-element-analysis and finite-difference methods. The main advantag
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