Transport phenomena during molten droplet pile-up in micromanufacturing
[thesis]
Stephan Eirik Ligaard Haferl, Jürg Dual, Dimosthenis Poulikakos
2001
Over the last few years a significant research effort has been devoted to the investigation of molten droplet impact phenomena. The reason for this activity is the pressing need of an indepth understanding of these phenomena for the successful development and implementation of a host of emerging technologies such as rapid prototyping, spray forming, spray coating and precision molten droplet dispensing in the manufacturing of microelectronics and other micromanufacturing applications. Most of
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... e existing work has been focused on the investigation of droplet impact on planar substrates. Little information can be found in the scientific literature on the basic problem of droplet impact on non-planar substrates. With reference to molten droplets of interest to this thesis, applications inc1ude structure-building (rapid prototyping) as well as deposition of a required precise amount of material, which is larger than that of the largest single droplet that can be reliably generated; here multiple drop lets are impinged one on top of the other. In addition, droplet impact on non flat surfaces finds a plethora of applications in nature and in technology (exemplified by spray coating, spray cooling, ablation technologies etc.). The limited work published to date in this challenging field consists of few oversimplified analyticalor computational models (neglecting e.g. the all important effect of fluid dynamics, for example) with or without some experimental validation of only the steady state regime. This thesis presents for the first time a detailed experimental and numerical investigation of the transient thermofluidic transport phenomena occurring during molten-microdropletdeposition-based micromanufacturing processes. Experimental visualization of phenomena lasting a fraction of a millisecond in severely deforming domains of typical size of a fraction of a millimeter, as well as highly versatile numerical results of the thermofluidic phenomena during the axisymmetric pile up (deposition one upon another) of molten picoliter size liquid metal droplets on a substrate are presented. The numerical model thereby solves the coupled Navier-Stokes and energy equations accounting for solidification, slip at the contact line as well as thermal contact resistance at the respective interfaces. Incompressibility of the flow as well as constant thermophysical properties are assumed. The prevailing physical mechanisms of the pile up process (occurring simultaneously) are identified and quantified both experimentally and numerically. These are the fluid mechanics of the bulk liquid (controlled by the initial momentum of the impinging droplet and the free, deforming surface of the drop let), capillarity effects at the liquid-solid interface, and solidification (controlled by the initial temperature of the droplet and the substrate) and the important effect of thermal contact 10 resistance at the respective interfaces. The predictive capabilities of the state of the art finite element numerical model, based on a Lagrangian formulation and involving unstructured grid generation in a continuously deforming domain, are presented and discussed. Furthermore, the parametric domain in which the numerical model performs reliably is identified in terms of the relevant dimensionless groups. These are the Reynolds and the Weber number for the fluid mechanics, the Stefan and the Biot number for the heat transfer and the solidification. In terms of values of the relevant dimensionless groups the following ranges are covered in this thesis: Re =281 -453, We =2.39 -5.99, Ste =0.187 -0.895. This corresponds to molten solder droplets impinging at velocities ranging between 1.12 -1.74 [m/s] having an average diameter of ==78 [um]. The initial substrate temperature ranges between 25 -150 [0C]. The initial droplet temperature is kept constant at 210 [0C]. The main results of the thesis clearly add originally and significantly to the knowledge base of molten droplet pile up and solidification, a process of importance, since it is the building block to a host of micromanufacturing applications. 11
doi:10.3929/ethz-a-004269680
fatcat:csvn5lltzne5hiz6xfwaxesp7y