Molten Metal Droplet-Powder Impact Interaction: Model For Spreading And Solidification

Molten droplet impingement is a promising technology with potential application in many industrial processes, such as plasma spaying, spay deposition processes, digital microfabrication, microcasting, rapid freeze prototyping, electronics packaging, etc. Better control of these processes requires a fundamental understanding of the physical phenomena during molten droplet impingement which involve fluid flow, heat transfer and rapid solidification. When a droplet of molten metal hits a rough, solid surface (powder surface), a composite solid-liquid-air interface (as opposed to the homogeneous solid-liquid interface) should form with air pockets trapped in the valleys between asperities. It gives a fluid-structure problem built on periodic domain, with three phases: an isotropic rigid solid, a Newtonian, incompressible, weakly viscous liquid and a barotropic gas. In this paper the influence of surface roughness on apparent contact angle has been studied. A model based Cassie-Baxter's theory is proposed to correlate microscopic contact angle (true contact angle) with apparent contact angle. The difference between the microscopic contact angle (true contact angle) and apparent contact angle can be explained by the ratio of the solid/liquid and liquid/vapor line length at the three phase line.An analytical model for droplet spreading has been developed which accounts for simultaneously effects of surface tension, viscosity, surface roughness. Based on this model, an analytical solution of spread factor has been obtained as a function of Reynolds, Weber numbers. This paper illustrates the importance of correctly determining the apparent contact angle (a parameter that quantifies the wetting of the substrate which is governed by the surface free energy and the geometrical structure of the substrates) for predicting the maximum spreading of the splat. A map for flattening ratio with different apparent angle has been generated for Reynolds number in the range of 1~1000 and Weber number in the range of 1~100. The interface thermal contact resistance between an impinging molten droplet and cold substrate plays an important role in the droplet solidification. The present study is also conducted to investigate the effect of contact thermal resistance on the solidification rate of a molten metal droplet which is deposited on a cool matrix of packed metal powders. An analytical model of the true area of contact between molten metal and a rough, solid surface has been used to calculate thermal contact resistance and to predict how it changes with surface roughness, substrate/droplet thermal properties, flattening ratio and droplet impact velocity. The analytical model of the solidification rate of the molten metal droplet is compare with the numerical results and found to agree well. This paper also proposes that there is a porosity distribution along the splat radius and that the porosity volume increases with increasing radius.A two-dimensional model has been developed to simulate the fluid dynamics, heat transfer, and phase-change that occurs when a molten droplet impact on a rough substrate. Surface tension is modeled as a volume force acting on fluid near the surface. Contact angle is applied as a boundary condition at the liquid-solid contact line. The energy equations in both the liquid and solid portions of the droplet are solved using the enthalpy method. Heat transfer within the substrate is by conduction alone. Thermal contact resistance at the droplet-substrate interface is included in the model. Calculated droplet shapes obtained from numerical model were compared with photographs taken in experiments. Qualitative agreement between the numerical and the experimental results testified the validity of the present model.