Chapter 7, Problem 7.78P

Worldwide. over a billion solder balls must be manufactured daily for assembling electronics packages. The uniform droplet spray method uses a piezoelectric device to vibrate a shaft in a pot of molten solder that, in turn, ejects small droplets of solder through a precision-machined nozzle. As they traverse a collection chamber, the droplets cool and solidify. The collection chamber is flooded with an inert gas such as nitrogen to prevent oxidation of the solder ball surfaces.

1. Molten solder droplets of diameter $130\mu \text{m}$ are ejected at a velocity of 2 m/s at an initial temperature of 225°C into gaseous nitrogen that is at 30°C and slightly above atmospheric pressure. Determine the terminal velocity of the particles and the distance the particles have traveled when they become completely solidified. The solder properties are $\rho =8230{\text{kg/m}}^{\text{3}},c=240\text{J/kg}\cdot \text{K,}k=38\text{W/m}\cdot \text{K,}{h}_{sf}=42\text{kJ/kg}\text{.}$ The solder's melting temperature is 183°C.
2. The piezoelectric device oscillates at 1.8 kHz, producing 1800 panicles per second. Determine the separation distance between the particles as they traverse the nitrogen gas and the pot volume needed in order to produce the solder balls continuously for one week.