Scientific and Technical Aerospace Reports Volume 39 April 6, 2001

tial for its successful commercial implementation. The study consists of a theoretical and an experimental component. The
theoretical work uses Navier-Stokes models based on finite element techniques to elucidate the fluid dynamics, heat transfer and
solidification phenomena, and in turn, improve fundamental understanding of the miniature solder deposition process. The experimental
component of the research tests the numerical predictions and provides necessary input data (contact angles) for the
theoretical model. The experiments are performed in microgravity (2.2s drop tower of the NASA GRC) in order to allow for the
use of larger solder droplets which make feasible the performance of accurate measurements, while maintaining similitude of the
relevant fluid dynamic groups (Re, Fr, We, Ste). The work aims to create a science base and identify the influence of the dominant
process parameters in solder droplet dispensing. These process parameters are: droplet size and velocity; droplet, substrate and
ambient gas temperatures; and contact angle between solder and substrate before and after solidification. The sensitivity of the
solidified-droplet (bump) shape and size to variations in the above parameters is critical because solder bump volume, position,
and height variation are key metrics for solder jet technology. Through a combination of experiments and numerical modeling,
the effect of the dimensionless groups Re, We, Fr and the physics these parameters represent are systematically documented. The
axisymmetric impingement of solidifying molten solder droplets onto smooth metallic substrates was investigated to provide fundamental
information relating to the apparent (macroscopic) contact angle and free surface behavior during fluid spreading, and
to determine which parameters govern the process. Molten eutectic 63%Sn-37%Pb solder droplets of approximately 1 mm in
diameter were used in simulation of microcasting in normal gravity. In addition, mm-sized droplet impact events in reduced gravity
were employed for scale-up modeling of the impingement of picoliter size droplets used in electronic chip packaging. Experiments
were conducted in both normal and reduced gravity with technically relevant impact velocities of about 1m/s and about
0.2m/s, respectively, defining the domain of the dimensionless groups believed to govern the droplet spreading, recoiling and
solidification behavior. In normal gravity, the conditions investigated correspond to Re = O(1000), We = O(10), and Fr = O(100).
In reduced gravity of 5x10(exp -4) g (characteristic of the levels attained at the 2.2s drop tower), the impact conditions correspond
to Re = O(100), We = O(1), and Fr = O(10000). In both cases Ca=O(0.001). The experimental apparatus employed in the drop
tower experiments is displayed. The results, as reported in, showed the spreading velocity of the droplets to decrease with time
after impact. The apparent contact angle decreased with increasing contact-line speed, contrary to the classic behavior established
using creeping flows or rolling droplets. Using previously defined relations for droplet impingement, it was reported that for the
current experimental matrix, viscosity, capillarity, solidification, and surface tension all influence the spreading of the metal droplet
and must be simultaneously considered in modeling efforts if accurate results are sought. The results provided a clear demonstration
of the effect of the free-surface dynamic motion on the instantaneous value of the contact angle during spreading and
recoiling of the bulk fluid. These results do not follow established trends from studies of slow spreading or rolling droplets. The
first phase of the program has investigated the axisymmetric impact of liquid-metal droplets on flat stationary substrates. The second
phase, which is about to commence, will examine oblique (non-axisymmetric) impact events, which are necessary in highthroughput
configurations. The offset impact introduces an array of new scientific challenges and constitutes the main goal of the
new generation of this technology.
Author (revised)
Drops (Liquids); Fluid Dynamics; Heat Transfer; Liquid Metals; Microgravity; Solders; Solidification
20010024905 Michigan Univ., Naval Architecture and Marine Engineering, Ann Arbor, MI USA
Fluid Flow in a Rotating Circular Cylinder
Liu, Z., Michigan Univ., USA; Schultz, W., Michigan Univ., USA; Perlin, M., Michigan Univ., USA; Proceedings of the Fifth
Microgravity Fluid Physics and Transport Phenomena Conference; December 2000, pp. 372-391; In English; See also
20010024890; No Copyright; Avail: CASI; A03, Hardcopy; A10, Microfiche
We study the motion of a fluid layer confined by a horizontally oriented, axially rotating, circular cylinder. This physical system
facilitates a simple framework for investigating the dynamics of a viscous flow with a fluid-fluid interface or that of a free-surface
that makes a trijunction with a solid, all in the presence of gravity. The periodicity of the boundary conditions simplifies the
analysis. Surface tension is included, and disjoining pressure is applied to avoid a contact line. Two simple limiting cases exist
for zero and for infinite rotation speed, and represent that of a fluid pool on the cylinder bottom and that of a uniform film experiencing
solid-body rotation, respectively. Two dimensionless quantities are introduced and used in perturbation analyses: delta,
the ratio of average film thickness to cylinder radius that represents the fullness of the cylinder; and Gamma, the ratio of the
Reynolds number to Froude number that therefore represents the ratio of gravitational to viscous forces. Three sets of approximations
and their analytic/numeric solutions are presented: steady and unsteady lubrication approximations through three orders in
delta; steady high-speed flow approximations through two orders of small Gamma; and steady creeping-flow approximations in
the limit of large Gamma. Also a draining, thin film for zero rotation speed will be presented. Lubrication theory is used with
perturbation expansion of dependent variables in terms of delta to study a thin film for steady and unsteady flow. Gamma is
assumed order one, and the expansion is conducted and solved through second order (i.e. zeroth, first, and second orders) for the
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