Scaling Effect on Velocity Profiles in Capillary Underfill Flow

Abstract

In this paper, the scaling effect of ball grid array (BGA) device on the capillary underfill (CUF) flow and its velocity profiles is thoroughly investigated by means of fluid-structure interaction (FSI) numerical simulation. It is found that generally the flows front profiles attained from device of different scale sizes are comparable to the actual miniature BGA, with relative error approximately under 10%. Based on dimensionless number analysis, the scaling limit is estimated at 20, to maintain low scaling error. The velocity profiles attained on the CUF flow in each models of different scales are relative similar in magnitude and trend. Although the increases in gap height reduces the strength of capillary flow, the flow's velocity still be maintained and the scaling effect is counter-balance with the increases in driving pressure force. The magnitude of entrant velocity is higher at earlier stage of CUF (less than 40% filling); while higher magnitude of exit velocity is found at later stage of CUF (beyond 60% filling). Additionally, the pressure and velocity distributions of CUF flow in miniature device were also studied thoroughly.