Application of D-optimal design for modeling micro channel flow with different dispensing patterns

The dispensing pattern of fluids along the periphery of two parallel plates with full micro channels plays an important role for an effective underfilling process. In this paper, a capillary-driven flow model was used to examine the effect of different dispensing patterns such as U-type and L-type on the filling time. A response surface modeling (RSM)-based D-optimal design is employed to construct statistical models relating filling time and designed effective parameters known as bump diameter, bump height and clearance between each bump. The experimental plan consists of a four-factorʹs (three numerical plus one categorical) matrix. The results show that the U-type dispensing pattern has significant effect on the reduction of filling time than that done at the L-pattern condition. Besides, bump height is the most influential factor on the filling time in both dispensing patterns. Meanwhile, the variations of filling time are compared between the raw data and the values obtained from RS models and have good agreement to each other. Through the desirability function approach, the optimal combination of effective factors is also determined for the U-type pattern and the values of bump height, diameter and clearance are 172 μm, 146 μm and 120 μm, respectively. Finally, the improvement of filling time is around 18.3%.