Modeling of Unsteady Laminar Flow Based on Steady Solution in Jetting Dispensing Process

This paper proposes a new approach to model unsteady laminar flows of dispenser systems in the semiconductor packaging industry. The approach is based on the exact steady solution. After an overview of dispensing technology and historical modeling of the unsteady flows, a new modeling approach of the unsteady laminar flow in a circular pipe and annular duct is developed. From the proposed model, the modeling results of unsteady flow in an arbitrary circular pipe and annular duct are obtained and compared with the spectral solution. In addition, a comparative work between the proposed analytical dynamic model and the finite-element model is undertaken in order to demonstrate the effectiveness of the proposed modeling methodology.