Optimal Shape Design of Pressure-Driven Curved Micro Channels with Hydrophilic and Hydrophobia Walls

摘要

In this study, we perform an optimal shape design of a pressure-driven curved micro channel with minimum pressure drop using a mathematical theory. We consider two different wall types such as hydrophobic and hydrophilic walls where the slip and no-slip conditions are applied, respectively. Optimal shapes are obtained from the initial circular shapes, which are commonly used in most curved channels, at three different bulk Reynolds numbers of 0.1, 1 and 10 for both the 90° and 180° curved channels. In the optimal shape, the height of the curved channel is widened according to the optimality condition, and the pressure drop is significantly reduced by about 10%～20% as compared to that with the initial circular shape.