Flow in a Microchannel Filled with Arrays of Numerous Pillars

The pressure drop of microchannels filled with arrays of numerous pillars drastically increases while scaling-down in particular for the low micrometer scale. In this study, one numerical model and two mathematical models are developed to predict the pressure drop of such systems through the dimensionless permeability by using the unit cell technique. The numerical model includes the effects of complex geometries and inertia forces. The first mathematical model is derived from the Stokes equation and can be used for simplified problems. The second mathematical model combines the numerical and first mathematical model by using a 5D-Lagrange approximation to include geometrical and inertia effects. In this model, the support points are obtained by numerical simulation to adjust the result of the first mathematical model. All models show a similar trend to experimental results from the literature. With the result of the developed models, the pressure drop can be predicted for a wide range of applications.