Microfluidics: Modeling, Mechanics and Mathematics

18.5 Entrance Effects in Hagen-Poiseuille Flow

18.5.1 Introduction

Until now we have worked with the equations for time-dependent flow phenomena. We will now turn to effects which are mathematically very similar, yet of a different physical nature. We will assume a fluidic system as depicted in Fig. 18.10. A fluid is driven by a pressure drop $\frac{dp}{dz}$ from a reservoir. Depending on the shape of the container, a stable velocity profile will have developed. We will assume this velocity to be constant v_av. The fluid is driven into the capillary by the pressure drop. Initially the fluid will have a constant velocity profile which will gradually converge ...