Microfluidics: Modeling, Mechanics and Mathematics

Chapter 16

Analytical Solutions to Poiseuille Flow Problems in Different Geometries

16.1 Elliptical and Circular Profiles

16.1.1 Analytical Solution: An Approach

Circular profiles are a special case of elliptical profiles, which is why we will treat them together. Obviously, these profiles are very relevant to microfluidics as they represent the case of a circular tube or a squeezed capillary in the case of the elliptical profile.

16.1.1.1 Approach for v_x

We do not have an intuitive approach for v_x, which is why we first default to the ellipses equation that is given by

${\left(\frac{x}{a}\right)}^2+{\left(\frac{y}{b}\right)}^2=1$

This function simply describes the contour of our cross-section, ...