Microfluidics: Modeling, Mechanics and Mathematics

Chapter 11

Conservation of Momentum: The Navier-Stokes Equation

11.1 Introduction

We now turn to arguably the most important equation in fluid mechanics: The Navier-Stokes¹ equation. The Navier-Stokes equation describes the conservation of momentum and can thus be thought of as the fluid mechanical version of Newton’s famous second law of motion

$F=ma$

  (Eq. 11.1)

In fact, it is possible to derive the Navier-Stokes equation more or less directly from Eq. 11.1, but we will first attempt to get a better understanding of the underlying physics. As stated in section 9.5, conserving momentum is nothing other than applying the laws of motion. However, ...