Introduction

This chapter sets forth the mathematical models commonly used to describe the equilibrium and dynamics of fluids. Unless stated otherwise, all of the analysis is performed using a standard right-handed Cartesian coordinate system: ($x_1$ , $x_2$ , $x_3$ ). Moreover, the Einstein summation convention is employed (which means that repeated roman subscripts are assumed to be summed from 1 to 3). (See Appendix B.) More information on the fundamental assumptions that underlie conventional fluid mechanics, as well as the basic equations that describe fluid motion, can be found in Batchelor 2000.