Microfluidics: Modeling, Mechanics and Mathematics

Chapter 10

Conservation of Mass: The Continuity Equation

10.1 Fluid Flow in the Bulk

10.1.1 Field Variables

As we will see, the properties of a fluid flow are described by the field variables. The field variables are the physical properties of the fluids that are usually required in order to adequately describe the behavior of the fluid. These variables are either scalar or vector quantities. The scalar field variables of interest are:

• pressure p

• density ρ

• temperature T

The only vector variable that needs to be considered is the velocity

$\overrightarrow{v}=\left(\begin{array}{l}{v}_x\hfill \\ v_y\hfill \\ v_z\hfill \end{array}\right)$

with $\overrightarrow{v}=\frac{d\overrightarrow{s}}{dt}$ and $\overrightarrow{a}=\frac{d\overrightarrow{v}}{dt}$. However, this vector has three components (along each axis of ...