9.3 The stress tensor in Cartesian coordinates

In general, the viscosity tensor C^ijmn contains 81 degrees of freedom ( $81 = 3 \times 3 \times 3 \times 3$). However, the properties just described, and others to follow, greatly reduce this number. The purpose of this section is to provide such a reduction. Thereafter, the form of the stress tensor and friction vector will be written. For simplicity, the coordinates will again be assumed Cartesian in this section.