Newtonian fluid

A Newtonian fluid is one that, when pressure is applied, acts as a liquid, as most would expect. This is of course opposed to the non-newtonian fluid, which acts as a solid when pressure is applied. Starch and water compositions are non-newtonian.

A Newtonian fluid is a fluid in which shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. The constant of proportionality is known as the viscosity. For a Newtonian fluid, the viscosity by definition depends only on temperature and pressure, and also the chemical composition of the fluid if the fluid is not a pure substance. If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress, in the Cartesian coordinate system, is

$\tau _{ij}=\mu \left({\frac {\partial v_{i}}{\partial x_{j}}}+{\frac {\partial v_{j}}{\partial x_{i}}}-{\frac {2}{3}}\delta _{ij}\nabla \cdot \mathbf {v} \right)$

where

τ_ij is the shear stress on the i^th face of a fluid element in the j^th direction

v_i is the velocity in the i^th direction

x_j is the j^th direction coordinate

δ_ij is the Kronecker delta

If a fluid does not obey this relation, it is termed a non-Newtonian fluid.

Category: Fluid dynamics