A Short Review of Velocity Gradient Measurement Techniques

Abstract

The properties of fluid flow are to a large extent determined by the forces which exert adjacent regions onto each other. The force per area separating the two neighbouring regions is called stress $\widehat\sigma$ . Common to all fluids is an isotropic stress normal to the considered area, it is known as pressure. In ideal fluids this pressure is the only force which acts within it. Real flowing fluids exhibit also stresses within the area which is known as shear stress. In any fluid one source of this shear stress is the velocity gradient. The most simple model of a real fluid is the Newtonian fluid where the connection between velocity gradient and the stress is assumed to be linear. There is a large class of fluids where this assumption is justified. For those there are two parameters which establish the connection between velocity gradient and stress. There are, however, also fluids where the stress depends in a more complex way on the velocity gradient, especially if the fluid is composed of complex molecules or of different species of molecules. It may even explicitly depend on time. This is caused by an increase of the molecular order within the fluid caused by the velocity gradient, a possible result is for instance visco-elasticity.