Particle Dynamics

The particle dynamics as outlined by Adrian (1991) for successful PIV measurements is discussed in this section.The PIV technique measures in principle the Lagrangian velocities of the particle, . If the particle velocity is being used to infer Eulerian fluid velocity one must consider the accuracy with which the particle follows the fluid motion. With subscript denoting particle-level properties, the equation of motion of a single particle in a dilute suspension is a balance between inertia and drag force is written as:

	(1)

The above equation requires a correction for the added mass of the fluid, unsteady drag forces, pressure gradients in the fluid, and nonuniform fluid motion. In gaseous flows with small liquid particles, we may ignore all these terms except the static drag law with drag coefficient . This term incorporates finite Reynolds number effects.

Particle response is often described in terms of the flow velocity and a characteristic frequency of oscillation. The first question is, how fast can the flow be, before the particle lag creates an unacceptably large error. An appropriate approach is to evaluate the particle slip velocity as a function of the applied acceleration. For the simplified drag law of the above equation, one has

	(2)

This shows that the slip velocity for finite particle Reynolds number, where constant, is only proportional to the square root of the acceleration. In the limit of small particle Reynolds number Stokes' law may be used to evaluate resulting in

	(3)