Particle drift:

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Particle drift:

Consider a simple model of a particle undergoing Stokes friction in an unsteady flow u(t).

$\begin{displaymath} \frac{du_{p}}{dt}=-(u-u_{p})/t_{F}\end{displaymath}$

, where $t_{F}=(2/9)a^{2}/\nu$ =0.008 s, is the ratio of the Stokes force $6\pi \eta \nu u$ to the particle mass. If u(t) is assumed a pure oscillation $u=u_{0}cos(\omega t)$ , we find a relative error $(u-u_{p})/u=(i+1/(\omega t_{F}))^{-1}$ . For a wave at frequency 1 Hz, $\omega =2\pi$ , it yields a relative error 5 %. Since we are studying lower frequencies, we can consider that the particles follow well the fluid motion.

Particle sedimentation by gravity could be a direct source of error, but it is mostly an indirect one, by decreasing the density of particles in the field of view. The speed of sedimentation is given by the balance between weigth minus Archimede's force and Stokes force ( $6\pi \nu \rho av_{s}$ ), where a is the radius of the particle. We obtain then the speed of sedimentation $v_{s}=(2/9)ga^{2}(\rho _{p}-\rho )(\rho \nu )^{-1}$ . For a relative density difference $\rho _{p}-\rho =10^{-4}$ and a radius $a=150\mu m$ , the speed is equal to $5\mu m/s$ or 5cm in 3 hours.

Next: Laser sheet position and Up: Analysis of uncertainty and Previous: Analysis of uncertainty and Contents

Joel Sommeria 2003-02-14