(168e) Velocity Gradient Effects in Microscopic Particle Image Velocimetry

The measurement depth in microscopic particle image velocimetry (microPIV) is not equal to the depth of field of the imaging system, because out-of-focus particles can contribute to the measured velocity. Instead, the measurement depth (or depth of correlation) is a complex function dependent on the optics of the system, the seed particle diameter, the fluorescent wavelength of the seed particles, and to a lesser extent Brownian motion and out-of-plane motion. Until recently, the effects of velocity gradients or fluid shear on the depth of correlation were unknown. To answer this question, the effects of fluid shear on the depth of correlation were analyzed by deriving an analytical model of microPIV interrogation for flowfields containing velocity gradients. For in-plane shear, the depth of correlation for the velocity component perpendicular to the shear was found to be unaffected by the shear rate. However, the depth of correlation for the velocity component in the direction of the shear was found to increase as shear rate increased. Thus, in a flow with shear, the depth of correlation exhibits directional dependence, with a different depth of correlation for each of the two measured velocity components. For out-of-plane shear, the model shows that out-of-plane velocity gradients reduce the depth of correlation compared to flowfields without gradients, but this decrease in depth of correlation is smaller than the increase in depth of correlation for a flowfield containing only in-plane velocity gradients. By combining the analysis for flows with in-plane shear and with the analysis for flows with out-of-plane shear, an equation for depth of correlation for a flowfield containing both in-plane and out-of-plane velocity gradients was derived. This equation suggests that unless the out-of-plane gradients are significantly larger than the in-plane gradients, the effect on the depth of correlation due to the out-of-plane gradients is negligible.