Flow rate estimation in large depth-of-field micro-PIV

In micro-Particle Image Velocimetry, the requirement of a large field-of-view often results in a large depth-of-correlation, i.e. large depth of the measurement volume. When the velocity varies substantially over the depth-of-correlation, special attention should be paid to a correct interpretation of the measured velocities. When a specialized microscope is needed to meet the requirements of a setup, the resulting more complex optical arrangements can have additional effects on the measurement results. In order to determine flow parameters such as the flow rate, it is sufficient to have a robust estimate of the maximum velocity when the flow is Poiseuille flow. In this paper, an interpretation of the results from particle image velocimetry measurements with low magnification in a round capillary is given for two types of microscopes: a conventional and a specialized microscope. The measured velocity appears to be lower than the maximum velocity, yet is still above the average velocity. The interpretation of the measured velocity differs for the two types of microscopes. The under-estimation of the maximum velocity obtained from the conventional microscope remains small (within 6%) for low-magnification measurements, while the under-estimation of the maximum velocity obtained from the specialized microscope increases up to 25% for a large depth-of-correlation. The images of the in- and out-of-focus particles turn out to play a crucial role in this difference between the two microscopes. Validation of the optical properties of a microscope is important, especially for specialized microscopes where particle images deviate substantially from the existing theory, and this theory is also used to derive the analytical expression for the depth-of-correlation. A procedure is recommended to obtain a correct interpretation of the measured velocity. This procedure is generally applicable, but mainly of importance for specialized microscopes.