On the calibration of Astigmatism particle tracking velocimetryfor suspensions of different volume fractions

Abstract

In the present study we demonstrate for the first time how Astigmatism Particle Tracking Velocimetry (APTV) can be utilized to measure suspensions dynamics. Measurements were successfully performed in monodisperse, refractive index matched suspensions of up to a volume fraction of $Φ=19.9\%$. For this, a small percentage of the particles is labeled with fluorescent dye acting as tracers for the particle tracking procedure. Calibration results show, that a slight deviation of the refractive index of liquid and particles leads to a strong shape change of the calibration curve with respect to the unladen case. This effect becomes more severe along the channel height. To compensate the shape change of the calibration curves the interpolation technique developed by Brockmann et al. (Experiments in Fluids, 61(2), 67, \citeyear{brockmann2020utilizing}) is adapted. Using this technique, the interpolation procedure is applied to suspensions with 6 different volume fractions ranging from $Φ<0.01\%$ to $Φ=19.9\%$. To determine the effect of volume fraction on the perfomance of the method, the depth reconstruction error $σ_z$ and the measurement volume depth $Δz$, obtained in different calibration measurements, are estimated. Here, a relative position reconstruction accuracy of $σ_z$/$Δz$=0.90\% and $σ_z$/$Δz$=2.53\% is achieved for labeled calibration particles in dilute ($Φ<0.01\%$) and semi-dilute ($Φ\approx19.9\%$) suspensions, respectively. The measurement technique is validated for a laminar flow in a straight rectangular channel with a cross-sectional area of 2.55$\times$30\,mm$^2$. Uncertainties of 1.39\% and 3.34\% for the in-plane and 9.04\% and 22.57\% for the out-of-plane velocity with respect to the maximum streamwise velocity are achieved, at solid volume fractions of $Φ<0.01\%$ and $Φ=19.9\%$, respectively.