On the micro-PIV accuracy and reliability utilizing non-Gaussian particle images

Abstract

Optical investigations of the dynamics of concentrated suspensions, such as in blood flows (Fitzgibbon et al. in Biophys J 108(10):2601–2608, 2015. http://doi/org/10.1016/j.bpj.2015.04.013) or slurry flows (Li et al. in Ocean Eng 163(October 2017):691–705, 2018. http://doi/org/10.1016/j.oceaneng.2018.06.046), are challenging due to reduced optical accessibility. Furthermore, the suspension particle image size can strongly deviate from the optimal particle image size for PIV measurements. Optical accessibility can be achieved by refractive index matching of surface labelled suspension particles. This results in particle images that are transparent in the particle image centre, but fluoresce at the particle image rim, resulting in ring-shaped particle images. In the present study, the influence of the particle image size on the cross-correlation result of such ring-shaped particle images is compared with Gaussian and plateau-shaped particle images. Particles of Gaussian image shape result from fully labelled particles with small image diameters and are commonly used in PIV measurements. Such particles are also utilized for the determination of the continuous phase velocities in the experimental part of the present study. With increasing image diameter, fully labelled particles are observed to assume plateau-shaped particle images. Monte Carlo simulations of synthetically generated images show that ring-shaped particle images have a superior behaviour, i.e. they assume a reduced displacement estimation error for noisy as well as for noise-free image data, compared to Gaussian and plateau-shaped particle images. This is also true for large particle image diameters when particle images are intersected at interrogation window borders or when different values of nonzero particle image displacements are considered. The detectability is similar for all three particle image shapes as long as particles do not intersect with the interrogation window border. Interestingly, for intersected particles of large image diameter, ring-shaped particle images show a slightly improved detectability compared to particle images of Gaussian and plateau shape. Furthermore, the detectability is insensitive against a nonzero particle image displacement. The usage of refractive index matched, ring-shaped particle images results in a good optical accessibility of the suspension. This allows to perform simultaneous cross-correlation evaluations on large ring-shaped particle images and fluid tracers with Gaussian particle images that are two orders of magnitude smaller compared to suspension particle images. Velocity measurements are taken on a suspension containing 5 vol% surface labelled, refractive index matched 60 $$\upmu \hbox {m}$$ μ m polymethylmethacrylate (PMMA) particles. Simultaneously, $$\upmu$$ μ PIV measurements of the carrier liquid flow are performed utilizing 1.19 $$\upmu \text {m}$$ μ m fluorescent polystyrene (PS) particles. Measurement results reveal a parabolic shape of the velocity profiles of both phases with a mean slip velocity of 7.4% at the position of maximum streamwise velocity in a 580 $$\upmu \text {m}$$ μ m high trapezoidal channel. An error analysis confirms the presence of these slip velocities within a 68.5% confidence interval. A measurement uncertainty in the order of magnitude of $${\mathcal {O}}(10^{-1}\ \mathrm{px})$$ O ( 10 - 1 px ) is reached for both fluid tracers and suspension particles. Overall, the present study demonstrates theoretically and experimentally that the usage of suspension particles with ring-shaped images is superior compared to Gaussian and plateau-shaped particle images of the same size. Additionally, the present study demonstrates that the usage of ring-shaped particle images allows to investigate suspension bulk dynamics by measuring velocity fields of both the suspended and the continuous phase simultaneously and with an overall uncertainty that is in the same order of magnitude as for standard $$\upmu$$ μ PIV measurements. Graphic abstract

Flow visualization: state-of-the-art development of micro-particle image velocimetry

“…Using the fit functions of experimental data (e.g. smoothing spline), other distribution functions can be obtained, such as ring-and plateau-shaped distribution functions (Blahout et al 2021). Figure 9 shows the images of a particle utilizing three distribution functions.…”

“…For synthetically generated images, self-labeled and commercially-labeled polymethylmethacrylate particles with a diameter of 60 µm are used, which perform ring-and plateau-shaped images of the particles. Reproduced from Blahout et al (2021), with permission from Springer Nature. arterioles and venules that deliver specific amounts of blood and its components throughout the human body.…”