Neural Networks For Particle Diffusometry In The Presence Of Flow And With Defocused Particles

Abstract

Diffusion is a natural phenomenon in fluids. Its measurement can be done optically by seeding an otherwise featureless fluid with tracer particles and observing their motion. However, existing algorithms for particle-based diffusion coefficient measurement have multiple failure modes especially when the fluid has a flow or the particles are defocused. We present a method based on Convolutional Neural Networks (CNNs) for predicting diffusion coefficients in the presence of these real-world effects. The CNNs were trained, validated, and tested on crops from four-frame temporally averaged images. The study includes three simulated datasets: Gaussian-shaped particles under no fluid flow condition, Gaussian-shaped particles under an arbitrary flow condition, and defocused particles under no fluid flow condition. The results show that the CNNs have a low Mean Absolute Error (MAE) of 0.12 µm 2 /s between the true and predicted diffusion coefficient values for the dataset with Gaussian-shaped particles under no fluid flow condition. The CNNs have a slightly higher MAE of 0.19 µm^2 /s for Gaussian-shaped particles under arbitrary flow and defocused particles under no fluid flow conditions. The performance of the CNNs was also benchmarked against four conventional algorithms on these simulated datasets. The results show that the conventional algorithms perform better than the CNNs when the particles are assumed to be Gaussian and the fluid has no flow. However, the CNNs outperform conventional methods in the presence of flow or if the particles are defocused. Finally, the outputs of CNNs were compared against the outputs of conventional algorithms on experimental datasets. This provides uncertainty in the range of 0.19 µm^2 /s - 0.47 µm^2 /s, which is slightly larger than the errors obtained from simulated datasets. Hence, the study shows that CNNs can be used to reliably predict diffusion coefficients from complex particle datasets with as little as four frames.