Voltage Induced Fluid Mixing Video Data based Volumetric Ratio Modelling using Fractional Order Time Series Methods

Fluid mixing process under direct current (DC) voltage stress is a complex phenomenon when the physical and chemical properties of the two streams are different. We experimentally investigate two streams of fluid flow one with added ink, changing its density and electro-chemical properties, followed by the application of different DC voltage levels. In this experiment, we found that as the applied voltage increases, volumes of the two fluids – with and without ink keep oscillating. Using the state-of-the-art image segmentation methods based on k-means clustering on the transformed La*b* colour image space, we carry out the pixel counting based volume calculation in the voltage induced fluid mixing experiments. Here, each frame of the video is considered as a separate image, undergoing segmentation process yielding estimated pixel numbers in each cluster. Repeating this frame-by-frame clustering-based image segmentation process on the whole video data yields a fluctuating time-series data, showing the ratio of the two fluids within the closed chamber. Due to the high complexity of the noisy fluctuating time series data, we then apply the autoregressive fractionally integrated moving average (ARFIMA) model to quantify the two-fluid volumetric ratio fluctuation data in compact and simple discrete time models. The hyperparameter tuning of the ARFIMA models have also been demonstrated. The efficacy of the fractional order discrete time models or estimators change with the length of data being modelled which may be useful in getting better insights into the stability of fluid mixing process using the volumetric ratio data analysis, irrespective of the timescale of the experiments.