Machine learning approach to predict viscous fingering in Hele-Shaw cells

The Stokes flow between two flat parallel plates caused when the plates are separated by an infinitesimal distance is termed Hele-Shaw flow. This flow is replicated with the help of a lifting plate Hele-Shaw Cell. This system allows a low viscous liquid to penetrate a high viscous liquid, leading to the Saffman-Taylor instability. This instability at the interface promotes the branching of low viscous fluid into minute fractal branches. There have been various methods to control this branching. This paper aims at providing a novel way to use machine learning to predict this fractal pattern. Since the fractal pattern is radical but unpredictable in nature, geometrical anisotropy is introduced in the experiment with the help of holes to control the formation of fractals. The fluid is initially represented with the help of a mesh grid consisting of grid points, and a machine learning model is used to train on the grid points to be able to predict the branching pattern using these grid points, given the initial experimental conditions. The paper describes the steps and processes that were required to perform the experiment, build the dataset, pre-process and post-process the images, train, test, and tune the model and dataset. Moreover, model modifications and setup deficiencies are also described in detail in this paper. The nature of the described model could provide an accurate and robust method to predict these irregular branches.