Interface Fluctuations in a Turbulent Binary Fluid using Data-Driven Methods

Abstract

Interfacial fluctuations in a two-phase binary fluid mixture reveal signatures of underlying physical processes that occur within each phase and on a range of spatial and temporal scales. In this study, we investigate a model binary fluid system consisting of a single droplet of one phase moving in the background of the second phase. The binary fluid system is subjected to turbulent forcing. We perform extensive direct numerical simulations of the turbulent system to examine how quantities such as interfacial dynamics and droplet acceleration can be systematically decoded. Extensive simulations of binary fluid systems are computationally expensive and time-consuming. In contrast, data-driven models have shown promise in recent times in reducing computational cost. In this work, we build and compare the performances of four interpretable data-driven models, i.e., dynamic mode decomposition (DMD), Hankel DMD, sparse identification of nonlinear dynamics (SINDy), and Stochastic Langevin regression (SLR), each using dimensionality reduction via proper orthogonal decomposition, to identify simplified dynamical equations governing interfacial dynamics and center-of-mass acceleration. We show how these learned models can be generalized to encode physical properties, such as the interfacial surface tension and droplet size. In particular, we show that SLR predicts the underlying dynamical equations of the binary-fluid system with the greatest accuracy over a wide range of interfacial tension values and droplet sizes. In addition, SLR requires fewer terms compared to SINDy to capture the underlying dynamics, and is thus computationally the most efficient among the four methods. These data-driven techniques can be used in many practical applications, such as the dynamics of biological cell membranes, thin films, and other industrial applications.