Liquid-Liquid Dispersion Performance Prediction and Uncertainty Quantification Using Recurrent Neural Networks.

We demonstrate the application of a recurrent neural network (RNN) to perform multistep and multivariate time-series performance predictions for stirred and static mixers as exemplars of complex multiphase systems. We employ two network architectures in this study, fitted with either long short-term memory and gated recurrent unit cells, which are trained on high-fidelity, three-dimensional, computational fluid dynamics simulations of the mixer performance, in the presence and absence of surfactants, in terms of drop size distributions and interfacial areas as a function of system parameters; these include physicochemical properties, mixer geometry, and operating conditions. Our results demonstrate that while it is possible to train RNNs with a single fully connected layer more efficiently than with an encoder-decoder structure, the latter is shown to be more capable of learning long-term dynamics underlying dispersion metrics.

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches.

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Ra_{c}, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration.

Simulation of immiscible liquid-liquid flows in complex microchannel geometries using a front-tracking scheme.

The three-dimensional two-phase flow dynamics inside a microfluidic device of complex geometry is simulated using a parallel, hybrid front-tracking/level-set solver. The numerical framework employed circumvents numerous meshing issues normally associated with constructing complex geometries within typical computational fluid dynamics packages. The device considered in the present work is constructed via a module that defines solid objects by means of a static distance function.

Hysteretic Faraday waves.

We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As a critical control parameter is surpassed, small amplitude surface waves bifurcate subcritically toward highly nonlinear ones with twice their amplitude. We relate this hysteresis with the change of shear stress using a simple stress balance, in agreement with numerical results.