On the dispersion dynamics of liquid–liquid surfactant-laden flows in a SMX static mixer

Liquid–Liquid Dispersion Performance Prediction and Uncertainty Quantification Using Recurrent Neural Networks

“…where β, Bi, and Da stand for the elasticity, Biot, and Damkohler numbers, characterizing surfactant "strength" (interfacial tension sensitivity on concentration), desorptive capability vs convective surface transport, and adsorption depth into the bulk, respectively. 31 These parameters are used to label the surfactantladen cases employed herein and broadly describe the nature of each surfactant modeled (e.g., highly/weakly adsorptive/ desorptive, etc.). Further details into the equations governing surfactant transport and the specifics behind the interfacetracking algorithm (i.e., LCRM) are found in previous publications.…”

“…Further details into the equations governing surfactant transport and the specifics behind the interfacetracking algorithm (i.e., LCRM) are found in previous publications. 29,31,32,45 Data Preprocessing: Scaling, Smoothing, and DSD Binning. The initial set of features considered in this study consists of two scalar quantities, namely, IA and ND, and a variable-sized list of scalars (i.e., drop volumes) representing the DSD.…”

“…In this work, M was initially set to 20 and 12 for the stirred and static mixing cases, respectively, aiming to provide sufficient resolution for the DSD data based on statistical analyses conducted in previous publications. 29,31 To eliminate outliers and uninteresting features (i.e., bins that mostly remain as 0 throughout the time domain), M was ultimately cut to 10 bins for both mixers (B 0 − B 9 ), dropping the boundary bins at each end of the size range proportionally, yielding 12 features overall for the RNN to handle. Finally, the ND and IA features were scaled and smoothed individually to mitigate potential biases arising from their substantially different scales [∼O(10 2 ) vs ∼O(1)] and the sharply fluctuating trend observed for the ND data.…”

“…Simulations were carried out using in-house code BLUE, ,, which considers a three-dimensional single-field formulation of the Navier–Stokes equations in a Cartesian domain normal∇ · boldu = 0 ρ ( ∂ u ∂ t + u · ∇ u ) = prefix− normal∇ P + ρ boldg + normal∇ · [ μ false( normal∇ boldu + normal∇ u T false) ] + boldF where t , P , u , g , and F denote time, pressure, velocity, gravity, and a local surface force. For clean systems, this term follows a hybrid formulation of the form boldF = ∫ A σ κ boldn δ ( x − boldx f ) .25em normald A where σ is a constant interfacial tension coefficient, κ is the interface curvature, and the 3D Dirac delta function δ( x – x f ) is set to 0 everywhere and unity at the interface, which is located at x = x f . A numerical Heaviside function, scriptH ( x , t ) , is used to define density and viscosity fields throughout the domain, which are respectively given by .25ex2ex ρ ( x , t ) = ρ a + ( ρ normalo<...…”

“…Inspired by the work reviewed before, this study seeks to develop an inexpensive time-series model using RNNs by capitalizing on a comprehensive set of high-fidelity three-dimensional CFD simulations, some of which have been exploited in recent works − to unravel the fundamental governing mechanisms underlying extensively utilized mixing systems handling L–L dispersions across a range of industrially relevant scenarios. These simulations have been conducted with a state-of-the-art DNS code, which comprises a hybrid front-tracking/level-set interface-tracking algorithm, embedded along a well-validated multiphase solver for surfactant transport at the interface and in the bulk phase .…”