Determining interfacial tension and critical micelle concentrations of surfactants from atomistic molecular simulations.

Hypothesis Atomistically-detailed models of surfactants provide quantitative information on the molecular interactions and spatial distributions at fluid interfaces. Hence, it should be possible to extract from this information, macroscopical thermophysical properties such as interfacial tension, critical micelle concentrations and the relationship between these properties and the bulk fluid surfactant concentrations. Simulations and Experiments Molecular-scale interfacial of systems containing n-dodecyl ß-glucoside (APG12) are simulated using classical molecular dynamics. The bulk phases and the corresponding interfacial regions are all explicitly detailed using an all-atom force field (PCFF+). During the simulation, the behaviour of the interface is analyzed geometrically to obtain an approximated value of the critical micelle concentration (CMC) in terms of the surfactant area number density and the interfacial tension is assessed through the analysis of the forces amongst molecules. New experimental determinations are reported for the surface tension of APG12 at the water/air and at the water/n-decane interfaces. Findings We showcase the application of a thermodynamic framework that inter-relates interfacial tensions, surface densities, CMCs and bulk surfactant concentrations, which allows the in silico quantitative prediction of interfacial tension isotherms.

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. Details of the methodology are presented, which include data preprocessing, RNN model exploration, and methods for model performance visualization; an ensemble-based procedure is also introduced to provide a measure of the model uncertainty. The workflow is designed to be generic and can be deployed to make predictions in other industrial applications with similar time-series data.

Applying Convolutional Neural Networks to data on unstructured meshes with space-filling curves.

This paper presents the first classical Convolutional Neural Network (CNN) that can be applied directly to data from unstructured finite element meshes or control volume grids. CNNs have been hugely influential in the areas of image classification and image compression, both of which typically deal with data on structured grids. Unstructured meshes are frequently used to solve partial differential equations and are particularly suitable for problems that require the mesh to conform to complex geometries or for problems that require variable mesh resolution. Central to our approach are space-filling curves, which traverse the nodes or cells of a mesh tracing out a path that is as short as possible (in terms of numbers of edges) and that visits each node or cell exactly once. The space-filling curves (SFCs) are used to find an ordering of the nodes or cells that can transform multi-dimensional solutions on unstructured meshes into a one-dimensional (1D) representation, to which 1D convolutional layers can then be applied. Although developed in two dimensions, the approach is applicable to higher dimensional problems. To demonstrate the approach, the network we choose is a convolutional autoencoder (CAE), although other types of CNN could be used. The approach is tested by applying CAEs to data sets that have been reordered with a space-filling curve. Sparse layers are used at the input and output of the autoencoder, and the use of multiple SFCs is explored. We compare the accuracy of the SFC-based CAE with that of a classical CAE applied to two idealised problems on structured meshes, and then apply the approach to solutions of flow past a cylinder obtained using the finite-element method and an unstructured mesh.

Atomic Force Microscopy and Molecular Dynamic Simulation of Adsorption of Polyacrylamide with Different Chemistries onto Calcium Carbonate.

This study investigates the interaction of polyacrylamide (PAM) of different functional groups (sulfonate vs. carboxylate) and charge density (30% hydrolysed vs. 10% hydrolysed) with calcium carbonate (CaCO3) via atomic force microscopy (AFM) and partly via molecular dynamic (MD) simulations. The PAM used were F3330 (30% hydrolysed), AN125 (25% sulfonated), and AN910 (% hydrolysed). A total of 100 ppm of PAMs was prepared in 0.1% NaCl, 3% NaCl, and 4.36% NaNO3 to be employed in AFM experiments, while oligomeric models (30 repeating units) of hydrolysed polyacrylamide (HPAM), sulfonated polyacrylamide (SPAM), and neutral PAM (NPAM) were studied on a model calcite surface on MD simulations. AFM analysis indicated that F3330 has a higher average adhesion and interaction energy with CaCO3 than AN125 due to the bulky sulfonate side group of AN125 interfering with SPAM adsorption. Steric repulsion of both PAMs was similar due to their comparable molecular weights and densities of the charged group. In contrast, AN910 showed lower average adhesion and interaction energy, along with slightly longer steric repulsion with calcite than F3330, suggesting AN910 adopts more loops and tails than the slightly flatter F3330 configuration. An increase in salt concentration from 0.1% to 3% NaCl saw a reduction in adhesion and interaction energy for F3330 and AN125 due to charge screening, while AN910 saw an increase, and these values increased further at 4.36% NaNO3. MD simulations revealed that the salt ions in the system formed salt bridges between PAM and calcite, indicating that the adhesion and interaction energy observed from AFM are likely to be the net balance between PAM charged group screening and salt bridging by the salt ions present. Salt ions with larger bare radii and smaller hydrated radii were shown to form stronger salt bridges.

Atomic Force Microscopy of Hydrolysed Polyacrylamide Adsorption onto Calcium Carbonate.

In this work, the interaction of hydrolysed polyacrylamide (HPAM) of two molecular weights (F3330, 11-13 MDa; F3530, 15-17 MDa) with calcium carbonate (CaCO3) was studied via atomic force microscopy (AFM). In the absence of polymers at 1.7 mM and 1 M NaCl, good agreement with DLVO theory was observed. At 1.7 mM NaCl, repulsive interaction during approach at approximately 20 nm and attractive adhesion of approximately 400 pN during retraction was measured, whilst, at 1 M NaCl, no repulsion during approach was found. Still, a significantly larger adhesion of approximately 1400 pN during retraction was observed. In the presence of polymers, results indicated that F3330 displayed higher average adhesion (450-625 pN) and interaction energy (43-145 aJ) with CaCO3 than F3530's average adhesion (85-88 pN) and interaction energy (8.4-11 aJ). On the other hand, F3530 exerted a longer steric repulsion distance (70-100 nm) than F3330 (30-70 nm). This was likely due to the lower molecular weight. F3330 adopted a flatter configuration on the calcite surface, creating more anchor points with the surface in the form of train segments. The adhesion and interaction energy of both HPAM with CaCO3 can be decreased by increasing the salt concentration. At 3% NaCl, the average adhesion and interaction energy of F3330 was 72-120 pN and 5.6-17 aJ, respectively, while the average adhesion and interaction energy of F3530 was 11.4-48 pN and 0.3-2.98 aJ, respectively. The reduction of adhesion and interaction energy was likely due to the screening of the COO- charged group of HPAM by salt cations, leading to a reduction of electrostatic attraction between the negatively charged HPAM and the positively charged CaCO3.

Molecular Dynamics Simulation of Polyacrylamide Adsorption on Calcite.

In poorly consolidated carbonate rock reservoirs, solids production risk, which can lead to increased environmental waste, can be mitigated by injecting formation-strengthening chemicals. Classical atomistic molecular dynamics (MD) simulation is employed to model the interaction of polyacrylamide-based polymer additives with a calcite structure, which is the main component of carbonate formations. Amongst the possible calcite crystal planes employed as surrogates of reservoir rocks, the (1 0 4) plane is shown to be the most suitable surrogate for assessing the interactions with chemicals due to its stability and more realistic representation of carbonate structure. The molecular conformation and binding energies of pure polyacrylamide (PAM), hydrolysed polyacrylamide in neutral form (HPAM), hydrolysed polyacrylamide with 33% charge density (HPAM 33%) and sulfonated polyacrylamide with 33% charge density (SPAM 33%) are assessed to determine the adsorption characteristics onto calcite surfaces. An adsorption-free energy analysis, using an enhanced umbrella sampling method, is applied to evaluate the chemical adsorption performance. The interaction energy analysis shows that the polyacrylamide-based polymers display favourable interactions with the calcite structure. This is attributed to the electrostatic attraction between the amide and carboxyl functional groups with the calcite. Simulations confirm that HPAM33% has a lower free energy than other polymers, presumably due to the presence of the acrylate monomer in ionised form. The superior chemical adsorption performance of HPAM33% agrees with Atomic Force Microscopy experiments reported herein.

Analyzing drop coalescence in microfluidic devices with a deep learning generative model.

Predicting drop coalescence based on process parameters is crucial for experimental design in chemical engineering. However, predictive models can suffer from the lack of training data and more importantly, the label imbalance problem. In this study, we propose the use of deep learning generative models to tackle this bottleneck by training the predictive models using generated synthetic data. A novel generative model, named double space conditional variational autoencoder (DSCVAE) is developed for labelled tabular data. By introducing label constraints in both the latent and the original space, DSCVAE is capable of generating consistent and realistic samples compared to the standard conditional variational autoencoder (CVAE). Two predictive models, namely random forest and gradient boosting classifiers, are enhanced on synthetic data and their performances are evaluated based on real experimental data. Numerical results show that a considerable improvement in prediction accuracy can be achieved by using synthetic data and the proposed DSCVAE clearly outperforms the standard CVAE. This research clearly provides more insights into handling imbalanced data for classification problems, especially in chemical engineering.

Surfactant-laden droplet size prediction in a flow-focusing microchannel: a data-driven approach.

The control of droplet formation and size using microfluidic devices is a critical operation for both laboratory and industrial applications, e.g. in micro-dosage. Surfactants can be added to improve the stability and control the size of the droplets by modifying their interfacial properties. In this study, a large-scale data set of droplet size was obtained from high-speed imaging experiments conducted on a flow-focusing microchannel where aqueous surfactant-laden droplets were generated in silicone oil. Three types of surfactants were used including anionic, cationic and non-ionic at concentrations below and above the critical micelle concentration (CMC). To predict the final droplet size as a function of flow rates, surfactant type and concentration of surfactant, two data-driven models were built. Using a Bayesian regularised artificial neural network and XGBoost, these models were initially based on four inputs (flow rates of the two phases, interfacial tension at equilibrium and the normalised surfactant concentration). The mean absolute percentage errors (MAPE) show that data-driven models are more accurate (MAPE = 3.9%) compared to semi-empirical models (MAPE = 11.4%). To overcome experimental difficulties in acquiring accurate interfacial tension values under some conditions, both models were also trained with reduced inputs by removing the interfacial tension. The results show again a very good prediction of the droplet diameter. Finally, over 10 000 synthetic data were generated, based on the initial data set, with a Variational Autoencoder (VAE). The high-fidelity of the extended synthetic data set highlights that this method can be a quick and low-cost alternative to study microdroplet formation in future lab on a chip applications, where experimental data may not be readily available.

Ensemble latent assimilation with deep learning surrogate model: application to drop interaction in a microfluidics device.

A major challenge in the field of microfluidics is to predict and control drop interactions. This work develops an image-based data-driven model to forecast drop dynamics based on experiments performed on a microfluidics device. Reduced-order modelling techniques are applied to compress the recorded images into low-dimensional spaces and alleviate the computational cost. Recurrent neural networks are then employed to build a surrogate model of drop interactions by learning the dynamics of compressed variables in the reduced-order space. The surrogate model is integrated with real-time observations using data assimilation. In this paper we developed an ensemble-based latent assimilation algorithm scheme which shows an improvement in terms of accuracy with respect to the previous approaches. This work demonstrates the possibility to create a reliable data-driven model enabling a high fidelity prediction of drop interactions in microfluidics device. The performance of the developed system is evaluated against experimental data (i.e., recorded videos), which are excluded from the training of the surrogate model. The developed scheme is general and can be applied to other dynamical systems.

Drying-induced stresses in poroelastic drops on rigid substrates.

We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are reduced to a single thin-film equation for the drop thickness. We find that thin drops experience compressive elastic stresses but the total in-plane stresses are tensile. The mechanical response of the drop is dictated by the initial profile of the solid skeleton, which controls the in-plane deformation, the dominant components of elastic stress, and sets a limit on the depth of delamination that can potentially occur. Our theory suggests that the alignment of desiccation fractures in colloidal drops is selected by the shape of the drop at the point of gelation. We propose that the emergence of three distinct fracture patterns in dried blood drops is a consequence of a nonmonotonic drop profile at gelation. We also show that depletion fronts, which separate wet and dry solid, can invade the drop from the contact line and localize the generation of mechanical stress during drying. Finally, the finite element method is used to explore the stress profiles in drops with large contact angles.

Adsorption of Hydrolysed Polyacrylamide onto Calcium Carbonate.

Carbonate rock strengthening using chemical techniques is a strategy to prevent excessive fines migration during oil and gas production. We provide herein a study of the adsorption of three types of hydrolysed polyacrylamide (HPAM) of different molecular weight (F3330S, 11-13 MDa; F3530 S, 15-17 MDa; F3630S, 18-20 MDa) onto calcium carbonate (CaCO3) particles via spectrophotometry using a Shimadzu UV-2600 spectrometer. The results are compared to different adsorption isotherms and kinetic models. The Langmuir isotherm shows the highest correlation coefficient (R2 > 0.97) with equilibrium parameters (RL) ranging between 0 and 1 for all three HPAMs, suggesting a favorable monolayer adsorption of HPAM onto CaCO3. The adsorption follows pseudo-second order kinetics, indicating that the interaction of HPAM with CaCO3 is largely dependent on the adsorbate concentration. An adsorption plot reveals that the amount of HPAM adsorbed onto CaCO3 at equilibrium increases with higher polymer molecular weight; the equilibrium adsorbed values for F3330S, F3530S and F3630S are approximately 0.24 mg/m2, 0.31 mg/m2, and 0.43 mg/m2, respectively. Zeta potential analysis shows that CaCO3 has a zeta potential of +12.32 mV, which transitions into negative values upon introducing HPAM. The point of zero charge (PZC) is observed at HPAM dosage between 10 to 30 ppm, in which the pH here lies between 9-10.

Continuum-scale modelling of polymer blends using the Cahn-Hilliard equation: transport and thermodynamics.

The Cahn-Hilliard equation is commonly used to study multi-component soft systems such as polymer blends at continuum scales. We first systematically explore various features of the equation system, which give rise to a deep connection between transport and thermodynamics-specifically that the Gibbs free energy of mixing function is central to formulating a well-posed model. Accordingly, we explore how thermodynamic models from three broad classes of approach (lattice-based, activity-based and perturbation methods) can be incorporated within the Cahn-Hilliard equation and examine how they impact the numerical solution for two model polymer blends, noting that although the analysis presented here is focused on binary mixtures, it is readily extensible to multi-component mixtures. It is observed that, although the predicted liquid-liquid interfacial tension is quite strongly affected, the choice of thermodynamic model has little influence on the development of the morphology.

Surface Topography Effects on Pool Boiling via Non-equilibrium Molecular Dynamics Simulations.

In this work, we investigate nucleate pool boiling via non-equilibrium molecular dynamics simulations. The effect of nano-structured surface topography on nucleation and transition to a film-like boiling regime is studied at the molecular scale, by varying the cavity aspect ratio, wall superheat, and wettability through a systematic parametric analysis conducted on a Lennard-Jones (LJ) system. The interplay of the aforementioned factors is rationalized by means of a classical nucleation theory-based model. The solid surface is heated uniformly from the bottom in order to induce the nanobubble nucleation. Insight into the cavity behavior in heat transfer problems is achieved by looking at temperature and heat flux profiles inside the cavity itself, as well as at the time of nucleation, for different operating conditions. The role of the cavity size in controlling the vapor embryo formation is highlighted, and its dependence on the other investigated parameters is summarized in a phase diagram. Our results show that heterogeneity at the nanoscale plays a key role in determining pool boiling heat transfer performance, suggesting a promising approach to optimize nanostructured surfaces for energy and thermal management applications.

Film Control to Study Contributions of Waves to Droplet Impact Dynamics on Thin Flowing Liquid Films.

Droplet impact is a very common phenomenon in nature and attracts attention due to its aesthetic fascination and wide-ranging applications. Previous studies on flowing liquid films have neglected the contributions of spatial structures of waves to the impact outcome, while this has recently been shown to have a significant influence on the drop impact dynamics. In this report, we outline a step-by-step procedure to investigate the effect of periodic inlet forcing of a flowing liquid film leading to the production of spatiotemporally regular wave structures on drop impact dynamics. A function generator in connection with a solenoid valve is used to excite these spatiotemporally regular wave structures on the film surface while the impact dynamics of uniform-sized droplets are captured using a high-speed camera. Three distinct regions are then studied; viz. the capillary wave region preceding the large wave peak, the flat film region, and the wave hump region. The effects of important dimensionless quantities such as film Reynolds, drop Weber and Ohnesorge numbers parameterized by the film flow rate, drop speed, and drop size are also examined. Our results show interesting, hitherto undiscovered dynamics brought about by this application of film inlet forcing of the flowing film for both low and high inertia drops.

Moving Contact Lines: Linking Molecular Dynamics and Continuum-Scale Modeling.

Despite decades of research, the modeling of moving contact lines has remained a formidable challenge in fluid dynamics whose resolution will impact numerous industrial, biological, and daily life applications. On the one hand, molecular dynamics (MD) simulation has the ability to provide unique insight into the microscopic details that determine the dynamic behavior of the contact line, which is not possible with either continuum-scale simulations or experiments. On the other hand, continuum-based models provide a link to the macroscopic description of the system. In this Feature Article, we explore the complex range of physical factors, including the presence of surfactants, which governs the contact line motion through MD simulations. We also discuss links between continuum- and molecular-scale modeling and highlight the opportunities for future developments in this area.

Bulk viscosity of molecular fluids.

The bulk viscosity of molecular models of gases and liquids is determined by molecular simulations as a combination of a dilute gas contribution, arising due to the relaxation of internal degrees of freedom, and a configurational contribution, due to the presence of intermolecular interactions. The dilute gas contribution is evaluated using experimental data for the relaxation times of vibrational and rotational degrees of freedom. The configurational part is calculated using Green-Kubo relations for the fluctuations of the pressure tensor obtained from equilibrium microcanonical molecular dynamics simulations. As a benchmark, the Lennard-Jones fluid is studied. Both atomistic and coarse-grained force fields for water, CO2, and n-decane are considered and tested for their accuracy, and where possible, compared to experimental data. The dilute gas contribution to the bulk viscosity is seen to be significant only in the cases when intramolecular relaxation times are in the µs range, and for low vibrational wave numbers (<1000 cm-1); This explains the abnormally high values of bulk viscosity reported for CO2. In all other cases studied, the dilute gas contribution is negligible and the configurational contribution dominates the overall behavior. In particular, the configurational term is responsible for the enhancement of the bulk viscosity near the critical point.

Impact of droplets on immiscible liquid films.

The impact of droplets on liquid films is a ubiquitous phenomenon not only in nature but also in many industrial applications. Compared to the widely-studied impact of droplets on films of identical fluids, the impact of droplets on immiscible films has received far less attention. In the present work, we show using high-speed imaging that immiscibility has a profound effect on the impact dynamics. The impact of a water droplet on an oil film leads to the formation of a compound crown followed by a central jet, whereas that of an oil droplet on a water film results in rapid spreading on the film surface driven by a large, positive spreading factor. In the former scenario, the central jet occurs due to the severe stretching of the droplet during the formation of the crown and then the retraction of the droplet by capillarity, which leads to the collision of fluid at the impact point. A model for the elongation dynamics of the central jet is proposed based on energy conservation. The effects of key parameters controlling the impact process are analysed, including the droplet Ohnesorge and Weber numbers, the viscosity ratio, and the dimensionless film thickness. Different impact outcomes are discussed, such as bouncing, deposition, and oscillation of the impact droplet, the formation and collapse of the compound crown, and the formation and tip-pinching of the central jet. This study not only provides physical insights into the impact dynamics, but could also facilitate the control and optimisation of the droplet impact process in a number of applications as highlighted herein.

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. The construction combines primitive objects, such as a cylinder, a plane, and a torus, for instance, using simple geometrical operations. The numerical solutions predicted encompass dripping and jetting, and transitions in flow patterns are observed featuring the formation of drops, 'pancakes', plugs, and jets, over a wide range of flow rate ratios. We demonstrate the fact that vortex formation accompanies the development of certain flow patterns, and elucidate its role in their underlying mechanisms. Experimental visualisation with a high-speed imaging are also carried out. The numerical predictions are in excellent agreement with the experimental data.

Monomer diffusion into static and evolving polymer networks during frontal photopolymerisation.

Frontal photopolymerisation (FPP) is a directional solidification process that converts monomer-rich liquid into crosslinked polymer solid by light exposure and finds applications ranging from lithography to 3D printing. Inherent to this process is the creation of an evolving polymer network that is exposed to a monomer bath. A combined theoretical and experimental investigation is performed to determine the conditions under which monomer from this bath can diffuse into the propagating polymer network and cause it to swell. First, the growth and swelling processes are decoupled by immersing pre-made polymer networks into monomer baths held at various temperatures. The experimental measurements of the network thickness are found to be in good agreement with theoretical predictions obtained from a nonlinear poroelastic model. FPP propagation experiments are then carried out under conditions that lead to swelling. Unexpectedly, for a fixed exposure time, swelling is found to increase with incident light intensity. The experimental data is well described by a novel FPP model accounting for mass transport and the mechanical response of the polymer network, providing key insights into how monomer diffusion affects the conversion profile of the polymer solid and the stresses that are generated during its growth. The predictive capability of the model will enable the fabrication of gradient materials with tuned mechanical properties and controlled stress development.

Droplet impact on flowing liquid films with inlet forcing: the splashing regime.

The impact process of droplets falling obliquely on thin flowing films is studied using a high-speed imaging system with a focus on splashing. Frequency-forcing of the flow rate at the inlet is applied in order to form solitary waves prior to droplet impact. The outcomes associated with impact on targeted regions of the waves are examined; these include the capillary wave region preceding the large wave peak, the flat film region, and the wave hump region. The effect of varying the film flow rate, droplet size, and speed on the splashing regime for each of these regions is elucidated. The results are further compared with those associated with uncontrolled flowing films, and with quiescent films. The present work has demonstrated, for the first time, the contribution made by the spatial structure of waves to the outcome of droplet impact on flowing films.