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.

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.

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.

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.

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.

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.

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.

Physical insights into the blood-brain barrier translocation mechanisms.

The number of individuals suffering from diseases of the central nervous system (CNS) is growing with an aging population. While candidate drugs for many of these diseases are available, most of these pharmaceutical agents cannot reach the brain rendering most of the drug therapies that target the CNS inefficient. The reason is the blood-brain barrier (BBB), a complex and dynamic interface that controls the influx and efflux of substances through a number of different translocation mechanisms. Here, we present these mechanisms providing, also, the necessary background related to the morphology and various characteristics of the BBB. Moreover, we discuss various numerical and simulation approaches used to study the BBB, and possible future directions based on multi-scale methods. We anticipate that this review will motivate multi-disciplinary research on the BBB aiming at the design of effective drug therapies.

Impact of Droplets on Liquid Films in the Presence of Surfactant.

The impact of droplets on liquid films is ubiquitous in natural and industrial processes, and surfactants can significantly alter the impact process by changing the local surface tension. Here we study the impact of droplets on liquid films in the presence of surfactant using high-speed photography, and reveal the flow pattern by dye-tracing. The effects of the droplet size and speed, and the initial film thickness on the impact process are elucidated. The results show that the flow is significantly affected by adding surfactant to the droplet, the liquid film, or to both phases. In particular, the film dye patterns form concentric circles and flower-shaped structures at low and high droplet Weber numbers, respectively. We also show how surfactant-induced Marangoni stresses modify these flow patterns, and alter the characteristics of the phenomena associated with the impact process, such as the propagation of capillary waves, the evolution of the crown, and the formation of secondary droplets. During the impact of surfactant droplets on thin water films, the Marangoni stresses can be sufficiently strong so as to drive film dewetting.

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.

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.

Bulk advection and interfacial flows in the binary coalescence of surfactant-laden and surfactant-free drops.

This work focuses on the study of bulk flows accompanying the coalescence of two aqueous drops, one containing surfactant and the other surfactant-free, in silicone oils of various viscosities. It is observed that the surfactant-free drop intrudes into the surfactant-laden drop in the form of a penetrating jet whose speed increases and average radius decreases with increasing outer phase viscosity. Mixing patterns within the coalescing drops are due to the force imbalance caused by capillary pressure difference and surfactant-induced Marangoni stresses. The driving force for mixing associated with the difference in interfacial tension between the drops is considerably stronger than that related to the drop size. The long timescale mixing of the drops is driven by rapid interior convection, and the subsequent, slow, diffusive process. Three-dimensional numerical simulations show excellent qualitative and quantitative agreement with the experimental results. The implications of our results to formulation strategies of complex microstructures in practical applications are also discussed.

Evaporation of Sessile Droplets Laden with Particles and Insoluble Surfactants.

We consider the flow dynamics of a thin evaporating droplet in the presence of an insoluble surfactant and noninteracting particles in the bulk. On the basis of lubrication theory, we derive a set of evolution equations for the film height, the interfacial surfactant, and bulk particle concentrations, taking into account the dependence of liquid viscosity on the local particle concentration. An important ingredient of our model is that it takes into account the fact that the surfactant adsorbed at the interface hinders evaporation. We perform a parametric study to investigate how the presence of surfactants affects the evaporation process as well as the flow dynamics with and without the presence of particles in the bulk. Our numerical calculations show that the droplet lifetime is affected significantly by the balance between the ability of the surfactant to enhance spreading, suppressing the effect of thermal Marangoni stresses-induced motion, and to hinder the evaporation flux through the reduction of the effective interfacial area of evaporation, which tend to accelerate and decelerate the evaporation process, respectively. For particle-laden droplets and in the case of dilute solutions, the droplet lifetime is found to be weakly dependent on the initial particle concentration. We also show that the particle deposition patterns are influenced strongly by the direct effect of the surfactant on the evaporative flux; in certain cases, the "coffee-stain" effect is enhanced significantly. A discussion of the delicate interplay between the effects of capillary pressure and solutal and thermal Marangoni stresses, which drive the liquid flow inside of the evaporating droplet giving rise to the observed results, is provided herein.

Wrinkling Measurement of the Mechanical Properties of Drying Salt Thin Films.

We report a time-resolved approach to probe the mechanical properties of thin films during drying and solidification based on surface wrinkling. The approach is demonstrated by measuring the modulus of a ternary system comprising an inorganic salt (aluminum chlorohydrate), a humectant (glycerol), and water across the glassy film formation pathway. The topography of mechanically induced wrinkling of supported films on polydimethylsiloxane (PDMS) is experimentally monitored during mechanical extension and relaxation cycles. Nontrivial aspects of our method include the need to oxidize the (hydrophobic) PDMS surface prior to solution deposition to enable surface wetting, which simultaneously creates a glassy-layer skin, whose wrinkling can contribute to the overall topography. Film drying is studied as a function of solution concentration and time, and a range of pattern morphologies are found: sinusoidal wrinkling, transient double-wavelength wrinkling accompanying film "crust" formation, ridging associated with stress localization, and cracking. We quantify the evolution of the elastic modulus during the sinusoidal wrinkling stage, employing bi- and trilayer models, which are independently confirmed by nanoindentation. The method provides thus a simple and robust approach for the mechanical characterization of out-of-equilibrium thin films.

Surface waves on a soft viscoelastic layer produced by an oscillating microbubble.

Ultrasound-driven bubbles can cause significant deformation of soft viscoelastic layers, for instance in surface cleaning and biomedical applications. The effect of the viscoelastic properties of a boundary on the bubble-boundary interaction has been explored only qualitatively, and remains poorly understood. We investigate the dynamic deformation of a viscoelastic layer induced by the volumetric oscillations of an ultrasound-driven microbubble. High-speed video microscopy is used to observe the deformation produced by a bubble oscillating at 17-20 kHz in contact with the surface of a hydrogel. The localised oscillating pressure applied by the bubble generates surface elastic (Rayleigh) waves on the gel, characterised by elliptical particle trajectories. The tilt angle of the elliptical trajectories varies with increasing distance from the bubble. Unexpectedly, the direction of rotation of the surface elements on the elliptical trajectories shifts from prograde to retrograde at a distance from the bubble that depends on the viscoelastic properties of the gel. To explain these behaviours, we develop a simple three-dimensional model for the deformation of a viscoelastic solid by a localised oscillating force. By using as input for the model the values of the shear modulus obtained from the propagation velocity of the Rayleigh waves, we find good qualitative agreement with the experimental observations.

Superspreading: mechanisms and molecular design.

The intriguing ability of certain surfactant molecules to drive the superspreading of liquids to complete wetting on hydrophobic substrates is central to numerous applications that range from coating flow technology to enhanced oil recovery. Despite significant experimental efforts, the precise mechanisms underlying superspreading remain unknown to date. Here, we isolate these mechanisms by analyzing coarse-grained molecular dynamics simulations of surfactant molecules of varying molecular architecture and substrate affinity. We observe that for superspreading to occur, two key conditions must be simultaneously satisfied: the adsorption of surfactants from the liquid-vapor surface onto the three-phase contact line augmented by local bilayer formation. Crucially, this must be coordinated with the rapid replenishment of liquid-vapor and solid-liquid interfaces with surfactants from the interior of the droplet. This article also highlights and explores the differences between superspreading and conventional surfactants, paving the way for the design of molecular architectures tailored specifically for applications that rely on the control of wetting.

Frontal vitrification of PDMS using air plasma and consequences for surface wrinkling.

We study the surface oxidation of polydimethylsiloxane (PDMS) by air plasma exposure and its implications for the mechanically-induced surface wrinkling of the resulting glass-elastomer bilayers. The effect of plasma frequency (kHz and MHz), oxygen content (from O2 to air), pressure (0.5 ≤ P ≤ 1.5 mbar), as well as exposure time and power, is quantified in terms of the resulting glassy skin thickness h, inferred from wrinkling experiments. The glassy skin thickness is found to increase logarithmically with an exposure time t, for different induction powers p, and all data collapse in terms of a plasma dose, D ≡ p × t. The kinetics of film propagation are found to increase with the oxygen molar fraction yO2 and decrease with the gas pressure P, allowing both the wrinkling wavelength λ and amplitude A to be effectively controlled by gas pressure and composition. A generalised relationship for frontal vitrification is obtained by re-scaling all λ and h data by D/P. A coarse-grained wave propagation model effectively describes and quantifies the process stages (induction, skin formation and propagation) under all the conditions studied. Equipped with this knowledge, we further expand the capabilities of plasma oxidation for PDMS wrinkling, and a wavelength of λ ≈ 100 nm is readily attained with a modest strain εprestrain ≈ 20%.

Modelling the superspreading of surfactant-laden droplets with computer simulation.

The surfactant-driven superspreading of droplets on hydrophobic substrates is considered. A key element of the superspreading mechanism is the adsorption of surfactant molecules from the liquid-vapour interface onto the substrate through the contact line, which must be coordinated with the replenishment of interfaces with surfactant from the interior of the droplet. We use molecular dynamics simulations with coarse-grained force fields to provide a detailed structural description of the droplet shape and surfactant dynamics during the superspreading process. We also provide a simple method for accurate estimation of the contact angle subtended by the droplets at the contact line.

Thermocapillary-driven motion of a sessile drop: effect of non-monotonic dependence of surface tension on temperature.

We study the thermocapillary-driven spreading of a droplet on a nonuniformly heated substrate for fluids associated with a non-monotonic dependence of the surface tension on temperature. We use lubrication theory to derive an evolution equation for the interface that accounts for capillarity and thermocapillarity. The contact line singularity is relieved by using a slip model and a Cox-Voinov relation; the latter features equilibrium contact angles that vary depending on the substrate wettability, which, in turn, is linked to the local temperature. We simulate the spreading of droplets of fluids whose surface tension-temperature curves exhibit a turning point. For cases wherein these turning points correspond to minima, and when these minima are located within the droplet, then thermocapillary stresses drive rapid spreading away from the minima. This gives rise to a significant acceleration of the spreading whose characteristics resemble those associated with the "superspreading" of droplets on hydrophobic substrates. No such behavior is observed for cases in which the turning point corresponds to a surface tension maximum.

Electrostatic suppression of the "coffee stain effect".

The dynamics of a slender, evaporating, particle-laden droplet under the effect of electric fields are examined. Lubrication theory is used to reduce the governing equations to a coupled system of evolution equations for the interfacial position and the local, depth-averaged particle concentration. The model incorporates the effects of capillarity, viscous stress, Marangoni stress, elecrostatically induced Maxwell stress, van der Waals forces, concentration-dependent rheology, and evaporation. Via a parametric numerical study, the one-dimensional model is shown to recover the expected inhomogeneous ring-like structures in appropriate parameter ranges due to a combination of enhanced evaporation close to the contact line, and resultant capillarity-induced flow. It is then demonstrated that this effect can be significantly suppressed via the use of carefully chosen electric fields. Finally, the three-dimensional behavior of the film and the particle concentration field is briefly examined.