Spreading of aqueous surfactant solutions on oil substrates: Superspreaders vs non-superspreaders.

HYPOTHESIS: The question of why aqueous solutions of some surfactants demonstrate a rapid spreading (superspreading) over hydrophobic solid substrates, while solutions of other similar surfactants do not, has no definitive explanation despite numerous previous studies. The suggested hypothesis for this study assumes that once the spreading coefficient of surfactant is positive, there is a concentration range for solutions of any surfactant which demonstrates rapid spreading. As it is impossible to calculate spreading coefficients for solid substrates, we compare the spreading performance of known superspreaders and non-superspreaders on liquid (oil) substrate. EXPERIMENTS: The kinetics of spreading of aqueous solutions of a series of branched ionic surfactants and non-ionic trisiloxane surfactants on two liquid substrates was studied and compared with the spreading of a surfactant-free liquid, silicone oil. Both dynamic and equilibrium spreading coefficients were calculated using measured surface and interfacial tensions. FINDINGS: There is no difference in spreading rate on liquid substrate between solutions of surfactants proven as superspreaders (while spreading on solid substrate) or non-superspreaders. A rapid spreading (superspreading) with the characteristic rate of spreading O(102-103) mm2/s occurs if the dynamic spreading coefficients exceeds the positive threshold value. If the dynamic spreading coefficient is negative or slightly positive, complete wetting still occurs, but the spreading is slow with the spreading rate is O(1) mm2/s. Spreading exponents for surfactant solutions in the rapid spreading regime are considerably larger than for the surfactant-free liquid. A number of spreading and dewetting patterns were observed depending on the surfactant type, its concentration and substrate.

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.

Review of the role of surfactant dynamics in drop microfluidics.

Surfactants are employed in microfluidic systems not just for drop stabilisation, but also to study local phenomena in industrial processes. On the scale of a single drop, these include foaming, emulsification and stability of foams and emulsions using statistically significant ensembles of bubbles or drops respectively. In addition, surfactants are often a part of a formulation in microfluidic drop reactors. In all these applications, surfactant dynamics play a crucial role and need to be accounted for. In this review, the effect of surfactant dynamics is considered on the level of standard microfluidic operations: drop formation, movement in channels and coalescence, but also on a more general level, considering the mechanisms controlling surfactant adsorption on time- and length-scales characteristic of microfluidics. Some examples of relevant calculations are provided. The advantages and challenges of the use of microfluidics to measure dynamic interfacial tension at short time-scales are discussed.

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.

Mass Transfer Accompanying Coalescence of Surfactant-Laden and Surfactant-Free Drop in a Microfluidic Channel.

The coalescence of two different drops, one surfactant-laden and the other surfactant-free, was studied under the condition of confined flow in a microchannel. The coalescence was accompanied by penetration of the surfactant-free drop into the surfactant-laden drop because of the difference in the capillary pressure and Marangoni flows causing a film of surfactant-laden liquid to spread over the surfactant-free drop. The penetration rate was dependent on the drop order, with considerably better penetration observed for the case when the surfactant-laden drop goes first. The penetration rate was found to increase with an increase of interfacial tension difference between the two drops, an increase of flow rate and drop confinement in the channel (for the case of the surfactant-laden drop going first), an increase of viscosity of the continuous phase, and a decrease of viscosity of the dispersed phase. Analysis of flow patterns inside the coalescing drops has shown that, unlike coalescence of identical drops, only two vortices are formed by asymmetrical coalescence, centered inside the surfactant-free drop. The vortices were accelerated by the flow of the continuous phase if the surfactant-laden drop preceded the surfactant-free one, increasing the rate of penetration; the opposite was observed if the drop order was reversed. The mixing patterns on a longer time scale were also dependent on the drop order, with better mixing being observed for the case when the surfactant-laden drop goes first.

Effect of soluble surfactants on pinch-off of moderately viscous drops and satellite size.

HYPOTHESIS: Surfactant redistribution in a liquid bridge close to drop detachment depends on competition between the bridge deformation rate and surfactant equilibration rate. Surfactant effect can be different in situations when diffusion coefficient changes independently of thinning kinetics or in line with it. Using moderately viscous liquids should allow both situations to be explored experimentally. EXPERIMENTS: Formation of liquid drops at the tip of capillary is studied experimentally for silicone oils and for surfactant-laden and surfactant-free water/glycerol mixtures of moderate viscosity with particular attention to the kinetics of liquid bridge close to pinch-off and formation of satellite droplets. FINDINGS: Effect of surfactant depends on the dynamic regime of the bridge thinning. In the presence of surfactant, inertial kinetics slows down close to pinch-off demonstrating effective surface tension smaller than dynamic surface tension. An acceleration of thinning kinetics caused by depletion of surfactant from the liquid bridge was observed in viscous and visco-inertial regimes. The size of satellite droplets has a maximum versus viscosity; increasing with surfactant concentration at smaller viscosities and decreasing with an increase of surfactant concentration at largest studied viscosity, where inversion of the pinch-off point was observed for surfactant solutions.

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.

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.

Kinetics of Wetting and Spreading of Droplets over Various Substrates.

There has been a substantial increase in the number of publications in the field of wetting and spreading since 2010. This increase in the rate of publications can be attributed to the broader application of wetting phenomena in new areas. It is impossible to review such a huge number of publications; that is, some topics in the field of wetting and spreading are selected to be discussed below. These topics are as follows: (i) Contact angle hysteresis on smooth homogeneous solid surfaces via disjoining/conjoining pressure. It is shown that the hysteresis contact angles can be calculated via disjoining/conjoining pressure. The theory indicates that the equilibrium contact angle is closer to a static receding contact angle than to a static advancing contact angle. (ii) The wetting of deformable substrates, which is caused by surface forces action in the vicinity of the apparent three-phase contact line, leading to a deformation on the substrate. (iii) The kinetics of wetting and spreading of non-Newtonian liquid (blood) over porous substrates. We showed that in spite of the enormous complexity of blood, the spreading over porous substrate can be described using a relatively simple model: a power low-shear-thinning non-Newtonian liquid. (iv) The kinetics of spreading of surfactant solutions. In this part, new results related to various surfactant solution mixtures (synergy and crystallization) are discussed, which shows some possible direction for the future revealing of superspreading phenomena. (v) The kinetics of spreading of surfactant solutions over hair. Fundamental problems to be solved are identified.

Effect of Soluble Surfactants on the Kinetics of Thinning of Liquid Bridges during Drops Formation and on Size of Satellite Droplets.

The results of an experimental study on thinning and breakage of liquid bridges during detachment of a drop from the tip of a capillary are presented for a series of surfactant solutions (including cationic, anionic, and nonionic surfactants) over a broad range of molecular masses, values of critical micelle concentration, and concentrations. The used experimental protocol revealed that the kinetics of the bridge thinning depends much more on the dynamics of adsorption at the surface of the drop before it destabilizes, rather than on the depletion of surfactant from the surface of the thinning bridge due to its stretching as the instability develops. The kinetics of the bridge thinning and the size of satellite droplets formed after the bridge breakage depend considerably on the surfactant concentration and the value of critical micelle concentration. It is proposed that the dynamic surface tension on the time scale of the drop formation can be used as an effective surface tension for the description of the bridge kinetics over the broad range of experimental conditions used.

Current applications of foams formed from mixed surfactant-polymer solutions.

Foams cannot be generated without the use of special foaming agents, as pure liquids do not foam. The most common foaming agents are surfactants, however often for foam stability one active agent is not enough, it is necessary to add other component to increase foam lifetime. Foams on everyday use are mostly made from mixture of different components. Properly chosen combinations of two active ingredients lead to a faster foam formation and increased foam stability. During the last decade polymers (mainly polyelectrolytes and proteins) have become frequently used additives to foaming solutions. Mixtures of surfactants and polymers often demonstrate different foaming properties in comparison to surfactant only or polymer only solutions. The nature of surfactant-polymer interactions is complicated and prediction of resulting foaming properties of such formulations is not straightforward. Properties and foaming of surfactant-polymer mixtures are discussed as well as current applications of foams and foaming agents as foams are widely used in cosmetics, pharmaceutics, medicine and the food industry.

Simultaneous spreading and evaporation: recent developments.

The recent progress in theoretical and experimental studies of simultaneous spreading and evaporation of liquid droplets on solid substrates is discussed for pure liquids including nanodroplets, nanosuspensions of inorganic particles (nanofluids) and surfactant solutions. Evaporation of both complete wetting and partial wetting liquids into a nonsaturated vapour atmosphere are considered. However, the main attention is paid to the case of partial wetting when the hysteresis of static contact angle takes place. In the case of complete wetting the spreading/evaporation process proceeds in two stages. A theory was suggested for this case and a good agreement with available experimental data was achieved. In the case of partial wetting the spreading/evaporation of a sessile droplet of pure liquid goes through four subsequent stages: (i) the initial stage, spreading, is relatively short (1-2 min) and therefore evaporation can be neglected during this stage; during the initial stage the contact angle reaches the value of advancing contact angle and the radius of the droplet base reaches its maximum value, (ii) the first stage of evaporation is characterised by the constant value of the radius of the droplet base; the value of the contact angle during the first stage decreases from static advancing to static receding contact angle; (iii) during the second stage of evaporation the contact angle remains constant and equal to its receding value, while the radius of the droplet base decreases; and (iv) at the third stage of evaporation both the contact angle and the radius of the droplet base decrease until the drop completely disappears. It has been shown theoretically and confirmed experimentally that during the first and second stages of evaporation the volume of droplet to power 2/3 decreases linearly with time. The universal dependence of the contact angle during the first stage and of the radius of the droplet base during the second stage on the reduced time has been derived theoretically and confirmed experimentally. The theory developed for pure liquids is applicable also to nanofluids, where a good agreement with the available experimental data has been found. However, in the case of evaporation of surfactant solutions the process deviates from the theoretical predictions for pure liquids at concentration below critical wetting concentration and is in agreement with the theoretical predictions at concentrations above it.

Evaporation of droplets of surfactant solutions.

The simultaneous spreading and evaporation of droplets of aqueous trisiloxane (superspreader) solutions onto a hydrophobic substrate has been studied both experimentally, using a video-microscopy technique, and theoretically. The experiments have been carried out over a wide range of surfactant concentration, temperature, and relative humidity. Similar to pure liquids, four different stages have been observed: the initial one corresponds to spreading until the contact angle, θ, reaches the value of the static advancing contact angle, θad. Duration of this stage is rather short, and the evaporation during this stage can be neglected. The evaporation is essential during the next three stages. The next stage after the spreading, which is referred to herein as the first stage, takes place at constant perimeter and ends when θ reaches the static receding contact angle, θr. During the next, second stage, the perimeter decreases at constant contact angle θ = θr for surfactant concentration above the critical wetting concentration (CWC). The static receding contact angle decreases during the second stage for concentrations below CWC because the concentration increases due to the evaporation. During the final stage both the perimeter and the contact angle decrease. In what follows, we consider only the longest stages I and II. The developed theory predicts universal curves for the contact angle dependency on time during the first stage, and for the droplet perimeter on time during the second stage. A very good agreement between theory and experimental data has been found for the first stage of evaporation, and for the second stage for concentrations above CWC; however, some deviations were found for concentrations below CWC.

Formation of stable clusters in colloidal suspensions.

The experimental evidence and theoretical explanations of stable cluster formation in colloidal suspensions are reviewed. The clusters form in the intermediate range between a stable suspension built up by singlets and the irreversible coagulation or gelation of the suspension. The stable clusters develop as a result of a balance between competing short range attraction and long range repulsion between colloidal particles or due to reversible flocculation in the shallow secondary potential well. Heteroaggregation in binary colloids can also result in formation of stable clusters.

Colloidal dynamics: influence of diffusion, inertia and colloidal forces on cluster formation.

Computer simulations of colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. Comparison of two models, one taking into account inertial term in Langevin equation and another based on diffusional approximation proposed in [D.L. Ermak, J.A. McCammon, J. Chem. Phys. 69 (1978) 1352], has shown that both models enable the prediction of the correct values of the diffusion coefficient and residence time of particle in a doublet and are therefore suitable to study the dynamics of formation and breakage of clusters in colloidal suspensions. It is shown that the appropriate selection of the time step and taking into account inertia of particles provides also the correct value of the average kinetic energy of each particle during the simulations, what allows to use the model based on full Langevin equations as a reference model to verify the validity of the numerical scheme for simulation using diffusion approximation.