Binary Mixture Droplets Research Articles

Beyond-mean-field crossover from one dimension to three dimensions in quantum droplets of binary mixtures

The existence of quantum droplets in binary Bose-Einstein condensate mixtures relies on beyond-mean-field effects, competing with mean-field effects. Interestingly, the beyond-mean-field effects change from repulsive in three dimensions (3D) to attractive in 1D leading to drastically different behaviors. We quantitatively model quantum droplets in the beyond-mean-field crossover from 1D to 3D in the relevant case of an elongated harmonic trap and give realistic numbers for experimental realizations. We identify and quantify two main limiting factors: three-body losses and tiny energy scales. The crossover region is appealing as it offers a trade-off between these two main limitations opening the possibility of observing stable flat-top density profiles, a yet unobserved, characteristic feature of quantum droplets. It would permit testing of beyond-mean-field theories to an unprecedented precision.

Interconnected drying phenomena in nanoparticle laden water-ethanol binary droplets.

Understanding the evaporation of a multi-component droplet has found immense importance in various technological applications. This study investigates the evaporation behaviour of a colloidal binary droplet system comprising of the ethanol-water mixture and polystyrene nanoparticles. The wetting and evaporation dynamics were studied with an emphasis on the collective influence of ethanol and nanoparticle concentrations. The temporal behaviour of the contact angles, shapes and volumes of the droplets was monitored in order to analyse the evaporative behaviour. With increase of ethanol concentrations, the binary droplet volumes were found to decrease nonlinearly with time. Ethanol being more volatile evaporated in the initial stage. Towards the end of the evaporation process, the evaporation characteristics mimics the behaviour of pure water. Our study shows that the initial contact angle decreases monotonically with increased concentration of ethanol in the mixture. The contact angle is maximum for a particular nanoparticle concentration. Droplets with higher ethanol concentration show higher wettability which in its turn is maximum for low nanoparticle concentrations. This trend shows the interconnected effect of ethanol and nanoparticle concentrations on evaporation. Rim width of the final deposition pattern increases with nanoparticle concentration although it is almost independent of ethanol concentration. Finally, it is noticed that fast evaporation of a relatively more volatile component in a binary mixture droplet leads to nanoparticle segregation for low nanoparticle concentrations. Thus for binary mixtures, the evaporation of the more volatile component, ethanol for our case, offers characteristic differences in the resulting evaporation dynamics from that of pure water which finds applicability for multi-component evaporation processes.

Wettability model for water-ethanol binary mixture droplet on roughened low-surface-energy solids

Wettability of a droplet on rough solid surface exhibits complex behavior compared with a droplet on smooth solid surface. On a hydrophilic / hydrophobic solid substrate, hydrophilicity / hydrophobicity of a droplet changes as the surface roughness of the solid substrate varies. This kind of wettability is mainly discussed on the basis of Wenzel and Cassi-Baxter models where the wettability of droplets on roughened surface is analyzed by the concept of roughness ratio and contact area fraction. However, in an actual situation, it is very difficult to quantify the structure of the roughened surface and the contact area between liquid and solid surface strictly. In the present study, wettability of water-ethanol binary mixture droplet on roughened low-surface-energy solid is experimentally investigated in order to understand the wetting behavior in wide range of surface tension of liquid. A simple morphological model to quantify the surface roughness and critical surface tension of roughened solid surface is proposed. In addition, analytical model to predict the wettability on roughened solid surface is developed on the basis of the concept of adsorption of liquid molecules at solid–liquid interface, which can be applied to wetting behavior on both hydrophilic and hydrophobic roughened solid substrates.

Quantitative analysis of contact line behaviors of evaporating binary mixture droplets using surface plasmon resonance imaging

A sessile binary mixture droplet (BMD) has a relatively simple geometry; it is in the shape of a spherical cap. However, the contact line motion of a BMD during evaporation shows complex transient behavior that cannot be modeled using the current droplet evaporation model. The present study aims to quantitatively investigate the influence of initial ethanol concentrations on the contact line dynamics of an ethanol-water BMD. We use surface plasmon resonance imaging (SPRi) to simultaneously measure contact line motion and ethanol concentration during BMD evaporation. The visualization results show that non-monotonic contact line motions during evaporation can be subdivided into three stages: I) an initial spreading stage, II) a rapid sliding stage, and III) a moderate sliding stage. Results show behavior that is quite different from the typical motion of an evaporating DI water droplet, i.e., a simple pinning-depinning contact line motion. A weighted ethanol flux is newly introduced to consider the effect of spatial and temporal evaporative flux on the complex sliding motion of a BMD. Moreover, the weighted ethanol flux is quantitatively correlated with the receding velocity of the contact line in stage II.

Three-dimensional particle tracking velocimetry using shallow neural network for real-time analysis

Three-dimensional particle tracking velocimetry (3D-PTV) technique is widely used to acquire the complicated trajectories of particles and flow fields. It is known that the accuracy of 3D-PTV depends on the mapping function to reconstruct three-dimensional particles locations. The mapping function becomes more complicated if the number of cameras is increased and there is a liquid-vapor interface, which crucially affect the total computation time. In this paper, using a shallow neural network model (SNN), we dramatically decrease the computation time with a high accuracy to successfully reconstruct the three-dimensional particle positions, which can be used for real-time particle detection for 3D-PTV. The developed technique is verified by numerical simulations and applied to measure a complex solutal Marangoni flow patterns inside a binary mixture droplet.

Evaporation of ethanol-water sessile droplet of different compositions at an elevated substrate temperature

We experimentally investigate the evaporation dynamics of sessile droplets with different compositions of ethanol-water binary mixture at different substrate temperatures. At room temperature, a binary droplet undergoes two distinct evaporation stages unlike only the pinned stage evaporation for pure droplets. In the binary droplets, the more volatile ethanol evaporates faster leading to a nonlinear trend in the evaporation process. At elevated substrate temperature, we observed an early spreading stage, an intermediate pinned stage and a late receding stage of evaporation. Increasing the substrate temperature decreases the lifetime of binary droplets rapidly. At high substrate temperature, we found that the lifetime of the droplet exhibits a non-monotonic trend with the increase in ethanol concentration in the binary mixture, which can be attributed to the non-ideal behaviour of water-ethanol binary mixtures. Interestingly, the evaporation dynamics for different compositions at high substrate temperature exhibits a self-similar trend showing a constant normalised volumetric evaporation rate for the entire evaporation process. This indicates that the evaporation dynamics of a binary droplet of a given composition at high substrate temperature is equivalent to that of another pure fluid with a higher volatility at room temperature. The evaporation rates of pure and binary droplets at different substrate temperatures are compared against a theoretical model developed for pure and binary mixture droplets. The model predictions are found to be quite satisfactory for the steady evaporation phase of the droplet lifetimes.

Drying of Ethanol/Water Droplets Containing Silica Nanoparticles.

The evaporation of colloidal drop on a substrate with a pinned contact line usually results in a ring stain (the so-called coffee-ring effect). In this paper, we present an investigation of the evaporation of sessile picoliter droplets of binary solvent mixtures containing fumed silica nanoparticles (NPs). The internal flows in ethanol/water droplets are suppressed, and a uniform deposit morphology is achieved with a low loading (0.2-0.5 vol %) of hydrophobic fumed silica NPs. The effective control of the particle deposit morphology is based on a rapid sol-gel transition assisted by preferential evaporation of ethanol. For droplets of dilute suspensions, the fumed silica NPs tend to agglomerate and form an elastic network quickly, starting from the region close to the three-phase contact line and below the gas-liquid interface and growing toward the interior of the droplet as the solvents evaporate and the surface descends. Higher silica particle concentrations, lower ethanol concentrations, and weaker Marangoni flows all contribute to the sol-gel transition and hence to the suppression of the coffee-ring effect.

Internal flow near the triple line in sessile droplets of binary mixtures during evaporation at different ambient temperatures

The internal flow of an evaporating droplet is mainly influenced by capillary flow and Marangoni flow, which are affected by many factors including ambient temperature in the gas phase. For binary droplets, the internal flow near the triple line is of critical importance for understanding their evaporation characteristics. In this work, the internal flow near the triple line in evaporative sessile droplets of binary mixtures, including methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, and 1-heptanol of the same mass which were added to deionized water, at different ambient temperatures was experimentally investigated. An evanescent-wave based fluorescence microscope which has a depth of illumination field of about 360 nm was used to obtain the depinning times and near-wall average velocities of the samples. The relationship between the near-wall velocity V and the time t was described by V ∼ (tf − t)−1 for droplets without vortex, and changed to quadratic-functions due to the coexistence of the vortex and depinning phenomena. For droplets without vortex, an equation was derived for quantitatively describing the relationship between the near-wall velocity and the ambient temperature.

Self-bound Bose mixtures

Recent experiments confirmed that fluctuations beyond the mean-field approximation can lead to self-bound liquid droplets of ultra-dilute binary Bose mixtures. We proceed beyond the beyond-mean-field approximation, and study liquid Bose mixtures using the variational hypernetted-chain Euler Lagrange method, which accounts for correlations non-perturbatively. Focusing on the case of a mixture of uniform density, as realized inside large saturated droplets, we study the conditions for stability against evaporation of one of the components (both chemical potentials need to be negative) and against liquid-gas phase separation (spinodal instability), the latter being accompanied by a vanishing speed of sound. Dilute Bose mixtures are stable only in a narrow range near an optimal ratio $\rho_1/\rho_2$ and near the total energy minimum. Deviations from a universal dependence on the s-wave scattering lengths are significant despite the low density.

Direct measurement of selective evaporation of binary mixture droplets by dissolving materials

We investigate experimentally and theoretically how a droplet of a binary mixture evaporates when placed on a solid substrate. Our focus is the limit at which the two liquid components have different vapour pressures. Using physicochemical effects, we directly visualize the selective evaporation of the more volatile component and so document the space and time dependence of the chemical distribution in the droplet. In particular, we observe that a mixture consisting of an organic solvent and deionized water dissolves suspended fluorescent polystyrene particles if the lower volatility organic solvent reaches a critical concentration. Consequently, we show that for a small contact angle ($\unicode[STIX]{x1D703}<\unicode[STIX]{x03C0}/2$) the suspended polystyrene particles begin to disappear from near the contact line, which indicates that the volatile component, here water, evaporates rapidly compared to the other component(s). Finally, we show that a diffusion-dominated model for evaporation of a binary mixture can predict well the experimental results where convective and diffusive mixing effects are negligible, in which case there is significant chemical segregation in the drop.

Evaporation of a suspended binary mixture droplet in a heated flowing gas stream

Studying vaporization of binary mixture liquid droplets as a model system provides useful information for understanding several engineering applications involving multicomponent systems. The present study investigated vaporization behaviour of both polar and non-polar binary droplet systems in hot convective environment using a mathematical model and experiments. A lumped parameter rapid mixing evaporation model accounting for non-ideal solution behaviour and temperature dependent physical properties was presented. The model predicted temporal variation in droplet diameter and temperature were validated against the experimental data for heptane-decane and water-glycerol mixture. Experiments involving the water-glycerol system involved both size and temperature measurement of millimetre-size droplets at constant gas temperature ∼353 K and at free stream gas velocity ∼4.3 m/s. In general, model predictions were in good agreement with the experiments however some deviations in the model prediction were noted at the transition stage specifically for the water-glycerol system which was attributed to the liquid phase diffusional resistance not accounted in the present modelling framework. Inclusion of activity coefficient into the model was shown to have insignificant effect on the evaporation rate in both non-polar and polar systems. Internal motions induced by the external shear flow and internal density difference were quantified. Time scales based on heat transfer (convective heat transfer and thermal diffusion) and mass diffusion accounting for the internal motion were estimated. It was shown that the unsteady heating duration of the droplet fall within the two limits set by the heat transfer and mass diffusion time scales.

Patterns produced by dried droplets of protein binary mixtures suspended in water

Patterns formed by the evaporation of a drop containing biological molecules have provided meaningful information about certain pathologies. In this context, several works propose the study of protein solutions as a model to understand the formation of deposits of biological fluids. Generally, dry droplets of proteins in a saline solution create complex aggregates. Here, we present an experimental study on the formation of patterns produced by the evaporation of droplet suspensions containing a protein binary mixture. We explore the structural aspect of such deposits by using optical and atomic force microscopy. We found that salt is unnecessary for the formation of complex structures such as crystal clusters, dendritic and undulated branches, and interlocked chains. Such structural features allow us to differentiate among protein binary mixtures. Finally, we discuss the potential use of this finding to reveal the presence of a protein suspensions, the folded and unfolded state of a protein, as well as their structural changes.

Patterns from dried water-butanol binary-based nanofluid drops

In this work, the behavior of evaporating binary-based nanofluid sessile droplets deposited on a smooth silicon substrate at different temperatures is explored. The formation of deposition patterns during the evaporation is studied by tracking particle clusters using optical microscopy. Similarly to evaporation of pure water-based nanofluid droplets, three distinctive deposition patterns are left behind the complete evaporation: a relatively uniform coverage pattern (on a nonheated surface); a “dual-ring” pattern at higher temperature, i.e., 81 °C; and a “stick-slip” pattern at 99 °C. Infrared thermography technique was employed to visualize the evolution of thermal patterns on the surface of the drying droplets. Thermal imaging shows that the evaporation of binary mixture droplets can be classified into three regimes. In the first regime, multiple convection vortices can be observed at the droplet interface, corresponding to the chaotic motion of nanoparticles captured by video microscopy. This flow regime is believed to be driven by surface tension gradients arising from local concentration gradients. As evaporation time proceeds, the number of convection vortices decreases in regime I, and a few numbers of those are left in the second regime. The flow slows down and a rapid transition (the second regime) occurs; this is followed by the last regime. At the two highest temperatures of 81 and 99 °C, the end of the transition regime is associated with the existence of two distinctive counter-rotating vortices. For the third regime, the results from both infrared thermography and video microscopy show identical behavior to those of water-based nanofluid droplets at the same substrate temperatures. This reveals that most of the more volatile component (not all) has evaporated after the first two regimes; hence, the solutal Marangoni driven by local concentration gradients is significantly weakened and has no further role in the flow structure in the last regime. Instead, the thermocapillary effect and continuity are the underlying reasons for the internal flow structure of the evaporating droplets during the last regime.

Marangoni Contraction of Evaporating Sessile Droplets of Binary Mixtures.

The Marangoni contraction of sessile drops of a binary mixture of a volatile and a nonvolatile liquid has been investigated experimentally and theoretically. The origin of the contraction is the locally inhomogeneous evaporation rate of sessile drops. This leads to surface tension gradients and thus to a Marangoni flow. Simulations show that the interplay of Marangoni flow, capillary flow, diffusive transport, and evaporative losses can establish a quasistationary drop profile with an apparent nonzero contact angle even if both liquid components individually wet the substrate completely. Experiments with different solvents, initial mass fractions, and gaseous environments reveal a previously unknown universal power-law relation between the apparent contact angle and the relative undersaturation of the ambient atmosphere: θapp ∼ (RHeq – RH)1/3. This experimentally observed power law is in quantitative agreement with simulation results. The exponent can also be inferred from a scaling analysis of the hydrodynamic-evaporative evolution equations of a binary mixture of liquids with different volatilities.

Detailed finite element method modeling of evaporating multi-component droplets

The evaporation of sessile multi-component droplets is modeled with an axisymmetic finite element method. The model comprises the coupled processes of mixture evaporation, multi-component flow with composition-dependent fluid properties and thermal effects. Based on representative examples of water–glycerol and water–ethanol droplets, regular and chaotic examples of solutal Marangoni flows are discussed. Furthermore, the relevance of the substrate thickness for the evaporative cooling of volatile binary mixture droplets is pointed out. It is shown how the evaporation of the more volatile component can drastically decrease the interface temperature, so that ambient vapor of the less volatile component condenses on the droplet. Finally, results of this model are compared with corresponding results of a lubrication theory model, showing that the application of lubrication theory can cause considerable errors even for moderate contact angles of 40°.

Modeling the evaporation of sessile multi-component droplets

We extended a mathematical model for the drying of sessile droplets, based on the lubrication approximation, to binary mixture droplets. This extension is relevant for e.g. inkjet printing applications, where ink consisting of several components are used. The extension involves the generalization of an established vapor diffusion-limited evaporation model to multi-component mixtures. The different volatilities of the liquid components generate a composition gradient at the liquid-air interface. The model takes the composition-dependence of the mass density, viscosity, surface tension, mutual diffusion coefficient and thermodynamic activities into account. This leads to a variety of effects ranging from solutal Marangoni flow over deviations from the typical spherical cap shape to an entrapped residual amount of the more volatile component at later stages of the drying. These aspects are discussed in detail on the basis of the numerical results for water-glycerol and water-ethanol droplets. The results show good agreement with experimental findings. Finally, the accuracy of the lubrication approximation is assessed by comparison with a finite element method.

Microlayered flow structure around an acoustically levitated droplet under a phase-change process.

The acoustic levitation method (ALM) has found extensive applications in the fields of materials science, analytical chemistry, and biomedicine. This paper describes an experimental investigation of a levitated droplet in a 19.4-kHz single-axis acoustic levitator. We used water, ethanol, water/ethanol mixture, and hexane as test samples to investigate the effect of saturated vapor pressure on the flow field and evaporation process using a high-speed camera. In the case of ethanol, water/ethanol mixtures with initial ethanol fractions of 50 and 70 wt%, and hexane droplets, microlayered toroidal vortexes are generated in the vicinity of the droplet interface. Experimental results indicate the presence of two stages in the evaporation process of ethanol and binary mixture droplets for ethanol content >10%. The internal and external flow fields of the acoustically levitated droplet of pure and binary mixtures are clearly observed. The binary mixture of the levitated droplet shows the interaction between the configurations of the internal and external flow fields of the droplet and the concentration of the volatile fluid. Our findings can contribute to the further development of existing theoretical prediction.

Experimental Droplet Study of Inverted Marangoni Effect of a Binary Liquid Mixture on a Nonuniform Heated Substrate.

We present an experimental study on the inversion of the Marangoni effect of a binary mixture droplet under a horizontal temperature gradient. In particular, we studied the dynamics and the evaporation behavior under these conditions. We show that a binary mixture (97% water-3% butanol) droplet has a tendency to migrate to warmer areas, as opposed to spreading in pure fluids. During the evaporation process, we distinguish three stages of evaporation that are correlated to the dynamics of the droplet.

Flow regime and deposition pattern of evaporating binary mixture droplet suspended with particles.

The flow regimes and the deposition pattern have been investigated by changing the ethanol concentration in a water-based binary mixture droplet suspended with alumina nanoparticles. To visualize the flow patterns, Particle Image Velocimetry (PIV) has been applied in the binary liquid droplet containing the fluorescent microspheres. Three distinct flow regimes have been revealed in the evaporation. In Regime I, the vortices and chaotic flows are found to carry the particles to the liquid-vapor interface and to promote the formation of particle aggregation. The aggregates move inwards in Regime II as induced by the Marangoni flow along the droplet free surface. Regime III is dominated by the drying of the left water and the capillary flow driving particles radially outward is observed. The relative weightings of Regimes I and II, which are enhanced with an increasing load of ethanol, determine the motion of the nanoparticles and the formation of the final drying pattern.

Internal Flows and Particle Transport Inside Picoliter Droplets of Binary Solvent Mixtures

Internal Flows and Particle Transport Inside Picoliter Droplets of Binary Solvent Mixtures