The wetting and evaporation dynamics of sessile droplets have gained considerable attention over the last few years due to their relevance to many practical applications, ranging from a variety of industrial problems to several biological systems. Droplets made of binary mixtures typically undergo complex dynamics due to the differential volatility of the considered components and the ensuing presence of thermocapillary effects. For these reasons, many research groups have focused on the evaporation of binary droplets using a variegated set of experimental, numerical, and purely theoretical approaches. Apart from reviewing the state-of-the-art about the existing experimental, analytical, and computational techniques used to study the evaporation dynamics of binary sessile droplets, we also provide some indications about possible future research directions in this specific area.

The study of the wetting and evaporation dynamics of sessile droplets has seen a lot of advancement in recent years due to its relevance in many practical applications ranging from industrial to biological systems [

The present work undertakes an extensive review of wetting and evaporation dynamics for binary fluids. It is structured into five sections, namely the experimental, the semi-empirical (theoretical), the numerical, the influence of surface and fluid properties, and the future scope. The first three sections cover the various methodologies used in studying sessile binary droplets, and the last two sections discuss the effect of various parameters on the droplet dynamics and future scope, respectively. A deep look into this work shows the complexity involved in actually understanding the entire dynamics of sessile droplet evaporation. There are several ways of looking at a droplet evaporation problem based on the application. However, due to the inherent complexity, the physics considered in such an application-oriented approach remains limited and is difficult to generalize from one application to another. Hence, while work on understanding the evaporation of binary mixtures has gained momentum over the years owing to its practical applications, the theoretical models are limited in scope with regards to explaining the complete wetting and evaporation dynamics.

The evaporation of multi-component droplets is encountered in nature in many forms. In multi-component (binary, ternary) liquids, the interaction between different components produces new effects that are not observed in single-component (or pure) liquids. These effects have to be considered a part of the evaporation system. In many practical applications, such as combustion, ink-jet printing, drug delivery, assembly of autonomic fluidic machines, and nanostructure fabrication, binary mixtures are used (see [

Reference | Method | Binary mixture |
---|---|---|

Katre et al. [ |
Experimental (Optical & IR) | Water-Ethanol |

Sefiane et al. [ |
Experimental (Optical) | Water-Ethanol |

Cheng et al. [ |
Experimental (Optical) | Water-Ethanol |

Sefiane et al. [ |
Experimental (Optical) | Water-Methanol |

Wang et al. [ |
Experimental (Optical) | Water-Ethanol |

Shi et al. [ |
Experimental (Optical) | Water-Ethanol |

Innocenzi et al. [ |
Experimental (Interferometry & IR) | Water-Ethanol |

Christy et al. [ |
Experimental (PIV) | Water-Ethanol |

Bennacer et al. [ |
Experimental (PIV) | Water-Ethanol |

Mamalis et al. [ |
Experimental (IR) | Water-Butanol |

Chen et al. [ |
Experimental (IR & Acoustic) | Water-Ethanol, Water-1-Butanol |

Edwards et al. [ |
Experimental (OCT) | Water-Ethanol, Water-n-Butanol |

Gurrala et al. [ |
Experimental & Theoretical (Optical) | Water-Ethanol |

Ozturk et al. [ |
Experimental & Theoretical (Optical) | Water-Ethanol |

Diddens et al. [ |
Experimental & Numerical (micro-PIV & FEM) | Water-Ethanol, Water-Ethanol-anise oil |

Karpitschka et al. [ |
Experimental & Numerical (Optical & FVM) | Water-1,2-butanediol |

Li et al. [ |
Experimental & Numerical (PIV & FEM) | Water-1,2-hexanediol |

Li et al. [ |
Experimental & Numerical (micro-PIV & FEM) | Water-Glycerol, Water-1,2-propanediol |

Diddens et al. [ |
Numerical (FEM) | Water-Glycerol |

Diddens et al. [ |
Numerical (FVM) | Water-Glycerol, Water-Ethanol |

Diddens et al. [ |
Numerical (FEM) | Water-Glycerol, Water-Ethanol |

The motivation of the current work is to review the progress in binary component mixtures and present the challenges and future opportunities. A graphical representation of sessile droplet evaporation, which is similar to the one presented by [

The experimental techniques used in the study of sessile droplets are primarily optical, using a charge-coupled device (CCD)/complementary metal-oxide semiconductor (CMOS) camera to evaluate parameters such as droplet height, wetting radius, and contact angle. The setup typically includes a syringe (with/without a motor control), a suitable substrate on which the droplet is placed, and a CCD/CMOS camera that captures the evaporation of the droplet. The droplet is often illuminated by a light at the back to observe the contour very clearly. Many other techniques, such as infrared (IR) thermography, particle image velocimetry (PIV), and acoustic methods, have been used to study various thermal patterns and flow field visualizations, which are discussed in this section.

Sefiane et al. first studied the evaporation of a binary water-ethanol droplet on a rough polytetrafluoroethylene substrate in a controlled pressure environment [

The hydrothermal waves (HTWs) are traveling waves that are induced by thermal effects in the liquid. The thermal instability in sessile droplets can be experimentally observed using two techniques, viz. infrared thermography and laser refracted shadowgraphy [

The process of binary droplet evaporation is complex because the components exhibit different volatilities in the mixture, leading to Marangoni convection and HTWs [

Christy et al. [

The optical and infrared methods give macroscopic information about the phenomenon at the liquid-gas interface (drop surface). In contrast, acoustics-based methods also enable tracking of exchange mechanisms at the local interface, i.e., the liquid-solid interface at the bottom of the drop. Chen et al. [

Edwards et al. [

Recently, Ozturk et al. [

The droplet is allowed to evaporate for a known time and sucked into the syringe from the closed cell through a rubber septum, and the refractive index is determined rapidly by the refractometer.

A fresh drop of the same composition and volume is again placed and allowed to evaporate for a longer time, and the process is repeated to find the concentration of ethanol at various times throughout the evaporation.

For a 25% ethanol droplet by weight, the total evaporation process took about 80 min, but refractive index measurement could be made up to 48 min due to insufficient volume of the drop. For a 50% ethanol by weight, drop measurements were made up to 24 min. The measured refractive index at different times of binary drop is compared with the known values of refractive index (measured at the beginning) to obtain the bulk concentration of ethanol in the binary droplet. This experimentally obtained concentration of ethanol is used in their theoretical modeling, which is discussed in Section 3.5.

To understand the physics of the evaporation dynamics, several researchers have worked and developed theoretical models related to droplet wetting, dimensions of the deposit pattern, and evaporation rate. In general, to understand the dynamics very clearly, the numerical models (which have their limitations discussed in Section 4) prove more effective. However, the theoretical models are extremely useful in engineering applications given their simplicity compared to numerical models. The earlier theoretical models (for example [

In this section, our aim is to discuss the recent developments in the analytical methods used to model the evaporation of sessile binary droplets and present the challenges further. As several models are already devoted to the evaporation of single component (pure) droplets at room temperature (ambient condition maintained at 20°C–25°C) [

Assuming the shape of the droplet during the evaporation process is of a spherical cap, the experimental droplet volume is calculated as

where

Throughout the evaporation process, the droplet is considered to be isothermal and at the same temperature as the substrate, i.e., T_{i} = T_{s} (see

The evaporation rate for a pure droplet modeled by considering only diffusion is given by Hu et al. [

where

The steady-state diffusion model, although satisfactory in predicting the evaporation of the water droplet, under-predicts the evaporation rate of the pure ethanol droplet at

The evaporation mass transport rate due to the free convection can be expressed as

where

Neglecting the Stefan flow, the total mass transport rate is given by

where

However, practically the diffusion and convection phenomena occur simultaneously, and the combined mass transfer rate is calculated using the combined Sherwood number. The Sherwood numbers for the convective mass transfer and diffusion are defined as

Here,

where

Note:

In the case of a sessile droplet on a heated substrate, the temperature gradient results in free air convection. The associated transport mass flux

where

Here,

Considering the contributions from the diffusion, convection and passive transport, the mass evaporation rate of ethanol from the substrate at elevated temperatures is given by

From this expression,

For binary droplets, the volatility and the component mole-fractions in the evaporating vapor varies with the concentration of liquid water and liquid ethanol and is governed by the vapor-liquid equilibrium (VLE) of the binary mixtures.

The mass of the droplet,

where

, respectively.

The mole fractions of water,

Being a non-ideal solution, the ethanol-water mixture requires an estimation of the excess molar volume of mixing

Using

As mentioned earlier, Ozturk et al. [

The volume of the binary droplet

where

where

The theoretical models presented above and also in all related studies, to the best of our knowledge are mostly backed by experimental evidence. In the case of pure fluids, the limitations exist with certain assumptions, such as the contact angle and uniform surface temperature. For example, in calculating the rate of evaporation (

where,

wherein

It was also evident that at room temperature, the diffusion-driven mechanism dominates, and therefore the simple diffusion model predicts the mass transfer accurately for both pure and binary liquids (as observed from

From a physical perspective, an evaporating multi-component droplet in a host gas (example: Air or any controlled medium) involves combined multiphase and multi-component flow, including a phase transition, and therefore can be modeled in several ways. A complete description of this process should necessarily draw from various fields of fluid mechanics, thermodynamics, as well as some concepts in the field of chemistry.

The process of droplet evaporation is a complex phenomenon of diffusion, heat conduction, and Marangoni convection, and the underlying physics which controls these phenomena has been the topic of many recent reviews. For example, Hu et al. [

Recently, Chen et al. [

In the case of multi-component droplets, solutal Marangoni flow exists, which is stronger than the thermal Marangoni effect. The difference in the volatilities of the individual constituents leads to preferential evaporation of one or the other component, and thereby compositional gradients are induced. Since the surface tension varies with composition, a surface tension gradient across the liquid-gas interface can build up and result in a similar Marangoni circulation as in the thermally-driven case. The nature of the resulting flow can be quite different, mostly depending on whether the evaporation process leads to an overall decrease or increase in the surface tension, i.e., whether the more volatile component has a higher or lower surface tension than the less volatile component. In a binary droplet consisting, e.g., of water and glycerol, with water being more volatile and having the higher surface tension, the overall surface tension decreases during the preferential evaporation of water, and the resulting Marangoni flow is usually regular, axisymmetric, and directed towards the position of the lowest evaporation rate of water, i.e., towards the contact line for contact angles above 90° and towards the apex for contact angles below 90° [

Apart from surface tension gradients, i.e., in the interfacial forces, gradients in the mass density, i.e., in the bulk force due to gravity, also can influence the flow by natural convection. Mass density is a function of temperature (like surface tension) and, the in case of multi-component drops, of the composition. So it is possible to capture the thermal and solutal driven natural convection in evaporating droplets. However, most of the studies on droplet evaporation have not considered the natural convection attributing to the fact that natural convection occurs in large spatial dimensions and the small droplet, associated with the small Bond number is dominated by surface tension effect over gravity. Recent studies by Edwards et al. [

Over the last few years, studies show that the relative humidity of moist air also has a significant effect on droplet evaporation [

The numerical models developed in the recent years discussed above present a great challenge and potential in modeling the complexity underlying multi-component droplet evaporation. The discussion in this section indicates that a variety of numerical studies on sessile droplets are available in the literature, including several review articles on pure droplets. Thus, our objective here is to summarize the numerical work on pure droplets and those particularly on binary fluids and give a perspective of the complex high computational requirements involved as more and more considerations come into the picture.

In this section, we focus on the multi-component (binary) droplet evaporation and how the various factors that influence the capillary and Marangoni effects compete and combine to drive the evaporating fluid along different evolutionary trajectories through its lifetime. As mentioned earlier, the wetting behavior of the fluid, substrate system, and other external factors (refer to

The pinning/depinning of the Triple-Phase Contact Lines (TPCL) and contact angle in an evaporating droplet have a significant role to play in the mass transfer and the droplet internal flow. Picknett and Bexon, in 1977, have distinguished two modes of evaporation based on the behavior of the TPCL and the contact angle.

Constant Contact Radius (CCR) mode where the contact radius and thus contact area remains constant throughout the evaporation process and

Constant Contact Angle (CCA) mode, where the contact angle remains constant throughout the evaporation process while the radius of the drop decreases with time [

The observations were made on an evaporating methyl acetoacetate drop placed on a Teflon (polytetrafluoroethylene) substrate. It was also observed that a transition from one mode to another during the evaporation changes the liquid drop shape. The TPCL moves in steps, maintaining CCR mode (pinned phase) for a short time, and quickly moves into a new position. A Stick-slip (SS) mode [

Birdi et al. [

With the addition of another component in the fluid, as in the case of binary droplets, the prediction of these modes gets more complicated. Gurrala et al. [

He et al. [

It is evident that the binary components have a definite impact on the wettability, and with elevated substrate temperatures, the dynamics get even interesting. Added to this, Katre et al. [

Droplets formed by water-rich binary mixtures such as alcohol and water have been extensively studied in the last decade [

As mentioned earlier, several researchers have used infrared visualization techniques to study thermal patterns. Considerable literature already exists on single-component (pure fluid) droplets, but IR visualization in multi-component droplets still has a lot of potential. To the best of our knowledge, IR visualization on multi-component droplets is still qualitatively analyzed and not quantitatively in terms of the surface temperature. Chen et al. [

Mamalis et al. [

Parsa et al. [

Parsa et al. [

The study of the wetting and evaporation dynamics of sessile droplets has gained considerable attention because of its relevance in many practical applications ranging from industrial to biological systems. A pure fluid drop in itself exhibits many complicated phenomena that can affect droplet physics, such as wetting dynamics, evaporation, internal flow, thermal patterns, and deposition patterns. The dynamics of a binary fluid drop becomes even richer due to the difference between the fluid properties of the components of the binary mixtures. In many practical applications, binary mixtures are used, such as combustion, ink-jet printing, drug delivery, automatic fluidic system assembly, and nanostructure fabrication. Fuel mixtures have been considered by many researchers as alternative fuels, particularly for space applications, and this has been an evolving subject of current research. Several parameters, such as ambient conditions (temperature, humidity, etc.), substrate properties, compositions of the mixture affect the evaporation and wetting dynamics of a sessile droplet. At elevated temperatures, the resultant Marangoni flow inside the droplet and the competition between the evaporation rates of the binary mixtures lead to a nonlinear effect during the evaporation. Much interesting physics and the associated experimental and numerical techniques used to study the evaporation of binary sessile droplets are discussed in this article. Semi-empirical models that take into account the diffusion, convection, passive transport, and Stefan flow contributions to the total evaporation flux are able to adequately predict the binary droplet evaporation rates and lifetimes. The variations of the physical parameters, such as droplet height, wetting radius, evaporation rates, and lifetimes of the droplets, including the flow and temperature fields, have been investigated. Although many investigations have considered pure (single-component) droplets, the evaporation of binary droplets have received far less attention. Particularly, very few studies have considered PIV and infrared imaging to examine the evaporation of binary fluids due to the difficulties associated with the opacity of binary fluids. It is also difficult to perform numerical simulations for binary droplets. Newer experimental methods to track the concentration of one component [

The authors sincerely thank the anonymous reviewers for their helpful suggestions.