16] investigated the effect of substrate conductivity on the evaporation dynamics of a droplet by performing an asymptotic analysis. They found that the evaporation dynamics in the case of pure liquids is very different from that of the binary mixtures. Later [30] extended their previous study of ethanol–water mixtures to the study of the evaporation dynamics.
The reflection of the backlight is also visible as a white spot in the center of the drop. An example of the evolution of the wetting diameter (D) as a function of the normalized time scale (t/te) is shown in Figure 5(a). It can be seen in Figure 6 that the initial equilibrium wetting diameter of the droplet increases with the increase in the volume fraction of ethanol in the binary ethanol–water mixture.
In contrast, the drop of the (E 50% + W 50%) binary mixture enters an evaporation stage with constant contact angle fort/te>0.2 (in the retreating phase). The more complex evolution of the droplet shape for the binary mixture also has an effect on the evaporation rates. This initial hydrophobic behavior of the droplet on the substrate at Ts = 60◦C is visually evident in Figure 11.
It can be seen in Figure 17(a) that the height of the drop decreases rapidly at the early time due to the initial spreading of the drop on the substrate.
THEORETICAL MODELLING OF DROPLET EVAPORATION RATES
Therefore, our analysis assumes that the droplet is isothermal and at the same temperature as that of the substrate throughout the evaporation process. In this study, a modified version of the [42] correlation has been implemented to account for the evaporation of an ethanol droplet from a heated substrate. The convective mass transfer coefficient is usually expressed in terms of the convective Sherwood number, Shc ≡ hmR/D, where Dis is the vapor diffusion coefficient.
The values for the relevant physical properties for ethanol vapour, water vapour, liquid ethanol, liquid water and air are given in table V. When the value of Shcor is assessed based on Eq. 8), the combined evaporation mass transfer rate due to diffusion and convection from the droplet interface can be evaluated from the following relation. The volumetric change can be evaluated by dividing by the density of the corresponding liquids. This transport mass flux, denoted by (dm/dt)t, can be expressed as the air mass flow rate as.
The mass convection of air over the area of the heated substrate covered by the drop can be expressed as. oC) Water (liquid) Water (vapour). The density of ethanol is calculated by assuming that the temperature of the droplet is equal to the substrate temperature. The evaporation dynamics are thus controlled by the vapor-liquid equilibrium of the binary mixtures.
Details of the vapor-liquid equilibrium diagrams for the ideal and non-ideal solutions can be referred from a chemical thermodynamics book (e.g. [48]. We used the isothermal droplet assumption such that the temperature of the entire droplet is the same is as the substrate temperature For a given initial mole fraction based on the droplet composition and at a given substrate temperature, the saturated liquid line provides the vapor pressure of the evaporating binary mixture.
The new molar composition of liquid in the droplet for the next time step is then calculated and used in conjunction with the VLE diagram to estimate the new vapor pressure and composition of the bubble droplet. Excess volume values vary with mixture composition and mixture temperature, and are either tabulated [51] or expressed in terms of Redlich–Kister (R–K) correlations [52] . The theoretically estimated droplet volumes are then compared with the experimentally obtained values of the same.
COMPARISON OF THE THEORETICAL AND EXPERIMENTAL RESULTS
However, for binary mixtures, the droplet volatility and the mole fractions of the components in the evaporating vapor now change with the change in the concentration of liquid water and liquid ethanol within the evaporating droplet. Sample plots of the VLE diagrams of a binary mixture of water and ethanol at Ts = 25 °C and Ts = 60 °C are given in Figures 19 (a) and (b), respectively. Then, the intersection of the bond line with the saturated vapor line provides the molar composition of the newly evaporated vapor [48].
These vapor pressure and vapor phase mixture composition data from the VLE plot are used to calculate the instantaneous mass rate of evaporation of the individual components (water and ethanol) via the relationships developed in Section IV A. The ethanol-water mixture is a non-ideal solution and requires an estimate of the excess molar volume mixing V[51]. The theoretically evaluated histories of the mass fraction of individual components together with the reduction of the normalized mass (m/m0) for (E 50% + W 50%) droplets with t/te are shown in Fig. 20(d).
The VLE diagram shown in Figure 19(a) shows that a decreasing fraction of ethanol in the solution with a dilute ethanol concentration (χe<0.1) leads to a steep drop in the vapor pressure of the solution, which explains the experimentally observed flattening . curvature of the (V/V0) versus t/te curve in the later stages of the droplet lifetime. In Figure 22 we plot the relative contributions of the three evaporation mechanisms for a pure ethanol droplet at Ts= 60◦C. Thus, our experiments provide good validation of the importance of the three above mechanisms in jointly determining the evaporation history of ethanol from a sessile ethanol droplet deposited on a heated substrate.
Specifically, Figure 12 shows that even before the eventual separation of the droplet, the profile of the droplet (E 80% + W 20%) is clearly deviating from the shape of the spherical cap, while the droplet (E 60% + W 40%) maintains the cap profile spherical until the end of evaporation. Thus, while the simple analytical model remains adequate for predictions of steady-state droplet evaporation dynamics of binary solutions on hot substrates, instability-induced oscillations have a non-negligible impact on the evaporation behavior for some (though not all) binary. compositions. If the large concentration of ethanol and the corresponding low surface tension of the droplet interface near the final stages of evaporation are favorable for the greater volatility observed in the final stage and the tendency for the separation of the evaporation droplets (E 80% + W 20%) further investigation warrants.
Nevertheless, again, the simple analytical theory is seen to provide valuable insights into the physics behind some of the more complex dynamics observed in our experiments for binary sessile drops on heated substrates. It should be noted that the normalization of the time axis for ease of visualization obscures the fact that the absolute evaporation times of the (E 50% + W 50%) drop between the substrate at 25◦C and the substrate at 60◦C is widely varied, spanning two orders of magnitude, as can be seen in Figure 14. The ability of the model to accurately predict the evaporation rates over such a wide range of evaporation times and different substrate temperatures indicates its inherent robustness.
SUMMARY
The presence of low "residual" alcohol concentrations during late-stage evaporation of binary alcohol-water mixtures has also been shown in previous studies [30]. Due to the competition between the vaporization rates of the individual components in a binary ethanol-water mixture, we observed opposite dynamics at room and elevated temperatures. It is also found that the droplet height, contact angles and volume decrease monotonically for pure liquid droplets.
The contact angles of the drop during the entire evaporation process appear to be smaller than 90◦atTs= 25◦C. The theoretical modeling of the evaporation flux of droplets is done by combining the diffusion-limited vapor mass flux mechanism [20, 21] with the concentration gradient-induced convective flux model developed by [42]. The theoretical evaporation flux model appears to provide an excellent match with the experimental results for the evolution of the droplet volume over time for both the pure liquid and the binary mixtures.
At Ts= 60◦C, the lifetime of the te point shows a non-monotonic trend with increasing ethanol concentration in the binary mixture, which can be clearly divided into two regions (E<50% and E≥50%). For E<50%, it decreases linearly, but for E≥50%, it does not change much, which we believe is due to the non-ideal behavior of the vapor pressure phase of water-ethanol binary mixtures [37]. However, in the case of the mixture droplet (E 50% + W 50 %), we observe an early spreading phase, an intermediate fixed phase and a delayed removal phase.
In contrast to Ts= 25◦C, atTs= 60◦C, the contact angle of the drop of pure water at the early times is greater than 90◦ (hydrophobic), but for other compositions the contact angle is less than 90◦ (hydrophilic) during the entire evaporation process. We observed a self-similar nature in the variations of the normalized volume (V /V0) versus the normalized time (t/te) curves for different compositions at Ts= 60◦C. It is observed that the droplet lifetime decreases in a logarithmic scale with the increase in substrate temperature from 25◦C to 60◦C.
As expected, at all substrate temperatures, an increasing concentration of ethanol in the ethanol-water binary mixture decreases the droplet lifetime. While previous studies [23] predict four distinct phases in a sessile evaporating droplet of binary ethanol-water mixture at room temperature, our experiments highlight the strong dependence of the duration and intensity of these phases with different substrate temperatures and for different points the compositions of the binary mixture. We observe ripples (interfacial instability) at the liquid-vapor interface of droplets with high concentrations of ethanol (80% ethanol and pure ethanol) at room temperature and elevated substrates.
While the lower surface tension of a droplet with higher ethanol concentration near the final stages of evaporation may be responsible for the strengthening of the intensity of the instability waves that sometimes even lead to droplet breakup, according to the authors this is not yet clearly understood and in the future can be studied. H and R(t) are the height and the wetting radius of the drop; θ is the contact angle; TienT∞ is the temperature at the liquid-vapor interface and the temperature of the environment far away from the droplet, respectively.
