Correlation for the convective and diffusive evaporation of a sessile drop

Abstract

A simple correlation is developed to compute the evaporation rates of sessile drops and small puddles which are evaporating under the influences of both diffusion and natural convection of the vapor-air mixture surrounding the drop. The correlation is based on experiments conducted with eight hydrocarbons, which provide a factor of 16.6 variation in volatility as indicated by the equilibrium vapor pressures, a factor of 3.6 variation in molecular mass, and a factor of 2.2 variation in mass diffusivity, and thus the correlation is applicable for liquids having a broad range of properties. The correlation predicts the evaporation rates to within a root-mean-square (RMS) error of 6.5% over the broad range of conditions. Limitations of the correlation are investigated, and when one of the species is excluded, the RMS error is reduced to 4.9%.There are two main differences between this new correlation and the correlations that have been published previously. The first difference is the new correlation reduces to an expression for diffusion-limited evaporation as the density difference between the vapor-air mixture at the surface of the drop and the ambient air becomes negligible, or when the drop size becomes very small. The second difference is the form of the dependency on the density difference ratio, which in previous correlations is obtained solely through the Rayleigh number (Ra). This new correlation contains a term which represents the influence of natural convection on the evaporation rate and this term provides insight into the nature of the coupling of the diffusive and convective transport of the vapor.

Correlation for sessile drop evaporation over a wide range of drop volatilities, ambient gases and pressures

“…The R/C data had been correlated previously using a modified form of the Sh-Ra relationship given in Eq. 1 [6]. However, this correlation does not adequately predict the evaporation rates over the expanded range of the P/G data.…”

“…Included in Fig. 4 for reference is the RMS relative error of the four-parameter correlation that was previously developed for the R/C data and applied to the set of R/C and P/G data [6]. Clearly, more than four parameters are needed to accurately correlate the very broad range of conditions resulting from varying the ambient gas and pressure in addition to varying the drop size and component.…”

“…The open symbol indicates the error that results when applying the correlation that had been developed for the R/C subset of data, ref. [6], to the combined R/C and P/G data set.…”

“…2. As discussed in [6] the Sh-Ra and the Dalton correlations were applied to a large set of evaporation rate data of hydrocarbons evaporating in air. While neither correlation performed satisfactorily, the Sh-Ra correlation performed much better than the Dalton correlation.…”

“…o As the Rayleigh number tends to zero, suggesting a lack of convection, the correlation should reduce to a purely diffusive evaporation rate. o As was shown to be helpful in our previous correlation [6], we allow the Rayleigh number to be split into its dimensionless components and allow each dimensionless component to influence the correlation independently.…”