Correlation for the convective and diffusive evaporation of a sessile drop

TLDR: In this article, 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.

About: This article is published in International Journal of Heat and Mass Transfer.The article was published on 2013-09-01 and is currently open access. It has received 23 citations till now. The article focuses on the topics: Drop (liquid) & Natural convection.

Figures

Figure 2. Comparison of the percentage error in the computed evaporation rates from previously published correlations given by Eq. 1 (Fig. 2a) and Eq. 2 (Fig. 2b). The RMS errors are 12.7% for Eq. 1 and 70.1% for Eq. 2.

Figure 6. Measured and computed evaporation rates of each of the eight species studied as a function of drop size. Measured values are given by the datum symbols and the computed values by the lines. Error bars are included but are smaller than the datum symbols.

Figure 4. Plot of the difference between the measured and diffusion-limited evaporation rates as a function of drop size. The plotted differences are estimates of the convective contribution to the overall evaporation rate.

Figure 3. Plot of the measured evaporation rates as a function of drop size. The evaporation rates are plotted on a logarithmic scale to improve clarity. The measurement variation for each of the plotted values is smaller than the data symbol.

Figure 1. Schematic of a profile view of a sessile drop on the disk-shaped substrate. The drop is attached around the circular periphery of a short platform located at the center of the substrate, and in this way the drop size is maintained during evaporation.

Figure 5. Percentage error in the computed evaporation rate for Version A of the correlation. The RMS error considering all of the data is 6.5%.

Frequently asked questions

Q1. What have the authors contributed in "Correlation for the convective and diffusive evaporation of a sessile drop" ?

The correlation is based on experiments conducted with eight hydrocarbons, which provide a factor of 16. 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. 

Q2. What is the role of evaporation in the application of spray cooling?

Sessile drop evaporation has an important role in many technical applications, including spray cooling, painting and coating, and some lab-on-a-chip designs. 

Q3. Why did Bower and Saylor modify the Sh-Ra relationship?

Due to the relative success of Eq. 1 (despite having one fewer fitting constant) and the fact that this equation contains terms that are important for both diffusion and natural convection, their approach was to modify the Sh-Ra relationship given by Eq. 1 in order to develop an improved correlation that is valid for a broad range of species and drop sizes. 

Q4. What was the effect of venting on the evaporation rates of smaller drops?

Tests conducted with and without venting indicated that the evaporation rates of drops of radius 8 mm and larger reduced when the enclosure was not vented, whereas the evaporation rates of smaller drops were unaffected. 

Q5. What was the purpose of venting the enclosure?

Care was taken to vent the enclosure along the sides at the bottom in order to prevent the build-up of vapor while still isolating the experiment from drafts. 

Q6. What additional terms improves the dependency on the density difference?

One of the additional terms provides a limiting result that is equivalent to diffusion-controlled evaporation, and the other additional term improves the dependency on the density difference. 

Q7. What is the effect of natural convection on the evaporation rate?

The influence of natural convection on the evaporation rate may be estimated with a simplifying assumption that the rates of vapor transport by diffusion and convection are independent and their sum equals the evaporation rate. 

Q8. How was the substrate isolated from drafts in the room?

To isolate the experiments from drafts in the room and to ensure an initially still environment, the substrate was contained in an enclosure of volume approximately 6200 cm3. 

Q9. How many of the four computed values are within 8% of the measured values?

Excluding the methanol data, all but four of the computed values are within ± 8% of the measured values and nearly 60% of the computations have an error less than ± 5%. 

Q10. What is the reason why the dependence on diffusivity is stronger for Version A?

The authors are not certain why the dependence on diffusivity is stronger for Version A, but it may be a compensation for methanol’s very low density difference ratio.