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Background

            The overall goal of this project is to experimentally investigate the thermal and mass transport processes and film instability of evaporating hydrocarbon films.  Film evaporation involves a complex coupling between thermal and mass diffusion and the bulk flow (convection) of both the liquid and vapor phases.  Film instabilities may induce internal flows in the film and increase the interfacial surface area available for evaporation. Through systematic experimentation during which the relative influences of the transport processes and fluid motion are controlled, this project will provide fundamentally new understanding of the evaporation process and provide much needed experimental data for evaluating numerical and analytical models.

            Various experimental techniques including schlieren imaging, infrared spectroscopy, computerized tomography and gravimetric analysis will be applied to measure the mass and transient composition of both the evaporating film and the vapor surrounding it. The experimental setups will offer the capability to adjust the relative importance of the thermal and mass transport processes by controlling the substrate and initial film temperatures; and the pressure, temperature, and composition of the ambient gas.

Research Progress

            During the 2009-2010 reporting period, we worked to better understand the relative effects of vapor phase convection and diffusion on the evaporation rate of pinned hydrocarbon films of various sizes. We wanted to address what appeared to be a potential discrepancy over the role of vapor phase convection in the evaporation of films that are in a quiescent environment. Previously, we had conducted a series of experimental investigations which suggested that buoyancy-induced convection likely has a significant effect on the evaporation rate of hydrocarbon films. Other researchers found that the evaporation rate was limited by the rate of vapor diffusion, with no influence of convection, and showed that in this case, the evaporation rate is proportional to the diameter of the contact line around the perimeter of the film [1-3]. However, there are two big differences between our previous experiments and the diffusion-limited experiments, our film was much larger and the molar mass of the components we studied are significantly greater. Therefore, we initiated an experimental study in which we measured the evaporation rates of pinned hydrocarbon films of various sizes. A set of four hydrocarbons was selected for which the equilibrium vapor pressure varied by a factor of almost four.  Three of the hydrocarbons (3-methylpentane, hexane, and cyclohexane) were chosen because they are isomers, or nearly so, and the fourth hydrocarbon (heptane) was chosen to extend the range of equilibrium vapor pressures. Our goal is to determine how the size of the film affects the relative influence of diffusion and buoyancy-induced convection on the evaporation rate. As the size increases, is there a transition in the balance of the transport mechanisms which changes the size dependence of the evaporation rate from being proportional to the film perimeter to being proportional to the film area, as would be expected for a large film under forced convection? Does the density of the vapor-air mixture above the film control the transition, if such a transition exists?

            Our investigation involved gravimetric and imaging techniques to measure the evaporation rate. Additionally, we are developing a method to measure the vapor concentration distribution above the film and to quantify the rate of diffusive vapor transport. The gravimetric experiments used an analytical balance to measure the changing mass of an evaporating film. For small films, shadowgraph imaging was used to measure the evaporation rate because the balance's mass resolution coupled with the relatively slow evaporation rate increased the scatter in the measured values.

            For all of the experiments, the film was located in an enclosure to prevent room drafts from disturbing the initially quiescent environment. The films were generated by injecting liquid on a raised, circular surface as shown in profile in Fig. 1. The liquid completely covers the circular surface and attaches to its edge and thereby becomes pinned. Eventually, the film volume is reduced through evaporation to the point that the film can no longer cover the surface, at which time the film pulls from the edge. By controlling the size of the raised surface, the radius of the film was varied between 1 and 22 mm.

            The following are preliminary conclusions based on the past year's work:

1.      Diffusive transport alone is insufficient to account for the evaporation rates of the hydrocarbon films we measured.

2.      Convection of the vapor, instigated by the density imbalance between the vapor-air mixture above the film and the surrounding air, contributes to the transport of vapors from the film surface and results in an increase in the evaporation rate.

3.      Convective vapor transport becomes more significant as the film size increases.

4.      Convection appears to have a greater contribution to the evaporation rate for hydrocarbons having a high vapor pressure, which may be due to a greater vapor-air mixture density near the surface of the film.

5.      Even for the smallest films (1 mm radius) the measured evaporation rates were approximately  50% greater than the values computed using the results of a diffusion-limited analysis.

6.      At the largest radius (22 mm) the measured evaporation rates were 4.5 to 5.8 times greater than the values computed using the results of a diffusion-limited analysis.

7.      Over the range of radii from 1 to 22 mm, the evaporation rate was proportional to the radius raised to the power of approximately 1.4, which is between the value for diffusion-limited transport (r¹) and the value for convection dominated transport (limiting case, r²).       

References:

1.      R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, and T.A. Witten, Phys. Rev. E 62(1) (2000), pp. 756-765.

2.      H. Hu and R.G. Larson, J. Phys. Chem. B 106(6) (2002), pp. 1334-1344.

3.      G.J. Dunn, S.K. Wilson, B.R. Duffy, S. David, and K. Sefiane, Colloids Surf. A 323 (2008), pp. 50-55.