Reports: UR954712-UR9: Deciphering the Coupled Diffusive and Naturally Convective Transport during Hydrocarbon Evaporation
Peter L. Kelly-Zion, PhD, Trinity University
Christopher J. Pursell, Trinity University
This summary of our research during the past year reports on two primary research activities: 1) simultaneous measurements of two vapor concentrations above an evaporating bi-component drop, and 2) assessing the quasi-steady-state assumption for sessile drop evaporation. To appreciate the value of these two projects, some background information regarding our overall research goals and recent results are provided.
In recent years, the focus of our research has been the study of the vapor phase transport during sessile drop evaporation. We have developed a large database of experimental evidence that indicates that the evaporation rates of pure (single-component) drops are limited by the rates of vapor transport for a wide range of conditions. We developed an empirical correlation for the evaporation rates using simple terms representative of diffusive and convective vapor transport which matches our large data set to within an average RMS error of less than 5.2%. The success of the correlation has implications for computational models of sessile drop evaporation. Researchers have developed models to study various details of the evaporation process, e.g. drop surface temperature, contact angle, liquid convection inside the drop, among others, and the general method for validating the models is by comparing the computed evaporation rates to measured evaporation rates. The fact that the evaporation rate may be predicted without consideration of the details occurring at the drop-gas interface or within the drop suggests that the evaporation rate may be an inadequate measure for validating computational models.
For many conditions, we also question the validity of the very common assumption of computational models of sessile drop evaporation that the vapor transport is strictly diffusive. Our measurements of the vapor distribution surrounding a sessile drop differ markedly from what would be expected for a strictly diffusive distribution and strongly indicates that convection plays a significant role for many hydrocarbon drops.
As a consequence of our conclusion that the vapor transport controls the evaporation of pure drops for a wide range of conditions, we believe it is important to be able to measure the vapor distribution and to understand the coupled nature of diffusive and convective transport.
Bi-Component Vapor Phase Measurements
Previously we had developed a technique for measuring the vapor distribution surrounding an evaporating sessile drop using FT-IR spectroscopy and computed tomography. We had applied that technique to measure the vapor distributions of pure drops. During this past year, we worked to extend the technique to enable the simultaneous measurements of the vapor distributions of bi-component drops. By comparing vapor phase measurements of the different components with measurements of liquid phase concentrations in the drop, we expect to develop a better understanding of how the liquid phase and vapor phase transport are interdependent and to determine when or if the transport in one phase limits the evaporation of bi-component drops.
Figure 1 presents nominal vapor concentration values at a location 2 mm above a sessile drop as a function of time. The concentration values are considered nominal because we are still in the process of developing a technique for analyzing the transient spectroscopic data of mixtures. The vapor concentrations of 3-methylpentane (3MP) and isooctane are presented for measurements of a drop containing a 1:1 by mass mixture of the two components and for pure drops of each component.
Differences in the trends in the vapor concentration over time are evident in Fig. 1. The concentration of 3MP at this location from a pure drop is initially approximately constant. In contrast, the concentration of 3MP vapor from the bi-component drop reduces steadily. For isooctane, the vapor concentration from a pure drop remains constant whereas the concentration from a bi-component drop steadily increases. This behavior is consistent with the hypothesis that the surface of the bi-component drop becomes progressively depleted of the more volatile component (3MP) and consequently the drop surface contains more of the less volatile component (isooctane).
Figure 1. Nominal values of the measured vapor concentration 2 mm above the center of a sessile drop. The dashed vertical line indicates the time the drops were deposited.
Assessment of Quasi-Steady-State Assumption
Our evaporation rate measurements of pure drops generally support the common assumption that the evaporation process quickly attains a quasi-steady state. Quasi-steady evaporation is an assumption that we employ in our technique to measure the vapor distribution surrounding pure drops, and we used an expression for steady-state evaporation to develop our correlation for the evaporation rate. As we investigate the details of vapor phase transport, it is important to understand the parameters and implications of the common assumption of quasi-steady evaporation.
To investigate the quasi-steady assumption, a model of transient evaporation was used to explore the effects of changes in the drop geometry and to study different measures of quasi-steadiness, for example when the transient solution for the vapor concentration or for the vapor flux in a given region is nearly equal to the solutions for a steady-state condition. For simplicity, the model assumed that diffusion was the only vapor transport mechanism, which is a common assumption. The results suggest that quasi-steady evaporation does indeed occur relatively quickly, for example within 1.5 s for a large (6 mm radius) methanol drop.
Impact of the Research
This research program has a very large impact on the participating students. During the last year, four undergraduate students participated in the research and learned valuable lessons not only about the physical phenomena we are studying but, more importantly, about how to go about conducting research, i.e. how to think about problems, how to design and conduct experiments, and how to analyze measurement results. All of the students devoted 10 weeks during the summer to the research and thereby gained an intensive research experience.
For the first principal investigator, this PRF supported research is his primary research focus and, therefore, is very important for his continuous development as a researcher and academician. Furthermore, the research has become a prime example of interdisciplinary work at our university, with faculty from Engineering Science, Chemistry, and Mathematics working together.