(384a) Application Of Light Scattering Techniques For Determining Activity Coeficients From Multicomponent Droplet Evaporation

Authors: 
Ray, A., University of Kentucky
Tu, H., University of Kentucky


Evaporation rate of a multicomponent droplet depends on the transport and thermodynamic parameters, such as diffusion and activity coefficients, and vapor pressures of the constituents. We show that the diffusion coefficients and vapor pressures of the individual components of a multicomponent system can be determined from single component droplet evaporation data. Since the growth or evaporation of a droplet is driven by the chemical potential difference of constituent species between the droplet and the surrounding gas phase, it is possible to obtain activity coefficients of the constituents of the droplet by measuring growth or evaporation rates. Moreover, by manipulating experimental conditions, a single droplet can be subjected to evaporate or grow under unsteady conditions over a wide range of composition; thus activity coefficient data over that range can be determined from a single experiment on one droplet. In addition, a light scattering intensity vs. time spectrum from a droplet undergoing size or composition changes due to evaporation or growth shows a series of resonances (i.e., peaks). The position of a resonance depends on the refractive index of the droplet and the size parameter, which is the ratio of the circumference of the droplet to the wavelength of the incident light, ?Ü. We have shown that the size and the composition of a droplet can be determined with high accuracy from the times at which resonances appear in the spectrum. On the basis of these facts, we have developed a general technique for determining parameters of activity coefficient models from resonances observed during the unsteady evaporation of a multicomponent droplet in a vapor-free atmosphere. The method relies on the fact that for given initial radius and composition we can predict the size and composition of a multicomponent droplet as functions of time if the evaporation rates of pure droplets of the constituents and the activity coefficients as functions of composition are known. In this method we determine the evaporation rates of individual components of the multicomponent droplet from the single component droplet evaporation data, and assume an activity coefficient model and the values of the parameters associated with the model. We predict theoretical resonance appearance times from the Mie theory using the size and composition history predicted by the model. We compare theoretical resonance appearance times with times observed in the experimental spectra from the droplet and estimate optimum values for the model parameters from the minimum in the alignment errors between theoretical and observed resonance appearance times. The reliability of this technique is ensured by the complete agreement between experimental and theoretically calculated spectrum shapes. The technique has been validated with the experimental data from dimethylphthalate (DMP) - dipropylphthalate (DPP), DMP- diethyl-phthalate (DEP), and DMP - dioctyl phthalate (DOP) binary droplets and DMP-DEP-DPP ternary droplets. The technique yields highly reproducible activity coefficient relations and has been used to check whether the parameters of binary activity coefficient models for DMP-DEP, DMP-DPP, and DEP-DPP systems can be extended to ternary system of DMP-DEP-DPP. The accuracy of this technique is reflected by the minimum standard resonance alignment error, which accounts for a relative error of about 0.2% in droplet size or composition.