# Mass Transfer in Multi-Phase Single Particle Systems

This thesis addresses mass transfer in multi-phase single particle systems. By using a novel technique based upon the micropipette, the dissolution of liquid and gas droplets in a liquid medium can be observed. Three classes of experimental systems are observed: pure liquid droplet dissolution in a pure liquid environment, miscible mixture liquid droplet dissolution in a pure liquid environment, and solute-containing liquid droplet dissolution in a pure liquid environment. Experiments on the dissolution of pure droplets of water in n-alcohols and n-alkanes showed that water droplets dissolved ten times faster in the alcohols as compared to in the alkanes. When solubility was taken into account, however, and diffusion coefficients calculated using the Epstein-Plesset equation, diffusion constants for alkanes were twenty five times higher in alkanes than for the corresponding alcohol (for example 12.5 vs 0.5 x 10-8 cm2/s for pentane and pentanol). This difference in rates of diffusion of the single molecules reflects the effect of hydrogen bonding on small solute diffusion, which is expounded upon in Chapter 2.

A model for the dissolution of a droplet containing a mixture, each component of which is soluble in the surrounding liquid medium is presented in Chapter 3. The model is based upon a reduced surface area approximation and the assumption of ideal homogenous mixing : Mass flux (dm_i)/dt=〖Afrac〗_i D_i (c_i-c_s){1/R+1/√(πD_i t)}, where Afraci is the area fraction of component i, ci and cs are the initial and saturation concentrations of the droplet material in the surrounding medium, respectively, R is the radius of the droplet, t is time, and Di is the coefficient of diffusion of component i in the surrounding medium. This model was tested for the dissolution of ethyl acetate and butyl acetate in water and the dissolution of butyl acetate and amyl acetate in water, and was found to provide a good fit. In Chapter 4, a partial differential equation, R^2/D ├ ∂c/∂t┤|_η=(∝η)/D ∂c/∂η+(∂^2 c)/〖∂η〗^2 +2/η ∂c/∂η, is presented for the dissolution of a solute containing droplet in a liquid medium, and shell or bead formation is predicted. In Chapter 5, an application of the solute containing droplet dissolution is presented in which suspensions of glassified protein microspehres are used to improve the injectability of protein based pharmaceuticals. Injectability is related to viscosity, and the viscosity of a suspension may be predicted to follow the Krieger Dougherty equation: (η(Φ))/η_0 =(1-Φ/Φ_m )^(-2.5Φ_m ) , where Φ is the volume fraction of the suspensate, η is the viscosity of the overall suspension, η0 is the viscosity of the suspending fluid, and Φm is the maximum possible volume fraction. Finally, in Chapter 6, various experimental methods used to generate droplets are addressed.

*Mass Transfer in Multi-Phase Single Particle Systems.*Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/3944.

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.

Rights for Collection: Duke Dissertations