Date of Award

Spring 2013

Document Type


Degree Name

Master of Science in Chemical Engineering - (M.S.)


Chemical, Biological and Pharmaceutical Engineering

First Advisor

Edward L. Dreyzin

Second Advisor

Ecevit Atalay Bilgili

Third Advisor

Laurent Simon


A steady-state model of heterogeneous combustion for a spherical particle is developed accounting for the transition regime of heat and mass transfer. The model assumes formation of condensed products and reaction rate controlled by the transport of oxidizer to the particle surface. The model is based on the Fuchs’ limiting sphere approach. Calculations are performed for combustion of zirconium particles of different sizes. Temperature and oxygen concentration profiles are calculated and compared to those predicted by the continuous medium transfer model. It is shown that for particles in the range from 100 nm up to 30 gm heat and mass transfer occur in transition regime. The predictions are also compared with the available experimental data.

For coarse particles, both predicted combustion temperatures and burn rates match respective experimental data when the reaction is assumed to produce zirconium- oxygen solution with an enthalpy of formation reduced compared to that of the stoichiometric ZrO2. A weak effect of particle sizes on their burn times is predicted for small particles, in qualitative agreement with recent experiments. An implementation of time variability accounted for 30% change of particle diameter during particle burning for different particle diameter and the discrepancy is maintained. However, the model underestimates the burn times and overestimates the combustion temperatures for small particles. This discrepancy is likely associated with the finite reaction kinetics at the particle surface that must be accounted for in the future work.

In the heat transfer modeling, additional errors are predicted to be caused by an incorrectly assumed value of the thermal accommodation coefficient of gas molecules on the particle surface. The technique of finding the accommodation coefficient for small metal particles heated to high temperatures is developed and tested for the Zr – Ar system. The optical emission intensity decay times for micron-sized Zr particles heated and cooled in Ar are measured. The emission decay times are interpreted as cooling times. The cooling times are calculated using the two-layer Fuchs’ model. The calculated and measured results are matched by adjusting the value of the thermal accommodation coefficient. Thermal accommodation coefficient is shown to be much smaller than unity; with an estimate of 0.005. It is likely to be changing as a function of the particle size for the 1 – 10 µm particles.