Mathematical modelling of a pure liquid droplet suspended in a binary atmosphere
The process of spray drying is applied in a number of contexts. One such application is the production of a synthetic rock used for storage of nuclear waste. To establish a framework for a model of the spray drying process for this application, we here develop a model describing evaporation from droplets of pure water, such that the model may be extended to account for the presence of colloid within the droplet. We develop a spherically-symmetric model and formulate continuum equations describing mass, momentum, and energy balance in both the liquid and gas phases from first principles. We establish appropriate boundary conditions at the surface of the droplet, including a generalised Clapeyron equation that more accurately describes the temperature at the surface of the droplet. To account for experiment design, we introduce a simplified platinum ball and wire model into the system using a thin wire problem. The resulting system of equations is transformed in order to simplify a finite volume solution scheme. The results from numerical simulation are compared with data collected for validation, and the sensitivity of the model to variations in key parameters, and to the use of Clausius-Clapeyron and generalised Clapeyron equations, is investigated. Good agreement is found between the model and experimental data, despite the simplicity of the platinum phase model.
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|Item Type:||Working Paper|
|Keywords:||droplet evaporation, sol gel, spray drying, mathematical model, transport phenomena|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Applied Mathematics not elsewhere classified (010299)|
|Divisions:||Current > Schools > School of Mathematical Sciences|
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2012 [please consult the author]|
|Deposited On:||28 Aug 2012 08:51|
|Last Modified:||05 Sep 2013 18:32|
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