A Brownian motion model to describe a random crystallization of undercooled water dispersed within emulsions. (March 2021) - El-Otmany, Hammou; El Rhafiki, Tarik; Kousksou, Tarik; Zeraouli, Youssef
Abstract: This paper aims to propose a new mathematical model to describe heat transfers during stochastic crystallization of a metastable water dispersed inside an emulsion. This model is a combination between energy equation and nucleation laws. A finite volume method is chosen to solve the energy equation and a Brownian model with unknown parameters is introduced to explain the random behaviour of water crystallization within the emulsion. The inverse method is then used to estimate the unknown parameters for stochastic model by using the experimental temperature obtained from the literature. Finally, we present some numerical results to illustrate the inverse method and to validate our proposed stochastic model. Highlights: Mathematical model to describe heat transfers during stochastic crystallization of a metastable water dispersed inside an emulsion. Modelling of random crystallization of undercooled water droplets dispersed inside an emulsion modelling is challenging due to the combining supercooling effect and simultaneous heat transfer and solidification process. The energy equation was adopted to analyse the heat transfer during the crystallization of water droplets in the emulsion. Inverse method is then used to estimate the unknown parameters for stochastic model by using the experimental temperature obtained from the literature.