  In this paper, we present a mathematical model and numerical simulation of
the evaporation and drying process of a liquid droplet containing suspended
solids. This type of drying is commonly encountered in manufacturing processes
such as spray drying and spray pyrolysis, which have applications in industries
such as food and pharmaceuticals. The proposed model consists of three stages.
In the first stage, we consider the evaporation of the liquid in the presence
of solid particles. The second stage involves the formation of a porous crust
around a wet core region, with liquid evaporation occurring through the crust
layer. Finally, the third stage involves sensible heating of the dry particle
to reach ambient temperature. To solve the physical models governing these
processes, we use a finite difference method with a moving grid methodology.
This allows us to account for the moving interface between the crust and the
wet core region of the droplet. In this study, we use a non-uniform temperature
model that takes into account the spatial variation of temperature inside the
droplet. We also assess the validity of a uniform temperature model. To
validate our model, we compare it with experimental data on the drying of a
single droplet containing colloidal silica particles. We find that our model
agrees well with the experimental results. We rigorously examine assumptions
made in the model, such as the shape of the solid particles and the continuum
flow of vapor through the porous crust. In addition, we analyze the effects of
drying conditions, such as the velocity, temperature, relative humidity, and
concentration of solid particles, on the drying rate and the final morphology
of the particle. Finally, we develop a regime map that can be used to determine
whether the final particle will be solid or hollow, based on the operating
conditions.
