Modeling and Simulation of the Evaporation and Drying of a Two Component Slurry Droplet

TL;DR

The paper addresses the evaporation and drying of a two-component slurry droplet by developing a three-stage, spherical, transient model solved with a moving-grid method to capture crust formation and core–crust evolution under a binary drying gas. Key contributions include a nonuniform-temperature treatment across all stages, an assessment of solid-particle shape and non-continuum diffusion through crust pores, and a regime map to predict whether the final particle is solid or hollow under various drying conditions; the model is validated against experimental data for colloidal silica droplets and shows that drying gas temperature and velocity strongly influence morphology, while relative humidity has a more modest effect. The work provides a mechanistic framework that links operating conditions to final particle morphology, enabling improved design of spray-drying processes in the food and pharmaceutical industries. Overall, the study advances understanding of crust formation, pore transport, and thermal gradients in drying droplets, with practical implications for tailoring particle structure via process parameters.

Abstract

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.

Figures (17)

• Figure 1: Schematic of the three-stage drying process of a single droplet containing solids showing temperature variation with drying time.
• Figure 2: Schematic illustrating the physical processes occurring during (a) First drying stage and; (b) Second drying stage.
• Figure 3: Schematic of the grid configuration for the first stage of drying.
• Figure 4: Schematic of the grid configuration for the second stage of drying.
• Figure 5: Comparison of numerical and experimental results for colloidal silica droplet drying at an ambient temperature of 101 $^\circ$C showing the evolution (a) Mass and (b) Temperature.