Mathematical modeling of the drying of a spherical colloidal drop

Abstract In this article, we analyze, through mathematical modeling, the drying of a spherical drop of a colloidal suspension. The originality of our modeling lies in considering the transport phenomena in both the colloidal drop and the surrounding gas, allowing to describe and understand the problem comprehensively. We present a general model taking into account the diffusive and convective transports in the non-isothermal gas phase, and the unsteady diffusion of the particles within the drop. This general model involves a collective diffusion coefficient depending on the particle concentration to take into account the interactions between the particles, considered as hard spheres. This leads us to introduce a new expression of the Peclet number, Pe, comparing a characteristic time of the diffusion of the particles within the drop and a characteristic time of the evaporation of the drop. In particular, Pe appears to be independent of the drop size. The variation of Pe with the parameters of the system is analyzed and its influence on the dynamics of the colloidal particles is discussed. Furthermore, a new equation to evaluate the Darcy's stress arising in the drop during its drying is derived. In particular, it reveals that this mechanical stress continuously increases overtime until it diverges. Two simplified versions of the model are also presented. The comparison of the results obtained from the three versions of the model enables discussing what level of complexity of the modeling should be used for the quantification of several of its properties, depending on the system parameters.