How does a spherical colloidal drop dry?


Spray drying is widely used in drying of colloidal particles contained in colloidal suspensions. It comprises of complex processes involving multiple coupled mechanisms that can result in dried droplets of different morphologies depending on the drying conditions. Despite being well documented, many questions arising regarding spray drying of droplets need to be addressed. This means improving our fundamental understanding of the various mechanisms involved in drying and how the drying process can be optimized to realize droplets with desirable morphologies.

To this note, Dr. Benjamin Sobac (Postdoctoral Research fellow), Zakaria Larbi (PhD Student), Professor Pierre Colinet, and Professor Benoit Haut from the Université libre de Bruxelles in Belgium performed an analysis of drying of a spherical drop of a colloidal suspension based on mathematical modeling. Unlike the previous works that focused on phenomena occurring in one of the two phases, this study is quite innovative. The realistic heat and mass transport phenomena were taken into consideration in both the drop and the surrounding gas. The work is published in the journal, Colloids and Surfaces A: Physicochemical and Engineering Aspects.

Through this approach, a new Péclet number independent on the drop size was introduced. The Péclet is the dimensionless number found to have a significant influence on the dynamics of the colloids inside the drop. For instance, while a drop dries with a homogeneous concentration in particles within it for small values of the Péclet number compared to 1, larger values result in important gradients. Previously, the Péclet number was generally assumed to be proportional to the square of the drop diameter but, in this work, the authors predict that this number depends actually only on the diffusion of colloids within the solvent and the evaporation conditions. Moreover, a new equation was derived to evaluate Darcy’s stress emanating in the drop during the drying process. Contrary to the previous works, Darcy’s stress applied at the dense zone was predicted to diverge at the end of the consolidation stage.

Additionally, the modeling comprised of three different levels of decreasing complexity regarding the particle transport within the drop. First, the general model was the most complex. It involved a diffusion coefficient of the particles depending on their volume fraction. Secondly, the other two simple models considered either diffusive transport of the particles with a constant diffusion coefficient or the total absence of the diffusive particles inside the drop respectively. Finally, the results from all three modeling approaches were compared to provide insights on the level of complexity required, depending on the system parameters and properties to achieve the desired results and particularly in evaluating Darcy’s stress.

By comparing the three models, the research team was able to tell when it was necessary to take into account the interaction between the particles to describe the systems accurately. The first simplified model estimated the results of the general model with high accuracy for Peclet numbers smaller than 1 and larger than 100. On the other hand, the second simplified model provided favorable results for Peclet number large than 100 only. However, the simplified models were inadequate for the prediction of the dense zone formation time. Thus, the study provides an understanding of the complexity level needed to effectively quantify modeling properties based on the system parameters. In a statement to Advance in Engineering, Dr. Benjamin Sobac, first author noted that their study will be followed with investigations of potential mechanical instabilities in the systems.


Sobac, B., Larbi, Z., Colinet, P., & Haut, B. (2019). Mathematical modeling of the drying of a spherical colloidal drop. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 576, 110-122.

Go To Colloids and Surfaces A: Physicochemical and Engineering Aspects

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