Understanding the drying behavior of thin aqueous films is critical for a wide range of applications, from coatings and cosmetics to pharmaceutical and biotechnological processes. In this chapter, we develop a systemic framework to model the isothermal and isobaric drying of thin aqueous films in the absence of a convective boundary layer. Special emphasis is placed on the pivotal role of water activity, which directly governs the interfacial vapor pressure, evaporation kinetics, temporal evolution of film thickness, and final film composition. The study combines experimental observations, theoretical modeling, and numerical simulations to provide a detailed description of mass transport, interfacial dynamics, thermodynamic effects, and phase change phenomena involved in the drying process. The water-glycerol mixture is employed as a model system due to its well-characterized physicochemical properties and its relevance to a wide range of industrial formulations. The predictive capabilities of the model are validated against gravimetric measurements, which highlight the impact of solute enrichment on drying dynamics. This integrated framework offers a powerful predictive tool for the rational design of drying processes in multicomponent aqueous systems.

This paper focuses on the numerical study of spherical particle sedimentation, taking into account hydrodynamic interactions. Infinite impulse response (IIR) digital filters, specially tailored to solve the sedimentation dynamics, were used in the present study to numerically solve the coupled ordinary differential equations with the time-dependent coefficients of the problem. Hydrodynamic interactions are modeled using the Rotne–Prager–Yamakawa (RPY) approximation, to which a correction is made to better account for short-range interactions. In order to validate both the proposed numerical resolution method and the RPY correction, this paper begins with the study of two interacting spherical particle sedimentation methods. Comparisons with previously published analytical or numerical results confirm the relevance of the present approach.

Two-dimensional phosphorus–nitrogen (P–N) allotropes are emerging as promising candidates for advanced nanoelectronic and optoelectronic applications.