A polymer distribution is usually represented by its moments. Thus, to calculate transport in a polymer system, a formulation for the transport of moments of the polymer is needed. This is only possible if the moments close or if there is a suitable closing condition. To archive this, two simplifications of the Stefan–Maxwell diffusion are derived, which convert the transport equation of polymeric species to a closed set of transport equations for the polymer moments. The first approach corresponds to an infinitely diluted polymer system, whereas the second one describes a highly concentrated polymer system. Both formulations are compared with the full Stefan‐Maxwell model of a ternary mixture of a solvent and two polymer species of different chain length.
The development of a methodology for the simulation of structure forming processes is highly desirable. The smoothed particle hydrodynamics (SPH) approach provides a respective framework for modeling the self-structuring of complex geometries. In this paper, we describe a diffusion-controlled phase separation process based on the Cahn-Hilliard approach using the SPH method. As a novelty for SPH method, we derive an approximation for a fourth-order derivative and validate it. Since boundary conditions strongly affect the solution of the phase separation model, we apply boundary conditions at free surfaces and solid walls. The results are in good agreement with the universal power law of coarsening and physical theory. It is possible to combine the presented model with existing SPH models.
Reaktive Sprühtrocknungsprozesse wie Sprühpolymerisationen sind im Hinblick auf die Prozessintensivierung sehr interessant. Bisherige Forschungsarbeiten dazu basieren allerdings fast ausschließlich auf Experimenten. In diesem Beitrag wird ein Einzeltropfenmodell der Sprühpolymerisation vorgestellt, welches das Reaktions‐Diffusions‐System innerhalb eines Tropfens im Spray eindimensional ortsaufgelöst abbildet. Somit lassen sich Auswirkungen der Prozessparameter und Materialeigenschaften auf das Polymerisationsergebnis und wichtige Kenngrößen wie Zahlen‐ und Massenmittel der Kettenlängenverteilung abschätzen.
Summary: Acoustic levitation was investigated as a model for spray processes. The influence of different parameters on the drying process of aqueous polyvinylpyrrolidone (PVP) solutions was studied and compared to the evaporation of water. The adequacy of acoustic levitation as model for spray processes was demonstrated. Experiments with water and aqueous PVP solutions indicated no dependency of the droplet size on the drying process for droplets with a diameter between 300 mm and 1.5 mm. Particles dried in an acoustic levitator displayed good accordance of morphology with those obtained in a spray tower. Surprisingly the addition of PVP to water resulted in faster evaporation of the solvent. Mathematical models of single droplets within a spray process typically refer to spherically symmetric droplet geometries. The simulation of other morphologies and their evolution throughout the process is still very challenging. A new drying model based on a fully threedimensional meshfree approach is under development and shows good agreement to basic established models regarding the drying of a single droplet.
Summary
Spray polymerisation is a technique to carry out polymerisations in a highly efficient manner. As experimental optimisation of process parameters is tedious, simulations of the processes inside a single droplet are desirable. Today's models used in spray polymerisation assume ideal mixing and thus do not resolve the particle state along the radius. In this contribution we derive a single particle model for the case of free radical polymerisation, which spatially resolves the physical and chemical processes. The model allows for predicting inhomogeneity of the polymeric product as a function of drying conditions. The state of the polymer is calculated using the method of moments.
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