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.
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