Geometry-based modeling of dispersion in core-shell particle media

Hatipoğlu, Emre
Dispersion is an important physical phenomenon that heavily influences performances of systems such as chromatographic separation processes. Mathematical modeling of this phenomenon is therefore widely investigated. This thesis study investigates dispersion of random-walking particles, or tracers, around core-shell particles, a type of recently commercialized spherical and porous stationary phase used in liquid chromatography that has a solid impermeable core that limits diffusion near the center and a porous shell covering the core. A random-walk approach was used for modelling the diffusion events, coupled with an external fluid velocity field to simulate convection and diffusion simultaneously. Impermeable boundaries of an unbound, without wall-effects, liquid chromatography column packed with core-shell particles were created using basic principles of analytical geometry, defining core-shell particles as a collection of a large core spheres and much smaller shell side spheres coated around the core based on actual microscopy images of core-shell particles. Reconstruction method was very similar to the actual production methods of these type of materials where a silica core sphere is coated by silica nanospheres to create a core-shell particle with a very homogeneous geometry. Analytically reconstructed geometry was visually inspected using CAD images and found to be appropriate. The core-shell particle geometry was then copied into a periodic random jammed packing of monodisperse hardspheres generated independently by a software and scaled in size such that core-shell particles would flush-fit inside the hardsphere that make the random packing. Random packing of hardspheres were also used as the system boundaries of fluid flow calculations. Assuming no flow would occur inside the pores of core-shell particles, velocity field of the fluid flow obtained by these calculations were used in couple with random-walk diffusion to simulate dispersion in the periodic random jammed packing of core-shell particles. Predictions of the dispersion model were quantized in terms of reduced plate height at different operating Peclet numbers and the results were compared with experimental data found in the literature. Predictions of the model compares very well with the experimental data with deviations clearly explainable by the differences between the simulated system and the experimental system. Therefore the analytical geometry based reconstruction method of the core-shell particles was successful and it can potentially pose an alternative to complicated imaging and image processing for similar system geometries. .