Modelling of Diffusion in Random Packings of Core-Shell Particles

Abstract

Core-Shell particles are commonly used materials in chromatography. In this study, a mathematical model that mimics diffusion around Core-Shell particles was developed. A random-walk based algorithm was implemented to simulate diffusion and a Core-Shell particle geometry was computationally formed, based on simple geometric constructs and relations. Diffusion simulations were carried out on a randomly packed geometry formed from these particles. The behavior of time-dependent diffusivity data obtained from the model was found to be consistent with prior literature data from nuclear magnetic resonance experiments where transient diffusivity of a self-diffusing substance was measured in porous media.

Keywords

• Core-Shell,Diffusion,Random-Walk,Geometry

Çekirdek-Kabuk Parçacıklarının Raslantısal Paketlemelerinde Difüzyonun Modellenmesi

Abstract

Ç ekirdek-Kabuk tipi parçacıklar kromatografide sıklıkla kullanılan malzemelerdir. Bu çalışmada, ÇekirdekKabuk parçacıklarının etrafında gerçekleşen difüzyonu taklit etmeye yönelik bir matematik modeli geliştirilmiştir. Difüzyonun simulasyonu için rastgele-yürüyüş temelli bir algoritma oluşturulmuş ve basit geometrik yapılar ve bağıntılardan oluşan bir Çekirdek-Kabuk geometrisi hesaplanmıştır. Bu parçacıklardan oluşan rastgele-istiflenmiş bir yapı üzerinde difüzyon simülasyonları gerçekleştirilmiştir. Model sonuçlarından elde edilen zamana bağlı difüzyon katsayısının davranışı, nükleer manyetik rezonans deneyleri vasıtasıyla gözenekli ortamlarda bir maddenin zamana bağlı öz-difüzyon katsayısının ölçüldüğü daha önceki bir çalışmanın sonuçlarıyla uyumludur

Keywords

• Çekirdek-Kabuk, Difüzyon, Rastgele-Yürüyüş, Geometri.

References

1. C.G. Horvath, B.A. Preiss, S.R. Lipsky, Fast liquid chromatography. Investigation of operating parameters and the separation of nucleotides on pellicular ion exchangers, Anal. Chem., 39 (1967) 1422- 1428.
2. J.E. Macnair, K.C. Lewis, J.W. Jorgenson, Ultrahigh- Pressure Reversed-Phase Liquid Chromatography in Packed Capillary Columns, Anal. Chem., 69 (1997) 983-989.
3. K.K. Unger, R. Skudas, M.M. Schulte, Particle packed columns and monolithic columns in high-performance liquid chromatography-comparison and critical appraisal, J. Chromatogr. A, 1184 (2008) 393-415.
4. G. Guiochon, F. Gritti, Shell particles, trials, tribulations and triumphs, J. Chromatogr. A, 1218 (2011) 1915-1938.
5. F. Sattin, Fick’s law and Fokker–Planck equation in inhomogeneous environments, Physics Letters A, 372 (2008) 3941-3945.
6. H. Koku, R.S. Maier, M.R. Schure, A.M. Lenhoff, Modeling of dispersion in a polymeric chromatographic monolith, J. Chromatogr. A, 1237 (2012) 55-63.
7. A. Daneyko, D. Hlushkou, V. Baranau, S. Khirevich, A. Seidel-Morgenstern, U. Tallarek, Computational investigation of longitudinal diffusion, eddy dispersion, and trans-particle mass transfer in bulk, random packings of core–shell particles with varied shell thickness and shell diffusion coefficient, J. Chromatogr. A, 1407 (2015) 139-156.
8. E.I. Trilisky, H. Koku, K.J. Czymmek, A.M. Lenhoff, Relation of structure to performance characteristics of monolithic and perfusive stationary phases, J. Chromatogr. A, 1216 (2009) 6365-6376.

9. S. Bruns, T. Hara, B.M. Smarsly, U. Tallarek, Morphological analysis of physically reconstructed capillary hybrid silica monoliths and correlation with separation efficiency, J. Chromatogr. A, 1218 (2011) 5187-5194.
10. S. Bruns, U. Tallarek, Physical reconstruction of packed beds and their morphological analysis: Core– shell packings as an example, J. Chromatogr. A, 1218 (2011) 1849-1860.
11. M. Skoge, A. Donev, F.H. Stillinger, S. Torquato, Packing hyperspheres in high-dimensional Euclidean spaces, Physical Review E, 74 (2006) 1-11.
12. L. Latour, R. Kleinberg, P. Mitra, C. Sotak, Pore-size distributions and tortuosity in heterogeneous porous media, J. Magn. Reso., Ser. A, 112 (1995) 83-91.
13. P.N. Sen, Time-dependent diffusion coefficient as a probe of geometry, Concep. Magn. Reso., 23 (2004) 1-21.