Lec 50: Analysis of diffusion through porous solids, crystalline solids and polymers

This lecture, part of NPTEL’s Transport Phenomena in Bioprocess Engineering course, focuses on analyzing diffusion through porous solids, crystalline solids, and polymers. It begins with an introduction to porous solids, defining them as materials with void spaces and explaining their importance in bioprocesses for adsorption, immobilization, and separation. The classification of pores by diameter (micropores, mesopores, macropores) is presented, along with their typical examples and relevance. Two main diffusion mechanisms are discussed: molecular diffusion, when pore size is much larger than the mean free path, and Knudsen diffusion, when pore size is comparable to the mean free path. The Knudsen number (lambda/dp) is introduced to determine the dominant regime. The concepts of porosity and tortuosity are defined to account for irregular pathways, leading to the effective diffusivity formula D_eff = D * epsilon / tau. Applications to immobilized cells, biocatalysts, chromatography, and membrane filtration are highlighted, along with design trade-offs among pore size, porosity, tortuosity, and mechanical strength. The lecture then shifts to crystalline solids, explaining that diffusion occurs via defects like vacancies and interstitial sites. The vacancy hopping mechanism and the Arrhenius relationship for diffusivity (D = D0 exp(-Q/RT)) are detailed. Grain boundaries and dislocations are described as fast diffusion paths, illustrated with stainless steel used in bioreactors. The impact of thermal history on chromium carbide precipitation and corrosion resistance is discussed. Crystal behavior during freeze-drying and scaling due to crystallization is also examined. Finally, diffusion in polymers is introduced, emphasizing free volume theory, factors like molecular size, temperature, and swelling. The lecture concludes with applications in hydrogel systems for cell immobilization, highlighting that effective diffusivity in polymers is typically lower than in water.