Theoretical models for the electrokinetics of weakly permeable porous colloidal particles are absent from the literature. The understanding of this topic will be advanced through a systematic analysis of the standard electrokinetic equations, resulting in a theory for the electrophoretic mobility of weakly permeable porous colloidal particles. / The standard electrokinetic equations are employed to model the flux of solvent and ions outside the porous particle. To be consistent with this approach, the flux of solvent and ions in the pores must also be governed by the standard electrokinetic equations. However, in practice, only transport phenomena on the particle scale are observed and it is sufficient for information regarding pore-scale behaviour to be retained purely in the form of averaged quantities. To complete the theoretical description, the standard electrokinetic equations outside the particle must be coupled to particle-scale transport equations inside the particle via boundary conditions at the porous/free-fluid interface. / It has been shown experimentally and theoretically for coupled Stokes and Darcy flows, that the correct interfacial boundary condition for the tangential external flow is given by the Beavers-Joseph-Saffman (BJS) condition. The effect of the BJS boundary condition on the hydrodynamic drag on an oscillating porous particle is investigated. It is found that the particle may be regarded as impermeable with a slip length independent of frequency, and the resulting drag is significantly reduced in comparison with an equivalent impermeable particle that does not exhibit a slip length. / The transport of a general electrolyte solution through a rigid porous body subjected to a static (d.c.) electric field is studied. The pore-scale description is given by the standard electrokinetic equations, including the effects of ion diffusion, electromigration and convection. Homogenization theory is used to derive transport equations that capture the particle-scale behaviour. It is proven that the transport coefficient tensors obey Onsager’s reciprocal relations and the diagonal coefficient tensors are positive definite. / New interfacial boundary conditions are derived using conservation arguments supplemented by Stern-layer theory. When combined with the particle-scale transport equations, these boundary conditions incorporate four principal effects into the standard electrokinetic model: solvent slip and Stern-layer ionic conduction at the interface, and macroscopic ionic conduction together with the electroosmotic flow of solvent through the particle. / The method of matched asymptotic expansions is then used to construct an approximate solution to the aforementioned system, in the thin double-layer limit. An expression for the electrophoretic mobility of a weakly permeable colloidal sphere is produced that consists of a generalization of Smoluchowski’s formula to encompass porous particles, and a next order correction. For the first time, the effects of solvent slip and Stern-layer ionic conduction within the porous/free-fluid interface, in conjunction with macroscopic ionic conduction and electroosmosis through the particle, are exhibited. It is shown that solvent slip at the porous interface is overwhelmingly the dominant effect on the mobility of weakly permeable porous colloidal particles.
| Identifer | oai:union.ndltd.org:ADTP/245356 |
| Creators | Looker, Jason Richards |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
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