| Summary: | Previous research on particle deposition in channels has emphasized the mass transfer aspects of the process. Little attention has been paid to the problem of determining whether or not particles, which have been transported to the channel walls, will actually adhere there. This adhesion step is complicated in most practical deposition situations by the presence of turbulent flow, chemical interactions, polydisperse particles, and wall roughness. Thus, as a first step towards providing a more fundamental understanding of the adhesion process, a theoretical and experimental study of a simplified deposition system was undertaken. In this idealized system, a dilute aqueous suspension of spherical, uniformly-sized, colloidal particles flows in steady, fully-developed laminar motion through geometrically simple channels. Under these circumstances, deposition onto the walls of the channels takes place by convective diffusion in a force field arising from the electrical double layer, London-van der Waals, and viscous interactions between each suspended particle and the wall. Because the range of these interaction forces is confined to a narrow region near the channel walls, their influence on the deposition process can be treated approximately by assuming convective diffusion in the bulk of the suspension with a first-order reaction at the walls. Explicit expressions for the surface reaction coefficient are derived in terms of the parameters which affect these interactions. The resulting extended Graetz problem is solved for both parallel-plate and cylindrical channels. Through the use of confluent hypergeometric functions combined with asymptotic techniques, an evaluation of these series solutions is made possible which is more accurate than all previous solutions, especially for the deposition of colloids and for cylindrical channels. Simple Leveque-type asymptotic solutions are also obtained for the case of large Peclet numbers, and when the reaction rate constant is infinite, these reduce to the corresponding well-established results for convective diffusion. These solutions describe only the initial state of the deposition process. To assess the derived model, an experimental investigation of the same idealized deposition system was carried out using uniform, spherical, silica particles (0.40, 0.60, and 0.65 μm dia.) and a parallel-plate channel (0.08 mm gap-thickness) constructed from plate glass and coated with different plastics to achieve a variety of surface chemical conditions. The use of particles doped with the γ-emitter Co⁵⁸, in conjunction with a collimated scintillation detector mounted on the outside of the channel, greatly facilitated the measurement of particle deposition. In addition, the tracer technique, when used with a second suspension of identical, but non-radioactive particles, allowed a separate measurement of particle release from the surface. It was found that, under the conditions of the present experiments, the re-entrainment of previously deposited particles was essentially nonexistent. Thus, the declining rate of particle accumulation with time observed for most runs could only be interpreted as a declining deposition rate. The measured initial rates of deposition of negatively charged particles onto positively charged plastic substrates were found to be in reasonable quantitative agreement with those predicted by the above theory if it was assumed that the process was mass-transfer controlled. For this case, the decrease in accumulation with time was best interpreted by a model which accounted for the change in surface area available for further deposition as the walls became progressively covered. It was shown that this surface coverage effect is enhanced by double layer exclusion (due to the repulsive interaction of the diffuse layers surrounding each particle), geometric exclusion (due to the finite size of particles and their random distribution on the particle wall), and hydrodynamic exclusion (due to the movement of fluid around the deposited particles). The maximum surface coverages attained never exceeded 10%. For negative particles and negative walls, the initial deposition rates were generally much less than for positive substrates, and the process was found to be surface-reaction rate controlled. For this case, the theory provided an accurate qualitative description of the experimental results; e.g. decreasing the double layer thickness (by adding neutral salts) or — decreasing the magnitude of the surface zeta potentials (by lowering the suspension pH) both served to increase the initial deposition rate. However, the measured values were generally much greater than those predicted theoretically. The evidence suggests that when repulsive electrical double layer interactions control the rate of particle deposition, deposition occurs preferentially onto areas of locally-favourable potential or geometry (or both). Thus, it was typically observed that the deposition rates fell off quickly at very low surface coverages as these preferred sites were presumably filled. === Applied Science, Faculty of === Chemical and Biological Engineering, Department of === Graduate
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