This Ph.D. thesis proposes a novel theoretical framework for filtration by porous media character- ized by heterogeneity. The Classical Filtration Theory (CFT) is formulated adopting a macroscopic point of view in which filtration is described in terms of two main processes: transport and reten- tion. The former is formulated at the scale of the porous medium, where its real structure is replaced with a virtual/effective system (a collector or a pipe) whose average flow properties match the aver- age porous medium ones. The latter is formulated in terms of the outlet to inlet concentration ratio and, a posteriori, related to the product of particle’s probability of getting close to the solid walls of the filter (collector or pipe walls) times the particle’s probability of finally attaching. Thus, CFT provides a description of filtration that, through a simple and macroscopic formulation, overcomes the difficulties associated to the complex nature of filtration that rises due to the coupling of i) the process of attachment via colloidal forces (formulated in terms of the Derjaguin-Landau-Verwey- Overbeek’s theory, DLVO, for surface’s forces interaction) and ii) transport within a porous material.
However, observations via laboratory column experiments showed that the macroscopic diagnostic quantities that are typically defined to describe filtration, breakthrough curves and deposition pro- files, deviate quantitatively and qualitatively from the predictions of CFT. While, these deviations are justified in terms of the complex chemistry of the attachment process (in particular the presence of a secondary minimum in the colloids-surfaces interaction energy profile), recent experiments re- ported the deviation from CFT also in the absence of such a secondary energy minimum. Thus, we hypothesize that the anomalous filtration observed (anomalous with respect to the CFT predic- tions) is associated with the physical heterogeneity of the structure of the host medium that is also reflected in the flow through it. This thesis focuses on two main axes.
With this Ph. D thesis we intend to propose a novel theoretical framework for filtration by porous media by adopting the point of view of the individual particle (a colloid or a microorganism) that is flowing through the confined space of a porous medium. On the one hand, we formulate the filtration problem in terms of the transport and attachment fundamental mechanisms experienced by individual particles in terms of three stochastic Markovian processes (chapter 3): the particle’s retention length, its velocity over such piece of length and the attachment rate. The proposed model predicts anomalous filtration behaviors, similar to those reported in literature. On the other hand, we develop a novel experimental setup, based on microfluidics and time-lapse video-microscopy that allow us to investigate the multi-scale nature of the filtration phenomenon of colloids (chapter 4) and microorganisms (chapter 5) and, finally, the aggregation of individual bacteria particles into larger aggregates that our experiments indicate are responsible for the onset of streamers (chapter 6).