Hydrodynamics of Microbial Filter Feeders

The flows generated by filter-feeding microorganisms are complex, due to the microscopic flows critical dependence on the geometry of the system. Most investigations into the hydrodynamics of filter feeders have focused on detailed simulations of specific organisms, successfully capturing experimental behavior and disproving some hypotheses about how filter feeders function. However, these complex models often obscure the general hydrodynamic principles that underlie microscopic filter geometry and function. Understanding these underling principles is important, as a similar filter feeding strategy employed by numerous species. This thesis aims to uncover these fundamental principles by developing simplified models to analyze the hydrodynamics of three key aspects of the filter feeding process: the influence of the filter on the swimming speed, the relationship between geometry, fluid flux and particle uptake, and the fluid flows through the filter. The research begins with an exploration of a two-dimensional Taylor swimming sheet beneath a Brinkman layer of finite thickness, serving as a model for a swimmer confined within a porous, non-Newtonian boundary. The findings indicate that ignoring the effects of jump stress and porosity leads to a decrease in swimming speed as the Brinkman layer's thickness and lower boundary increase, with similar trends observed for decreasing permeability. Including porosity effects with zero jump stress enhances the swimming velocity for near-unity porosity values, while non-zero jump stress introduces complex behavior in the swimming speed, particularly in thin or low-permeability layers. These results highlight the delicate balance between physical parameters that influence the swimming dynamics of microorganisms in porous environments. Building on this foundation, the study extends to a cylindrical Taylor swimming sheet to study the feeding mechanism of microscopic filter feeders. Here, the interplay between swimming speed, flux, and Brinkman layer characteristics is examined. The analysis reveals that swimming speed and flux decrease with increasing layer thickness and boundary distance but are enhanced by porosity for small values. Importantly, the study finds that flux remains unaffected by the position or thickness of the Brinkman layer relative to the swimming sheet, underscoring the robustness of the feeding mechanism. The biological relevance of these findings is further explored, with data suggesting that microbial filter feeders optimize their feeding structures, such as microvilli, to maximize flux multiplied by catchment area. This optimization is achieved through specific combinations of microvilli radius and spacing, indicating evolutionary fine-tuning for efficient feeding in various environmental conditions. The third study advances the research into three-dimensional geometry, applying the principles established in the previous studies to more complex and realistic configurations. This exploration into three-dimensional spaces allows for a deeper understanding of the interactions between geometry, swimming speed, and flux, particularly in environments that closely mimic natural settings. The results not only corroborate the trends observed in two-dimensional and cylindrical models but also introduce new insights into how three-dimensional structures influence the feeding efficiency and swimming dynamics of microscopic filter feeders. These findings have significant implications for our understanding of the evolutionary adaptations of these organisms, as they suggest that the morphology and behavior of microbial filter feeders are finely tuned to their ecological niches. In general, this thesis provides a detailed and rigorous examination of the physical mechanisms underlying the swimming and feeding behaviors of microscopic filter feeders. By developing simplified models that capture the essential hydrodynamic principles, this research contributes to a broader understanding of the evolutionary pressures that shape the morphology and behavior of these organisms, offering new perspectives on their survival strategies in diverse and often challenging environments.<p></p>