| Summary: | Many microorganisms utilize their flagella, which are hair-like appendages, to swim in fluid environments. The research of locomotion of flagellated microorganisms involves the study of flagella’s behaviors. Since flagellated microorganisms swim by propelling their flagella through liquid environment, the propulsion of flagella plays a key role in hydrodynamics of the swimmers. In reality, the microorganisms are constantly subjected to flows and other external forces during swimming. Therefore, it is very important to understand how behaviors of the flagella contribute to the swimming in the presence of flow and external forces. In this thesis, I investigate the behavior of helically flagellated bacteria in external force field as well as the shape of a flagellum in shear flow.
First, I present a model to analyze the effect of dielectrophoretic (DEP) force on a swimming helically flagellated bacterium, particularly on its swimming direction and velocity. I consider simple DEP force that is acting along X-direction, and the force’s strength varies with Y-positions. Both DEP force and rotational diffusion are considered when analyzing the swimming of the bacterium. In most cases, DEP force is main factor that determines the steady swimming orientation of the bacterium; however, the impact of rotational diffusion is more significant when the DEP force’s strength varies strongly in the Y-direction. Interestingly, the variation in DEP force’s strength in the Y-direction causes the bacterium to translate perpendicular to its primary axis. This phenomenon is the consequence of the interaction between helical shape of the flagellum and the external force, and it could be applied to focus the bacteria. The model developed here would contribute to our knowledge on how external force affects the swimming behavior of flagellated bacteria, emphasizing on the interaction between the helical geometry of the flagellum and the external force.
For the investigation of the flagellum’s shape in shear flow, I derive the governing equation for the shape of a 2D beating flagellum in shear, and discuss the results at various shear strengths. The governing equation for the flagellum’s shape allows us to obtain the shape of the flagellum at different degrees of shear strength as well as flagellum’s flexibility. The numerical results show that shear flow has significant influence on the shape of the flagellum, especially when the flagellum is highly flexible, and in many cases, changes in the beating patterns of the flagellum positively promote the swimming speed of the swimmer. Furthermore, there exists an optimal shear rate that maximizes the effects of flexibility on the swimming speed. In most cases, the interaction between shear and flexibility of the flagellum plays a key role in determination of beating patterns. The results show that shear flow could be utilized to detect the difference in characteristics of flagellated swimmers, and to improve some existing sorting devices. I believe the analysis of the flagellum’s shape in shear flow has great contribution as to the best of my knowledge, this kind of governing equation of the flagellum’s shape in shear flow has not been mentioned in the literature.
On the experimental aspect, I conduct experiments to characterize the morphology of B. subtilis flagella and analyze the shape of flagella at different shear strengths. The proposed experimental method allows us to analyze the morphology of the bacterial flagella in great detail, including length, pitches, diameters, pitch angle. The experimental results show that external flow has different effects on different regions of the flagella. The regions of the flagella that are closer to the cells body are less influenced by the flow, and I believe the presence of the cells body reduces the effect of flow on the nearby regions of the flagella, and the bacteria have some mechanism to maintain the shape of the flagella in the regions close to the cells’ body.
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