Physics of low Reynolds number locomotion
Date of Issue2018-12-17
School of Mechanical and Aerospace Engineering
The propulsion of microscopic organisms and their mechanisms of detecting and responding to the environmental cues are the areas of interest to many physicists and biologists. Microorganisms of complicated geometries induce interesting flow patterns when swimming in a viscous fluid. Their swimming trajectories can be affected by the hydrodynamic interactions with nearby boundaries. Moreover, microorganisms, as a component in the food chain, consistently trace the nutrients or preys while in the risk of being captured by its predators. It is important to understand how the flow induced by the prey plays a role in activating the sensory mechanism of the predator. The objectives of this thesis are two folded: firstly, to understand the boundary effects on nearby microswimmers, and secondly, to analyze the role of the mechanoreceptional sensor of marine copepods in detecting the presence of phytoplankton. The influence of a plane boundary on a low-Reynolds-number swimmer is investigated using the multipole expansion and wall traction approach. Previous research frequently studied the boundary effect using image systems for flow singularities. In the proposed model, the boundary effect is expressed using a boundary integral representation over the traction on the boundary. Examining the traction pattern caused by a swimmer is found to yield physical insights into determining when the far-field multipole model is accurate. As a demonstration, the swimming velocities and the traction of a three-sphere swimmer initially placed parallel to an infinite planar wall is investigated. In the far field, the instantaneous effect of the wall on the swimmer is well approximated by that of a multipole expansion consisting of a force dipole and a force quadrupole. On the other hand, the swimmer close to the wall must be described by a system of singularities reflecting its internal structure. These limits and the transition between them can be independently identified by examining the traction pattern on the wall, either using a quantitative correlation coefficient or by visual inspection. Furthermore, for non-constant propulsion, correlations between swimming stroke motions and internal positions are important and not captured by time-averaged traction on the wall, indicating that care must be taken when applying multipole expansions to study boundary effects in cases of non-constant propulsion. Copepods sense the hydrodynamic disturbances induced by the swimming planktonic preys through the bending of their setae on the first antennule pair. This thesis presents a mechanical model in the Stokes limit to address the fundamental characteristics associated with the setal deformation in the copepod-prey detection. The presence of the copepod is first demonstrated to have non-negligible contributions on the flow profile across the distal seta. A comparison between the proposed model and previous models for the sensed flow that consider the velocity field or far-field strain rate due to free-swimming prey shows that those approximations fail to determine the flow profile across the distal seta with a decent accuracy. Moreover, the setal deformations induced by the flow is evaluated as a function of oscillating frequencies of the prey; lower frequency signals are found to lead to larger setal bending, described by a low pass filter. Finally, the effects of setal length, velocity amplitude and frequency of the prey on the response time of the setal bending are investigated. The short response time is consistent with the rapid behavioral and neurological response of copepods.