Sunday, October 18, 2020

The relationship between the yaw rate and the pitch angle is shown in Fig. 9(c). The yaw rate is affected by the pitch angle only when the cell swims close to the wall and is oriented with the flagellum close to the wall. In such cases, for forward swimming motion, the yaw rate becomes negative and the resultant trajectory will curve in a clockwise direction when the motion is ob-served from above. For backward motion, similar to the pitch rate data, the signs of all data will be inverted with respect to the horizontal axis. Thus, the yaw rate becomes positive and the trajectory will curve in a counterclockwise direction if the motion is observed from above. Using the numerical results, the image of the motion of the cell model swimming close to a rigid boundary shown in Fig 10 can be generated: 1. As drawn in Fig. 10(a), since the pitching motion is stable in forward motion (Fig. 9(b)), the cell model tends to swim parallel to the surface maintaining a certain distance. However, the swimming speed of the parallel motion is slower than that achieved in free space

 14 Significant circular motion is not observed since the yaw rate is negligible when 0^0° (Fig. 9(c)). 2. In backward motion, the pitch motion of the cell model is unstable. The model is either departing from or approaching the surface. 3. In the departing motion depicted in Fig. 10(b), the cell model motion is steadily increasing its distance from the surface and is influenced very little. It swims almost in a straight line (Fig. 9(c), 9<0°) at an average speed nearly equal to that in free space (Fig. 9(a)). 4. In the approaching motion shown in Fig. 10(c), the interaction between the flagellar filament and the surface is strong and the average speed is larger than that achieved in free space because the orientation places the flagellum close to the wall (Fig. 9(a)). The positive pitch angle induces rotation in the yaw direction which, in turn, results in a circular trajectory in the counterclockwise direction when viewed from above (Fig. 9(c), e>o°). These diagrammatic representations are consistent, at least qualitatively, with the circular trajectories observed when the cells swim backward close to the surface. They are also consistent with the speed in the backward direction exceeding the speed in the forward direction. Moreover, the results clarify that the broadness in the residence time distribution for the backward direction is due to the unstable motion. The approaching cells tend to stay near the wall longer than the departing cells. Therefore, it is concluded that the observed asymmetrical characteristics of the motions are primarily caused by fluid-dynamic interactions between the cell and a rigid boundary when the cell has a non-parallel attitude relative to the boundary. These representations may be verified if the pitch angle is experimentally measured in conjunction with the swimming speed and trajectory, although the direct measurement of the pitch angle is very difficult.

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