Study of the settling and interactions of a pair of two-dimensional bottom-heavy squirmers in a vertical channel

In this study, the squirmer model with a prescribed tangential velocity is used as a model for swimming microorganisms where its geometric center is offset from the center of mass (bottom-heavy). The settling behavior and interactions of two bottom-heavy squirmers in a vertical channel are simulated numerically under low Reynolds number. Five settling modes, i.e. stable vertical settling, stable inclined settling, wall-attracting oscillatory, oscillatory, and chaotic motion are identified. In addition to the swimming Reynolds number Re _s [0.1,1.0], density ratio γ [1.1,2.1], and swimming strength β [−7,7], another bottom-heavy parameter ER (the ratio of the distance from the center of mass to the geometric center relative to the radius, in the range of [0a ₀,0.75a ₀] is introduced. The effects of these parameters on the settling modes of bottom-heavy squirmers, terminal Reynolds number Re _t, and interactions of the two bottom-heavy squirmers are discussed. The results showed that a pair of neutral bottom-heavy squirmers more easily achieved a stable structure at the channel center. In contrast, a pair of bottom-heavy pushers were more likely to be captured by the channel walls, leading to a stable structure near the walls. The stable symmetric structure of a pair of bottom-heavy pullers was disturbed, resulting in turbulence. Increasing the swimming strength β accelerates the settling of a pair of pushers. For different ER, the settling speed of two bottom-heavy pushers is greater than that of two bottom-heavy pullers. Additionally, the difference in settling speed between two bottom-heavy squirmers becomes more pronounced with an increase in Re _s. As γ increases, the settling behavior of bottom-heavy squirmers with high β differs from that of those with low β. Moreover, Re _t of a pair of pushers gradually approaches that of neutral bottom-heavy squirmers.