Swimming Mode of Two Interacting Squirmers under Gravity in a Narrow Vertical Channel

Abstract

The swimming mode of two interacting squirmers under gravity in a narrow vertical channel is simulated numerically using the lattice Boltzmann method (LBM) in the range of self-propelling strength 0.1 ≤ α ≤ 1.1 and swimming type −5 ≤ β ≤ 5. The results showed that there exist five typical swimming patterns for individual squirmers, i.e., steady upward rising (SUR), oscillation across the channel (OAC), oscillation near the wall (ONW), steady upward rising with small-amplitude oscillation (SURO), and vertical motion along the sidewall (VMS). The parametric space (α, β) illustrated the interactions on each pattern. In particular, the range of oscillation angle for ONW is from 19.8° to 32.4° as α varies from 0.3 to 0.7. Moreover, the swimming modes of two interacting squirmers combine the two squirmers’ independent swimming patterns. On the other hand, the pullers (β < 0) attract with each other at the initial stage, resulting in a low-pressure region between them and making the two pullers gradually move closer and finally make contact, while the result for the pushers (β > 0) is the opposite. After the squirmers’ interaction, the squirmer orientation and pressure distribution determine subsequent squirmer swimming patterns. Two pushers separate quickly, while there will be a more extended interaction period before the two pullers are entirely separated.

Study of sedimentation characteristics of an elliptical squirmer in a vertical channel

“…In addition, the angle at which the two squirmers separated from each other and swimming velocity were important for the mutual transitions between the different motion modes. Subsequently, Guan et al [56] obtained similar conclusions in their simulations of the rise of two self-propelled particles in a 2D vertical channel. Qi et al [57] used an immerged-boundary-lattice Boltzmann method to numerically simulate the sedimentation motion of a single 2D bottom-heavy squirmer in a narrow vessel.…”

Motion characteristics of squirmers in linear shear flow

“…In this work, the improved bounce-back scheme proposed by Lallemand and Luo (2003) was used, and after improvement, this interpolationbased bounce-back scheme is stable, robust, and easy to implement in simulations. Note that a similar scheme was used in our earlier research (Guan et al 2022(Guan et al , 2021. The improved bounce-back scheme is shown in figure 3, where solid squares indicate solid nodes inside the curved boundary, solid circles indicate fluid nodes outside the curved boundary, and hollow triangles indicate boundary nodes where the bounce-back occurs.…”