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.