Locomotion of a micro-swimmer towing load through shear-dependent non-Newtonian fluids

Abstract

This paper simulates the locomotion of a micro-swimmer towing cargo through a shear-dependent non-Newtonian fluid. We investigate the effect of the shear-dependent rheology (refers to the power-law index n), swimming Reynolds numbers (Re), and the relative position (refers to the distance ds and the concerning angle θ) between the swimmer and the cargoes on the assemblies' locomotion. For a swimmer towing a cargo, we find that a cargo-puller, cargo-pusher, or pusher-cargo (three typical towing models) swims faster in the shear-thickening fluids than in the shear-thinning fluids at Re ≤ 1. Moreover, the pusher-cargo swims significantly faster than the counterpart puller-cargo at Re ≤ 1. For a swimmer towing two cargoes, we find that the maximum negative swimming speeds can be achieved at θ = 30° and 150°, corresponding to two typical regular-triangle structures assembled by the squirmer and the cargoes. Interestingly, some regular-triangle assemblies (puller with θ = 30° and pusher with θ = 150°) can maintain a swimming opposite to their initial orientation. In addition, we obtain a relation of energy expenditure P ∼ Ren−1; it is also found that the assembly swimming in the shear-thinning fluids is more efficient than in the shear-thickening ones. Our results provide specified guidance in the designing of cargo-carrying micro-swimming devices.