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

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.