Collective transport efficiency of microswimmer swarms optimized by tactic run-tumble dynamics

Abstract: The collective motion of microorganisms and microrobots can be used for particle delivery, especially when guided by external magnetic fields, phototaxis, or chemotaxis. This cargo transport is enhanced significantly by hydrodynamic entrainment, where the surrounding fluid and any dissolved molecules or suspended cargo particles are dragged along with a collectively moving swarm. However, it remains unclear how this directed entrainment is affected by stochastic run-tumble motion, and how such motility patterns couple to particle dispersion. Here, we combine theory and simulations to compute the entrainment velocity and diffusivity for different degrees of swimmer directedness. Surprisingly, we find that the transport efficiency P\'{e}clet number, the ratio of advective to diffusive transport, is optimal for intermediate directedness values, so perfectly guided active suspensions perform worse than those with stochastic reorientations. These results could have implications for microrobotic drug delivery and nutrient transport in microbial environments.