Hydrodynamics of a microswimmer in a variable viscosity medium

The locomotion of microswimmers in spatially varying viscous media is governed by a complex interplay between fluid heterogeneity and surface-driven activity. In the present analysis, the viscosity profile μ(r) is modeled based on concentration gradients, aligning with the formulation by Housiadas and Beris [Phys. Fluids 31, 113105 (2019)]. The viscosity variation is governed by a control parameter ξ, while surface activity is induced by diffusiophoresis. We employ a reduced form of the governing equations and use an asymptotic power series expansion to derive analytical expressions for the velocity field, swimmer speed, power dissipation, and swimming efficiency. In the depletion regime (0≤ξ≤1), the swimmer's speed increases with the viscosity contrast η, reflecting improved propulsion efficiency in low-viscosity surroundings. In contrast, for the accumulation regime (ξ>1), swimmer velocity exhibits non-monotonic dependence on η, rising initially but dropping at higher η, indicating a transition in hydrodynamic response. This complex behavior reveals how viscosity gradients modulate flow and swimmer performance. Flow field analysis further shows distinct disturbance patterns in depletion vs accumulation zones, emphasizing the impact of environmental heterogeneity. Unlike simple neutral squirmers, the swimmer in our model exhibits a far-field flow decay of r−1 due to uncompensated Stokeslet contributions arising from spatial viscosity variations. These findings enhance our understanding of microswimmer dynamics and offer design insight for microrobotic applications in medicine and environmental monitoring.