Microscale swimming in viscosity gradients near a plane wall
Phys. Rev. Fluids 10, 104201 – Published 3 October, 2025
DOI: https://doi.org/10.1103/7bxx-6ssw
Abstract
The interaction of microswimmers with solid surfaces in heterogeneous viscous environments is prevalent in various natural and engineering settings, which motivates efforts to unravel the underlying hydrodynamics. In this work, we semi-analytically investigate the influence of an imposed spatially linearly varying viscosity field on near-wall motion of a model microswimmer (squirmer). We explore its associated phase portraits and swimming trajectories for different swimming gaits and compare them with their constant-viscosity analogs. The observations are validated with stability analysis and finite-element-based numerical simulations. We find that even a slight transverse (wall-perpendicular) viscosity gradient disrupts the typical leading-order wall-escaping behavior of neutral squirmers, resulting in its near-wall periodic oscillations regardless of the initial conditions. Similarly, the gradient also modifies behavior of obliquely oriented puller and pusher squirmers (not initialized perpendicular to the wall) from their usual constant-viscosity patterns, leading to its near-wall stabilization with damped temporal oscillations (orientation towards wall). These swimming trends persist across all viscosity-gradient strengths and squirmer parameters tested. In longitudinal (wall-parallel) gradient, although squirmers predominantly exhibit viscophobic motility; we show that depending on initial conditions, pullers and pushers can also display viscophilic tendencies. Moreover, while transverse gradient preserves the puller-pusher duality, in longitudinal gradient it breaks. To elucidate underlying mechanisms behind these observations, we decompose the problem into its corresponding drag and thrust counterparts and observe that apart from leading-order effects and bulk viscotactic responses, the gradient-induced hydrodynamic couplings in drag components play a significant role in modifying these near-wall trajectories. We further extend these findings to arbitrarily oriented viscosity gradients. The results reveal that neutral squirmers either escape wall or settle near it, depending on the relative strength of the gradient's longitudinal and transverse components. For pullers and pushers, the phase portraits remain qualitatively similar; however, a critical gradient direction induces Hopf bifurcations and stable limit cycles, with the onset increasing with swimmer strength. This indicates that strong pullers and pushers require a more transverse-aligned gradient to maintain stable near-wall swimming. Overall, this study demonstrates the substantial role of even simplistic ambient viscosity profile on near-wall squirmer motility, which provides valuable insights for understanding and controlling microswimmer motion in heterogeneous biological and microfluidic systems.
