Dynamics of a helical swimmer crossing viscosity gradients

TL;DR

This study investigates how a helical microswimmer moves across viscosity gradients, revealing that its speed and crossing difficulty depend on the swimmer's configuration and the viscosity change direction, supported by experiments and hydrodynamic modeling.

Contribution

The paper introduces a combined experimental and theoretical analysis of helical swimmer dynamics across viscosity gradients, including a model that accounts for buoyancy effects in negative gradients.

Findings

Swimmer speed varies when crossing viscosity interfaces, increasing or decreasing depending on conditions.

Pusher swimmers find it harder to cross from low to high viscosity, while puller swimmers face less resistance.

The hydrodynamic model accurately predicts experimental results for positive viscosity gradients.

Abstract

We experimentally and theoretically study the dynamics of a low-Reynolds number helical swimmer moving across viscosity gradients. Experimentally, a double-layer viscosity is generated by superposing two miscible fluids with similar densities but different dynamic viscosities. A synthetic helical magnetically-driven swimmer is then made to move across the viscosity gradients along four different configurations: either head-first (pusher swimmer) or tail-first (puller), and through either positive (i.e. going from low to high viscosity) or negative viscosity gradients. We observe qualitative differences in the penetration dynamics for each case. We find that the swimming speed can either increase or decrease while swimming across the viscosity interface, which results from the fact that the head and the tail of the swimmer can be in environments in which the local viscosity leads to different relative amounts of drag and thrust. In order to rationalize the experimental measurements, we next develop a theoretical hydrodynamic model. We assume that the classical resistive-force theory of slender filaments is locally valid along the helical propeller and use it to calculate the swimming speed as a function of the position of the swimmer relative to the fluid-fluid interface. The predictions of the model agree well with experiments for the case of positive viscosity gradients. When crossing across a negative gradient, gravitational forces in the experiment become important, and we modify the model to include buoyancy, which agrees with experiments. In general our results show that it is harder for a pusher swimmer to cross from low to high viscosity, whereas for a puller swimmer it is the opposite. Our model is also extended to the case of a swimmer crossing a continuous viscosity gradient.