Active particles crossing sharp viscosity gradients

Abstract

Active particles (living or synthetic) often move through inhomogeneous environments, such as gradients in light, heat or nutrient concentration, that can lead to directed motion (or taxis). Recent research has explored inhomogeneity in the rheological properties of a suspending fluid, in particular viscosity, as a mechanical (rather than biological) mechanism for taxis. Theoretical and experimental studies have shown that gradients in viscosity can lead to reorientation due to asymmetric viscous forces. In particular, recent experiments with Chlamydomonas Reinhardtii algae swimming across sharp viscosity gradients have observed that the microorganisms are redirected and scattered due to the viscosity change. Here we develop a simple theoretical model to explain these experiments. We model the swimmers as spherical squirmers and focus on small, but sharp, viscosity changes. We derive a law, analogous to Snell’s law of refraction, that governs the orientation of active particles in the presence of a viscosity interface. Theoretical predictions show good agreement with experiments and provide a mechanistic understanding of the observed reorientation process.

Active spheroids in viscosity gradients

“…2021). When interacting with sharp viscosity gradients, this same alga displays dynamics analogous to the refraction of light, as observed experimentally (Coppola & Kantsler 2021) and modelled theoretically (Gong, Shaik & Elfring 2023). Experiments on the effects of viscosity differences on synthetic swimmers are as of yet limited to helical swimmers crossing perpendicular to a viscosity interface and thus not displaying reorientation (Esparza López et al.…”

“…Chlamydomonas reinhardtii, a type of green microalgae, demonstrates complex behaviour in viscosity gradients: it accumulates in high-viscosity regions when gradients are weak, but reorients towards low-viscosity regions in strong gradients (Stehnach et al 2021). When interacting with sharp viscosity gradients, this same alga displays dynamics analogous to the refraction of light, as observed experimentally (Coppola & Kantsler 2021) and modelled theoretically (Gong, Shaik & Elfring 2023). Experiments on the effects of viscosity differences on synthetic swimmers are as of yet limited to helical swimmers crossing perpendicular to a viscosity interface and thus not displaying reorientation (Esparza López et al 2021).…”

“…But one can certainly envision a scenario where for sufficiently sharp gradients, ε ln λ/λ 2 = O(1). Our formulas are not strictly valid in this setting, but formulas for spheres in weak gradients (Datt & Elfring 2019) reproduce accurately the reorientation found crossing sharp gradients (Gong et al 2023).…”

“…Later work included the effect of viscosity variations on thrust using the spherical squirmer model where the particle activity responsible for generating thrust is represented as a surface slip velocity (Lighthill 1952;Blake 1971). It was shown that hydrodynamic interactions between the active slip conditions on the squirmer's surface and the fluid with spatially varying viscosity generally lead to negative viscotaxis (Datt & Elfring 2019;Shaik & Elfring 2021;Gong et al 2023). The dynamics of a spherical squirmer in spatially varying viscosity that results from non-uniform distribution of nutrients has also been explored (Shoele & Eastham 2018).…”

“…It was shown that hydrodynamic interactions between the active slip conditions on the squirmer's surface and the fluid with spatially varying viscosity generally lead to negative viscotaxis (Datt & Elfring 2019; Shaik & Elfring 2021; Gong et al. 2023). The dynamics of a spherical squirmer in spatially varying viscosity that results from non-uniform distribution of nutrients has also been explored (Shoele & Eastham 2018).…”