[Paper Review] Dynamics of a simple model microswimmer in an anisotropic fluid: implications for alignment behavior and active transport in a nematic liquid crystal

Abdallah Daddi‐Moussa‐Ider, Andreas M. Menzel|arXiv (Cornell University)|Sep 3, 2018

Micro and Nano Robotics192 references33 citations

TL;DR

This study theoretically investigates the dynamics of a minimal model microswimmer in a uniaxially anisotropic fluid, such as a nematic liquid crystal, by deriving the hydrodynamic Green's function for fluid flow induced by localized forces. The analysis reveals that swimmer alignment—parallel, perpendicular, or oblique to the nematic director—depends on propulsion type (pusher vs. puller) and viscosity anisotropy, driven by hydrodynamic coupling between self-generated flow and fluid anisotropy, with results supporting controlled active transport in tunable anisotropic media.

ABSTRACT

Several recent experiments investigate the orientational and transport behavior of self-driven bacteria and colloidal particles in nematic liquid crystals. Correspondingly, we study theoretically the dynamics of a minimal model microswimmer in a uniaxially anisotropic fluid. As a first step, the hydrodynamic Green's function providing the resulting fluid flow in response to a localized force acting on the anisotropic fluid is derived analytically. On this basis, the behavior of both puller- and pusher-type microswimmers in the anisotropic fluid is analyzed. Depending on the propulsion mechanism and the relative magnitude of different involved viscosities, we find alignment of the swimmers parallel or perpendicular to the anisotropy axis. Particularly, also an oblique alignment is identified under certain circumstances. The observed swimmer reorientation results from the hydrodynamic coupling between the self-induced fluid flow and the anisotropy of the surrounding fluid, which distorts the self-generated flow field. We support parts of our results by a simplified linear stability analysis. Our theoretical predictions are in qualitative agreement with recent experimental observations on swimming bacteria in nematic liquid crystals. They support the objective of utilizing the, possibly switchable, anisotropy of a host fluid to guide individual microswimmers and active particles along a requested path, enabling controlled active transport.

Motivation & Objective

• To understand how hydrodynamic coupling between self-propelled microswimmers and anisotropic fluid rheology governs swimmer orientation in nematic liquid crystals.
• To derive an analytical hydrodynamic Green's function for fluid flow in uniaxially anisotropic fluids, accounting for viscosity tensor anisotropy.
• To determine the conditions under which microswimmers (pushers or pullers) align parallel, perpendicular, or at oblique angles to the nematic director.
• To provide a theoretical foundation for guiding active particles in switchable anisotropic fluids for controlled active transport applications.
• To validate theoretical predictions with simplified linear stability analysis and numerical simulations using boundary integral methods.

Proposed method

• Derive the hydrodynamic Green's function for a localized force in an anisotropic fluid using continuum mechanics and conservation laws, incorporating the Leslie-Ericksen theory framework.
• Model the microswimmer as a sphere with two asymmetric force centers to represent both pusher and puller propulsion mechanisms.
• Use the derived Green's function to compute self-mobility and pair-mobility tensors for motion parallel and perpendicular to the nematic director.
• Apply asymptotic expansions and analytical integration techniques (e.g., Fourier transforms, Legendre expansions) to obtain closed-form expressions for mobility functions.
• Validate results via boundary integral method (BIM) simulations with refined triangular meshes (320 and 1280 triangles) for accuracy assessment.
• Perform linear stability analysis to support the observed alignment behavior and predict steady-state orientations.

Experimental results

Research questions

• RQ1 How does the anisotropy of a nematic liquid crystal fluid influence the orientation and alignment of self-propelled microswimmers?
• RQ2 What determines whether a pusher or puller-type microswimmer aligns parallel or perpendicular to the nematic director?
• RQ3 Under what conditions does a microswimmer adopt an oblique steady-state orientation relative to the director axis?
• RQ4 How do the relative magnitudes of viscosity coefficients (ν2, ν3, ¯ν) affect the hydrodynamic coupling and resulting swimmer dynamics?
• RQ5 To what extent do analytical predictions of mobility functions match numerical simulations in the presence of fluid anisotropy?

Key findings

• The hydrodynamic Green's function for anisotropic fluids is derived analytically, enabling prediction of fluid flow in response to localized forces in nematic environments.
• For pusher-type swimmers, alignment parallel to the nematic director is predicted when viscosity anisotropy favors extensional flow, while pullers align perpendicularly under similar conditions.
• An oblique alignment state emerges when the ratio of viscosity coefficients (e.g., ν2/ν3 and ¯ν/ν3) reaches intermediate values, indicating a non-monotonic dependence on anisotropy.
• The self-mobility parallel to the director scales as 1/(4πhν3), while the perpendicular component scales as 1/(8πhν2), reflecting the anisotropic resistance to flow.
• Numerical boundary integral simulations show excellent agreement with analytical predictions for both self-mobility and pair-mobility functions across a wide range of viscosity ratios and interparticle distances.
• The results are qualitatively consistent with recent experiments on swimming bacteria in nematic liquid crystals, supporting the feasibility of using tunable fluid anisotropy for guiding active particles.