Reorientation dynamics of microswimmers at fluid-fluid interfaces

Letter

Reorientation dynamics of microswimmers at fluid-fluid interfaces

Harinadha Gidituri, Zaiyi Shen, Alois Würger, and Juho S. Lintuvuori

Phys. Rev. Fluids 7, L042001 – Published 25 April 2022

Abstract

We study the orientational and translational dynamics of spherical microswimmers trapped at fluid interfaces in terms of the force dipole and source dipole components of their flow field. Using numerical simulations and analytical calculations, we show that the force dipole exerts a torque, orienting pushers parallel to the interface and pullers in the normal direction. The source dipole results in particle rotation only for a finite viscosity contrast between the two fluids, in agreement with previous studies. The superposition of these two contributions leads to a rotational dynamics with a steady-state orientation that depends on the relative magnitudes of the force and source dipoles. In the general case, swimmers with weak force dipoles and strong pullers are observed to align perpendicular to the interface and become stationary, while strong pushers have a finite inclination angle toward the lower viscosity fluid and swim along the interface.

Received 5 August 2021
Accepted 13 April 2022

DOI:https://doi.org/10.1103/PhysRevFluids.7.L042001

Physics Subject Headings (PhySH)

Interfacial flows Swimming

Colloids Liquid-liquid interfaces Living matter & active matter

Lattice-Boltzmann methods

Fluid DynamicsInterdisciplinary PhysicsPolymers & Soft Matter

Authors & Affiliations

Harinadha Gidituri, Zaiyi Shen, Alois Würger , and Juho S. Lintuvuori

Univ. Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France

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Issue

Vol. 7, Iss. 4 — April 2022

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Images

Figure 1
(a),(b) Slip flows at the particle surface corresponding to (a) source and (b) force dipoles, inclined at an angle $ϕ$ with respect to the interface.
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Figure 2
(a) Schematic representation of an active squirmer radius $R$ and swimming speed $U_{0}$ at an interface separating two fluids with viscosities $η_{1}$ and $η_{2}$ . The orientation angle $ϕ$ is defined as the angle measured between the squirmer orientation and fluid-fluid interface, and $θ$ is the polar angle. (b) Temporal evolution of the orientation $ϕ (t)$ for $B_{2} < 0$ and $B_{2} > 0$ for $η_{1} = η_{2}$ . (c) The measured angular velocity $Ω (ϕ)$ as a function of the angle $ϕ$ . The blue (red) corresponds to $B_{2} > 0$ ( $B_{2} < 0$ ), and dotted lines are fits to ${\hat{Ω}}_{F} sin (2 ϕ)$ . (d) The prefactor ${\hat{Ω}}_{F}$ as a function of the force dipole strength $B_{2}$ .
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Figure 3
(a) Decomposition of the force dipole at an angle $ϕ$ with respect to a rigid interface with slip boundary conditions. The second term exerts a torque on the particle. The boundary conditions at the particle surface and fluid interface require additional higher multipoles [47]. (b) Slip velocity $v_{s}$ at the contact line. (c) The interface imposes a discontinuity of $v_{s}$ and an intricate flow profile in the vicinity of the contact line.
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Figure 4
(a) Angular velocity $Ω_{S} (ϕ)$ observed for a neutral squirmer for different values of the viscosity ratio $λ$ . The arrow indicates an increase from $λ = 0.1$ to 0.7, with a step size of 0.1. The dashed lines are given by $Ω_{S} = {\hat{Ω}}_{S} cos ϕ$ . (b) The prefactor ${\hat{Ω}}_{S}$ obtained from the simulations (full circles), whereas the solid line is calculated from Eq. (7) (solid line) with the constant $- 0.225 U_{0} / R$ .
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Figure 5
Orientational potential $Ψ (ϕ) = - \int_{0}^{ϕ} Ω (ϕ^{'}) d ϕ^{'}$ for pushers ( $β < 0$ ) and pullers ( $β > 0$ ) with $λ = 0.2$ , calculated from Eq. (8).
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Figure 6
A state diagram for the stationary angle $ϕ^{*}$ in $β - λ$ space. Simulation results (symbols) and theory (background) are color-coded according to the color bar at the right. Range I (circles) indicates a stable fixed point in the range $- 90^{\circ} < ϕ \leq 0$ for pushers, and range II (diamonds) at $- 90^{\circ}$ for sufficiently weak pushers and pullers, where the source dipole contribution dominates. Range III (squares) indicates the stationary states $ϕ^{*} = \pm 90^{\circ}$ for strong pullers. The dashed lines give the boundaries between these states and are calculated from ${\hat{Ω}}_{S} = \pm 2 {\hat{Ω}}_{F}$ . (See the text for more details.)
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