Dynamics of a fully wetted Marangoni surfer at the fluid–fluid interface

Gidituri, Harinadha; Panchagnula, Mahesh V.; Pototsky, Andrey

doi:10.1039/c8sm02102c

Cited by 15 publications

(13 citation statements)

References 23 publications

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“…At larger distances, a crossover to diffusive transport withc ∝ ρ −1 sets in. So far, we considered the leading order of our problem by settingŪ ≈ 0; going one order further, we get the linear response for smallŪ with the ansatzc =c (0) + Uc (1) withc (0) (ρ) given by (36) (1) is linear inŪ . In an advection dominated situation, the constant flux relation (34) still holds in the presence of Stokes flow, 1 ∼ (c (0) +Ūc (1)…”

Section: ũmentioning

confidence: 99%

“…A full quantitative theory of Marangoni boats including hydrodynamics, surfactant advection, direct Marangoni forces and Marangoni flows is still elusive despite previous progress [22,26,36,37]. Some theoretical approaches ignore the advection [35,38,39], several ignore the hydrodynamic flow fields [24,25,32,[40][41][42] or approximate it by uniform flow [28], which clearly oversimplifies the description of surfactant transport.…”

Section: Introductionmentioning

confidence: 99%

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Surfactant-loaded capsules as Marangoni microswimmers at the air–water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection

et al. 2021

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We present a realization of a fast interfacial Marangoni microswimmer by a half-spherical alginate capsule at the air–water interface, which diffusively releases water-soluble spreading molecules (weak surfactants such as polyethylene glycol (PEG)), which act as “fuel” by modulating the air–water interfacial tension. For a number of different fuels, we can observe symmetry breaking and spontaneous propulsion although the alginate particle and emission are isotropic. The propulsion mechanism is similar to soap or camphor boats, which are, however, typically asymmetric in shape or emission to select a swimming direction. We develop a theory of Marangoni boat propulsion starting from low Reynolds numbers by analyzing the coupled problems of surfactant diffusion and advection and fluid flow, which includes surfactant-induced fluid Marangoni flow, and surfactant adsorption at the air–water interface; we also include a possible evaporation of surfactant. The swimming velocity is determined by the balance of drag and Marangoni forces. We show that spontaneous symmetry breaking resulting in propulsion is possible above a critical dimensionless surfactant emission rate (Peclet number). We derive the relation between Peclet number and swimming speed and generalize to higher Reynolds numbers utilizing the concept of the Nusselt number. The theory explains the observed swimming speeds for PEG–alginate capsules, and we unravel the differences to other Marangoni boat systems based on camphor, which are mainly caused by surfactant evaporation from the liquid–air interface. The capsule Marangoni microswimmers also exhibit surfactant-mediated repulsive interactions with walls, which can be qualitatively explained by surfactant accumulation at the wall. Graphic Abstract

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Section: ũmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Surfactant-loaded capsules as Marangoni microswimmers at the air–water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection

et al. 2021

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“…As opposed to previous work [14,18,[27][28][29][30][31], we consider here completely symmetric Marangoni boats with isotropic surfactant emission as motivated by the experiments in Ref. [25].…”

Section: (): V-volmentioning

confidence: 99%

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

Ender

Kierfeld

2021

Eur. Phys. J. E

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We present a theory for the self-propulsion of symmetric, half-spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air–water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion–advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient along the air–water–swimmer contact line and Marangoni flow forces. We unravel whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occur for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.

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“…To get an in-depth understanding of how swimming spontaneously arises from chemical release, it is meaningful to isolate all contributions from surface tension. This is possible in the Stokes regime by using the Lorentz reciprocal theorem, which has proved very valuable in the context of self-propelled particles in general [77,78] and interfacial swimmers in particular [79,80].…”

Section: Flow and Surface Tension Contributionsmentioning

confidence: 99%

Role of Marangoni forces in the velocity of symmetric interfacial swimmers

et al. 2021

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Interfacial swimmers are objects that self-propel at an interface by autonomously generating a gradient of surface tension, often through the continuous release of a surfactant. While the case of asymmetric swimmers has long been studied, experiments have shown that spontaneous motion is also possible for symmetric swimmers. The basic mechanism of symmetry-breaking is qualitatively well-established but one key aspect of the phenomenon that has proved particularly difficult to elucidate is the role of Marangoni effects in the self-propulsion. We address this question by numerical methods, which can fully handle the complex interplay between swimmer motion, fluid flow, surfactant distribution, and Marangoni stresses. Our swimmer is a disk releasing a soluble surfactant in a deep-layer fluid. We investigate how the swimming velocity, represented by a Péclet number Pe * depends on its characteristics, as encapsulated in the Marangoni number M. We analyze the properties of the swimming diagram Pe * (M) and compare with approximate models to understand their origin. We find that the low-Pe * regime exhibits a bistability region: spontaneous swimming involves a threshold Marangoni number, a discontinuity in velocity and possibly hysteresis. Those features are present only for a full description of the problem and reveal the subtle but key role of Marangoni flows. The large-Pe * regime features a robust asymptotic scaling law Pe * ∼ M α , whose exponent α 0.72 is close to the 3/4 value predicted by a simplified model, indicating a much weaker influence of Marangoni flows. While our results were obtained assuming a point-source swimmer in the Stokes flow regime, we show that the picture remains very similar when considering a spatially extended source size, finite Reynolds number, or a fixed concentration swimmer. We discuss our findings in relation to experiments.

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Dynamics of a fully wetted Marangoni surfer at the fluid–fluid interface

Abstract: Marangoni flow created by the gradient of surface tension can be used to transport small objects along fluid interfaces.

Cited by 15 publications

References 23 publications

Surfactant-loaded capsules as Marangoni microswimmers at the air–water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection

Surfactant-loaded capsules as Marangoni microswimmers at the air–water interface: Symmetry breaking and spontaneous propulsion by surfactant diffusion and advection

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

Role of Marangoni forces in the velocity of symmetric interfacial swimmers

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