Self-propulsion on liquid surfaces

Pimienta, Véronique; Antoine, Charles

doi:10.1016/j.cocis.2014.04.001

Cited by 78 publications

(73 citation statements)

References 51 publications

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“…The issue is then to solve Eq. (7) in the regime where the spreading dynamics is controlled by both advection and reaction. Despite the simplification β = 0, Eq.…”

mentioning

confidence: 99%

Spreading dynamics of reactive surfactants driven by Marangoni convection

Bickel

2019

Soft Matter

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We consider the spreading dynamics of some insoluble surface-active species along an aqueous interface. The model includes both diffusion, Marangoni convection and first-order reaction kinetics. An exact solution of the nonlinear transport equations is derived in the regime of large Schmidt number, where viscous effects are dominant. We demonstrate that the variance of the surfactant distribution increases linearly with time, providing an unambiguous definition for the enhanced diffusion coefficient observed in the experiments. The model thus presents new insight regarding the actuation of camphor grains at the water-air interface.

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“…The issue is then to solve Eq. (7) in the regime where the spreading dynamics is controlled by both advection and reaction. Despite the simplification β = 0, Eq.…”

mentioning

confidence: 99%

Spreading dynamics of reactive surfactants driven by Marangoni convection

Bickel

2019

Soft Matter

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“…an axial anisotropy, is important to realize the rotational motion through spontaneous symmetry breaking. However, a mathematical modeling of such motion has not been developed yet, although some preliminary attempts have been made [5,16,17].…”

Section: Introductionmentioning

confidence: 99%

Relationship between the size of a camphor-driven rotor and its angular velocity

et al. 2017

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We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. The disks dissipate camphor molecules. The driving momentum comes from the nonuniformity of surface tension resulting from inhomogeneous surface concentration of camphor molecules around the disks. We investigate the stationary angular velocity as a function of rotor radius ℓ. For large ℓ the angular velocity decreases for increasing ℓ. At a specific value of ℓ the angular velocity reaches its maximum and, for short ℓ it rapidly decreases. Such behaviour is confirmed by a simple numerical model. The model also predicts that there is a critical rotor size below which it does not rotate. Within the introduced model we analyze the type of this bifurcation.

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“…In a two-dimensional axisymmetric system, a rotational or oscillatory motion is often observed [5][6][7][8][9][10][11]. Here we define a rotational motion as the motion where the particle moves at a constant distance from the system center with a nonzero constant speed, while an oscillatory motion as a motion where the particle reciprocally moves back and forth along a line through the system center.…”

Section: Introductionmentioning

confidence: 99%

Rotational motion of a camphor disk in a circular region

2019

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In a two-dimensional axisymmetric system, the system symmetry allows rotational or oscillatory motion as stable stationary motion for a symmetric self-propelled particle. In the present paper, we studied the motion of a camphor disk confined in a two-dimensional circular region. By reducing the mathematical model describing the dynamics of the motion of a camphor disk and the concentration field of camphor molecules on a water surface, we analyzed the reduced equations around a bifurcation point where the rest state at the center of the system becomes unstable. As a result, we found that rotational motion is stably realized through the double-Hopf bifurcation from the rest state. The theoretical results were confirmed by numerical calculation and well corresponded to the experimental results.

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Self-propulsion on liquid surfaces

Cited by 78 publications

References 51 publications

Spreading dynamics of reactive surfactants driven by Marangoni convection

Spreading dynamics of reactive surfactants driven by Marangoni convection

Relationship between the size of a camphor-driven rotor and its angular velocity

Rotational motion of a camphor disk in a circular region

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