The European Physical Journal E ( IF 1.8 ) Pub Date : 2021-03-08 , DOI: 10.1140/epje/s10189-021-00035-8 Hendrik Ender 1 , Ann-Kathrin Froin 2 , Heinz Rehage 2 , Jan Kierfeld 1
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Abstract
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
中文翻译：
表面活性剂负载胶囊作为空气-水界面处的马兰戈尼微型游泳器：表面活性剂扩散和平流的对称破缺和自发推进
摘要
我们通过空气-水界面上的半球形藻酸盐胶囊实现了快速界面马兰戈尼微型游泳器，该胶囊扩散释放水溶性扩散分子（弱表面活性剂，例如聚乙二醇（PEG）），充当“燃料”通过调节空气-水界面张力。对于许多不同的燃料，尽管藻酸盐颗粒和发射是各向同性的，但我们可以观察到对称性破缺和自发推进。推进机制类似于肥皂船或樟脑船，然而，它们通常在形状或排放上不对称以选择游泳方向。我们通过分析表面活性剂扩散和平流与流体流动的耦合问题，从低雷诺数出发，建立了马兰戈尼船推进理论，其中包括表面活性剂引起的流体马兰戈尼流动，以及空气-水界面上的表面活性剂吸附；我们还包括表面活性剂可能的蒸发。游泳速度由阻力和马兰戈尼力的平衡决定。我们表明，在临界无量纲表面活性剂排放率（佩克莱特数）之上，自发对称破缺导致推进是可能的。我们推导了佩克莱特数和游泳速度之间的关系，并利用努塞尔数的概念推广到更高的雷诺数。该理论解释了观察到的 PEG-藻酸盐胶囊的游动速度，并且我们揭示了与其他基于樟脑的 Marangoni 船系统的差异，这主要是由液-气界面的表面活性剂蒸发引起的。胶囊 Marangoni 微型游泳器还表现出表面活性剂介导的与壁的排斥相互作用，这可以通过表面活性剂在壁上的积累来定性地解释。
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