Feng Dong-xia, Nguyen Anh V
School of Chemical Engineering, The University of Queensland , Brisbane, Queensland 4072, Australia.
Langmuir. 2016 Mar 1;32(8):1988-95. doi: 10.1021/acs.langmuir.5b04098. Epub 2016 Feb 15.
Floating objects on the air-water interfaces are central to a number of everyday activities, from walking on water by insects to flotation separation of valuable minerals using air bubbles. The available theories show that a fine sphere can float if the force of surface tension and buoyancies can support the sphere at the interface with an apical angle subtended by the circle of contact being larger than the contact angle. Here we show that the pinning of the contact line at the sharp edge, known as the Gibbs inequality condition, also plays a significant role in controlling the stability and detachment of floating spheres. Specifically, we truncated the spheres with different angles and used a force sensor device to measure the force of pushing the truncated spheres from the interface into water. We also developed a theoretical modeling to calculate the pushing force that in combination with experimental results shows different effects of the Gibbs inequality condition on the stability and detachment of the spheres from the water surface. For small angles of truncation, the Gibbs inequality condition does not affect the sphere detachment, and hence the classical theories on the floatability of spheres are valid. For large truncated angles, the Gibbs inequality condition determines the tenacity of the particle-meniscus contact and the stability and detachment of floating spheres. In this case, the classical theories on the floatability of spheres are no longer valid. A critical truncated angle for the transition from the classical to the Gibbs inequality regimes of detachment was also established. The outcomes of this research advance our understanding of the behavior of floating objects, in particular, the flotation separation of valuable minerals, which often contain various sharp edges of their crystal faces.
空气 - 水界面上的漂浮物体在许多日常活动中都至关重要，从昆虫在水面行走，到利用气泡对有价值矿物进行浮选分离。现有理论表明，如果表面张力和浮力能够在界面处支撑球体，且接触圆所对的顶角大于接触角，那么一个精细的球体就可以漂浮。在此我们表明，接触线在尖锐边缘处的钉扎现象，即吉布斯不等式条件，在控制漂浮球体的稳定性和脱离方面也起着重要作用。具体而言，我们用不同角度截断球体，并使用力传感器装置测量将截断球体从界面推入水中的力。我们还开发了一个理论模型来计算推力，该模型与实验结果相结合，展示了吉布斯不等式条件对球体从水面的稳定性和脱离的不同影响。对于小截断角度，吉布斯不等式条件不影响球体脱离，因此关于球体漂浮性的经典理论是有效的。对于大截断角度，吉布斯不等式条件决定了颗粒 - 弯月面接触的韧性以及漂浮球体的稳定性和脱离。在这种情况下，关于球体漂浮性的经典理论不再有效。还确定了从经典脱离模式到吉布斯不等式脱离模式转变的临界截断角。这项研究的成果推进了我们对漂浮物体行为的理解，特别是对有价值矿物的浮选分离的理解，这些矿物的晶面通常包含各种尖锐边缘。
