Abstract Effect of bubble size on bubble-particle attachment and film drainage was studied based on the extended Derjaguin-Landau-Verwey-Overbeek theory and the Stefan-Reynolds flat film model. The disjoining pressure isotherms and wetting film drainage kinetics between a bubble and an model silica with different hydrophobic force decay lengths were calculated theoretically. It is found that the results depend on the shapes of total disjoining pressure isotherms. Film formed between a small bubble and silica surface always has faster drainage kinetics compared to that formed between a big bubble and silica surface due to the high Laplace pressure. For a monotonic repulsive total disjoining pressure, the wetting film is thermodynamically stable and the final equilibrium film thickness decreases with decreasing bubble size. In presence of a pressure barrier in total disjoining pressure, whether or not the film can rupture is determined by the magnitude between Laplace pressure and the pressure barrier. A small bubble is beneficial to the recovery of particles with weak and moderate floatability since the high Laplace pressure can drive the film to the range of hydrophobic force or even overcome the pressure barrier resulting in successful attachment. In flotation practice, much attention should be paid on bubble size since it not only affects collision efficiency but also influences the attachment behaviour.

中文翻译：

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气泡尺寸对气泡-颗粒附着和薄膜排水动力学的影响 - 理论研究

摘要 基于扩展的Derjaguin-Landau-Verwey-Overbeek 理论和Stefan-Reynolds 平膜模型，研究了气泡尺寸对气泡颗粒附着和薄膜排水的影响。理论上计算了不同疏水力衰减长度的气泡和模型二氧化硅之间的分离压力等温线和湿膜排水动力学。发现结果取决于总分离压力等温线的形状。由于拉普拉斯压力高，与大气泡和二氧化硅表面之间形成的薄膜相比，小气泡和二氧化硅表面之间形成的薄膜总是具有更快的排水动力学。对于单调排斥总分离压力，润湿膜是热力学稳定的，最终平衡膜厚度随着气泡尺寸的减小而减小。在总分离压力中存在压力屏障时，薄膜能否破裂取决于拉普拉斯压力与压力屏障之间的大小。小气泡有利于回收具有弱和中等可浮性的颗粒，因为高拉普拉斯压力可以将薄膜驱动到疏水力范围内，甚至克服压力障碍从而成功附着。在浮选实践中，气泡大小不仅会影响碰撞效率，还会影响附着行为，因此应特别注意气泡大小。小气泡有利于回收弱和中等可浮性的颗粒，因为高拉普拉斯压力可以将薄膜驱动到疏水力范围内，甚至克服压力障碍，从而成功附着。在浮选实践中，气泡大小不仅会影响碰撞效率，还会影响附着行为，因此应特别注意气泡大小。小气泡有利于回收弱和中等可浮性的颗粒，因为高拉普拉斯压力可以将薄膜驱动到疏水力范围内，甚至克服压力障碍，从而成功附着。在浮选实践中，气泡大小不仅会影响碰撞效率，还会影响附着行为，因此应特别注意气泡大小。