Abstract
Knowledge of bubble-particle interaction is important in many industrial processes such as in flotation. While the collision (first interaction sub-process) between bubbles and particles is influenced only by hydrodynamic forces, the bubble behaviour during the attachment (second sub-process) is influenced both by hydrodynamic and surface forces. This work is focused on the study of the three-phase contact (TPC) line expansion during bubble adhesion on hydrophobic surface and on its experimental and mathematical description. The experiments were carried out in pure water where mobile bubble surface is expected. The rising bubble was studied in dynamic arrangement, whereas the stationary bubble was analysed in static arrangement. The attachment process was recorded using a high-speed digital camera and evaluated using image analysis. The diameter of the expanding TPC line as well as the dynamic contact angle was determined. Two approaches - the hydrodynamic and the molecular-kinetic - were used for mathematical description of the TPC line expansion. According to our results, the hydrodynamic model is suitable for the description of the initial fast phase of the expansion. The molecular-kinetic model was assessed as appropriate for almost whole range of TPC expansion. Parameters of the model were evaluated and compared for both types of arrangement.
Highlights
Fundamentals of the hydrodynamic model were given by Cox [3], Huh and Scriven [4] and Voinov [5] whose described the three-phase contact (TPC) line from viewpoint of fluid dynamics
The TPC line motion in the inner region is influenced by molecular interactions and its shape could be represented by the microscopic contact angle șm
The expansion of the TPC line for a small bubble adhering on the horizontal hydrophobic surface was studied for the dynamic and the stationary experimental arrangements provided that the bubble surface is mobile
Summary
Fundamentals of the hydrodynamic model were given by Cox [3], Huh and Scriven [4] and Voinov [5] whose described the TPC line from viewpoint of fluid dynamics. The first models break down in a close proximity to the TPC line. Due to the application of “noslip” condition of classical hydrodynamics the stress singularity occurs directly at the TPC line. To avoid such problem several models were proposed [4,5,6]. Inner, intermediate and outer regions are distinguished for the description of the bubble close to the TPC line. The inner region applicable closest to the TPC line is determined by the slip length Ls of order of molecular distance. The TPC line motion in the inner region is influenced by molecular interactions and its shape could be represented by the microscopic contact angle șm.
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