Description of the Bubble Shape on a Planar Solid Surface with Variable Inclination Angle

The bubble-particle interaction is a common phenomenon used in numerous industrial applications. A stable attachment of the bubble on a hydrophobic surface is influenced by fast and stable creation of the three-phase contact line. All mathematical models which describe the TPC line expansion utilize the knowledge of dynamic and equilibrium contact angles. The description of a drop or a bubble placed on an inclined plane or curved surface is very complicated. Up to now few methods were published, but these methods are not suitable for the description of sizeable amount of data. Therefore, the aim of this project is to figure out the methodology for relatively simple and fast calculations of contact angles. The special attention was paid on the ability of the model to describe the bubble shape during the adhesion on hydrophobic solid surface.When compared with the liquid drop placed on an inclined plane, the bubble holds nearly a spherical shape and contact angles in the upper and lower bubble end differ only little. The basic idea of our method is to divide the bubble into two parts and describe these parts separately. A set of points around the bubble is obtained and then the ADSA methodology is used. The calculated data were compared with experimental data and a very good agreement was obtained. The variation number divided by number of points corresponds to the value of experimental error. According to the obtained results it is possible to conclude, that during the bubble adhesion on slightly inclined plane the dynamic contact angle differ insignificantly and along the whole contact line contact angles could be described using the average value. The error of such approximation does not exceed the experimental error. In the first part of bubble adhesion, the value of dynamic contact angle is influenced primarily by the bubble size and the contact angle decreases with increasing bubble size. Results of the work could have a great importance in the study of bubble-particles interactions on non-horizontal planes. We assume a noticeable simplification of the calculation of the TPC expansion.