(8d) A New Approach to Predict the Non-Equilibrium Interactions Between an Air Bubble and a Flat Solid Surface Using the Generic Stokes-Reynolds-Young-Laplace Model (GSRYL model)

The interaction between an air bubble and solid surface is central to a broad range of industrial and biological processes. In this paper the Generic SRYL model, which is basically similar to the alternative SRYL model, is proposed to predict the dynamic interaction forces between an air bubble and a flat solid surface when they are in relative axisymmetric motion in a Newtonian liquid. In the Generic SRYL model, the Stokes-Reynolds equation is combined with the non-linearized second order form of the Young Laplace equation which leads to the appearance of the capillary number in the scaled equations. This study reveals that the second power of the bubble curvature, i.e., (∂h/∂r)2 becomes very important towards the edge of bubble and tends to 0.34, 1, 4.2 and ∞ when (r/R) approaches to 0.5, 0.71, 0.9 and 1, respectively, in which R is the bubble radius. In fact, this term is negligible compared to 1 when the magnitude of (r/R) gets smaller, (∂h/∂r)2=(r/R)2/(1-(r/R)2) . Therefore the second power of the bubble curvature, i.e., (∂h/∂r)2, must not be ignored in the Young Laplace equation. In spite of the alternative SRYL model in which it is assumed that this term, (∂h/∂r)2, is negligible over all range of (r/R) and it is selectively ignored compared to 1 in the Young Laplace equation, in the GSRYL model the original form of the Young-Laplace equation is used without any changes. The main advantage of the GSRYL model is that this new model offers a circular shape of the bubble at the initial separation. As a result, the GSRYL model can eliminate the approximation of the elliptical bubble geometry used as the initial separation in the alternative SRYL model. Another important advantage of this new model over the alternative SRYL model is that in spite of the SRYL model in which the scaled equations of system have a universal nature over all ranges of the capillary numbers, the scaled equations of the GSRYL model depend on the physical parameters of system via capillary number. Due to the complexity and non-universality form of the bubble behavior, the GSRYL model provides a new opportunity to study the non-equilibrium interactions between bubble and solid surface over different range of capillary numbers. The accuracy of this model is tested with the recent experimental data and confirms that this model can be successfully applied to predict the non-equilibrium interactions between an air bubble and a flat solid surface. This new model is worth further investigation, as we can take into account the bubble deformation, the original shape of the bubble at initial separation and all the physical parameters of a system for this prediction.