(6co) A New Approach to Predict the Dynamic Interactions Between an Air Bubble/Drop and a Flat Solid Surface

In this study the Generic Stokes-Reynolds Young-Laplace model (GSRYL model) is proposed to predict the dynamic interaction forces acting 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, which is basically similar to the alternative SRYL model, the Stokes-Reynolds equation is combined with the non-linearized second order form of the augmented Young Laplace equation to relate the mean curvature of the fluid interface to the pressure difference across the interface. The non-linearized second order form of the augmented Young Laplace equation built in the GSRYL model, leads to the appearance of the capillary number in the scaled equations.

This new theoretical framework has two important advantages over the alternative SRYL model. First, this model offers an accurate perspective of the bubble geometry at the initial separation and eliminates the approximation of the elliptical bubble geometry used as the initial separation in the alternative SRYL model. The second advantage of this model is that in spite of the SRYL model in which the scaled equations of system have a universal nature which predicts the bubble behaves nearly in a universal way over all ranges of capillary numbers, the scaled equations of the GSRYL model do not have a universal nature and depend on the physical parameters of system via capillary number.

The accuracy of this model is tested with the recent experimental data reported in the literature 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 system for this prediction.