Model Order Reduction for Determining Bubble Parameters to Attain a Desired Fluid Surface Shape

In this paper, a new methodology for predicting fluid free surface shape using Model Order Reduction (MOR) is presented. Proper Orthogonal Decomposition combined with a linear interpolation procedure for its coefficient is applied to a problem involving bubble dynamics near to a free surface. A model is developed to accurately and efficiently capture the variation of the free surface shape with different bubble parameters. In addition, a systematic approach is developed within the MOR framework to find the best initial locations and pressures for a set of bubbles beneath the quiescent free surface such that the resultant free surface attained is close to a desired shape. Predictions of the free surface in two-dimensions and three-dimensions are presented.

Corner Flows in Free Liquid Films

A lubrication-flow model for a free film in a corner is presented. The model, written in the hyperbolic coordinate system ξ = x² – y², η = 2xy, applies to films that are thin in the η direction. The lubrication approximation yields two coupled evolution equations for the film thickness and the velocity field which, to lowest order, describes plug flow in the hyperbolic coordinates. A free film in a corner evolving under surface tension and gravity is investigated. The rate of thinning of a free film is compared to that of a film evolving over a solid substrate. Viscous shear and normal stresses are both captured in the model and are computed for the entire flow domain. It is shown that normal stress dominates over shear stress in the far field, while shear stress dominates close to the corner.