Hydrodynamic interaction between coaxially rising bubbles in elasto-visco-plastic materials: Bubbles with a wide range of relative sizes

The interaction of a pair of tandem bubbles is investigated rising in elastic yield stress fluids. The bubble radii have a wide range of relative sizes in 3.6\ensuremath{\mathit{m}}\ensuremath{\mathit{m}} \ensuremath{\le} \ensuremath{\mathit{R}} \ensuremath{\le} 16\ensuremath{\mathit{m}}\ensuremath{\mathit{m}}. Three distinct patterns are predicted: bubble approach, bubble separation and formation of an equilibrium distance. The latter appears when material elasticity comes into play. A distorted negative wake is formed and sustained behind the leading bubble, with two stagnation points, repelling the trailing bubble and maintaining the bubble distance. Maps of the trailing bubble radius versus bubble radii ratio are presented showing the three patterns for various initial separation distances and material properties.