LAUSR

For a floating bubble, in the range of Bond numbers based on an equivalent spherical radius, 0 < Boe < 1, we present analytical expressions for various shape parameters of the bubble as functions of Boe. Expressions are obtained for the radius of the rim Rr, the radius of the thin film cap Rc, the height of the top of the cap from the rim hcap, the height of the rim above the free surface hr, and the depth of the bubble cavity from the free surface Zc. To obtain these expressions, we solve equations formulated in terms of these shape parameters for the meniscus outside the bubble, the force balance of the bubble, the pressure balance at the centre line of the bubble, and geometrical constraints, after neglecting the deformation of the bubble cavity for Boe < 1. The obtained expressions are shown to match well with our experimental measurements of the shape of the bubble. In addition to these expressions, we also present simpler approximations that can be used accurately as scaling laws for these shape parameters up to Boe < 0.5.