Quasi-steady shape and drag of deformable bubbles and drops

The quasi-steady shape and drag of isolated drops and bubbles are reviewed in terms of quantitative results, particularly for deformed conditions. Data in the literature were investigated to provide a comprehensive description of observed theoretical, experimental and numerical trends. New descriptions of the aspect ratio and quasi-steady drag coefficient were developed which approach the theoretical limits for creeping flow and attached thin boundary layer conditions, while representing experimental data and resolved-surface simulations at other conditions (many of which are only recently available). These relationships are novel in the sense that they are formulated in terms of the local Weber and Reynolds numbers (as well as density and viscosity ratios), as opposed to static parameters only valid at terminal velocity conditions (e.g. Bond number and Morton numbers). The results indicate that aspect ratio is a unique function of Weber number for fluid particle Reynolds numbers over 100 (especially for clean bubbles and liquid drops in a gas). This is consistent with theoretical results for small deformations. General relations were developed for minimum drag (for a sphere) maximum drag (at maximum-deformation), from which drag increments for intermediate deformation could be defined. These increments correlated especially well with Weber number for clean bubbles and liquid drops in a gas in terms of a group parameter WeRep0.2. Further research is necessary to integrate these results with effects of neighboring fluid particles and/or walls.