Shapes of Single Drops Rising Through Stagnant Liquids

Abstract

Shapes of single drops rising through infinite stagnant liquids under terminal conditions were measured using a high-speed camera for a wide range of fluid properties. Aspect ratios E and distortion factors γ of drops were evaluated from drop images. Effects of initial shape deformation, surfactants and viscosity ratio κ on E and γ were investigated. As a result, the following conclusions were obtained. (1) Initial shape deformation does not affect E and γ of single drops. (2) Addition of surfactants decreases E and breaks the fore-and-aft symmetry of a drop shape especially in systems of low Morton numbers M. (3) The Tadaki number Ta is the best dimensionless number among the Eotvos number Eo, the Weber number We and Ta for correlating E of drops, and an empirical correlation of E in terms of Ta was proposed for clean drops under the conditions of -11.6 ≤ log M ≤ -0.9, 1.5 × 10-2 ≤ Re ≤ 8.5 × 102, 1.7 × 10-2 ≤ Eo ≤ 9.3, 7.4 × 10-3 ≤ Ta ≤ 3.6 and 0.1 ≤ κ ≤ 100. (4) The viscosity ratio κ does not affect E so much but influences γ. For κ > 1, γ decreases with increasing the drop diameter, that is, the front part of a drop is flatter than the rear part. On the contrary, the rear part is flatter than the front part when κ < 1. The fore-and-aft symmetry always holds for drops with κ ∼ 1.0. (5) Various drop shapes were presented as a database utilized for verification of numerical methods such as an interface tracking method and a boundary element method.