Terminal Velocity of Single Drops in Stagnant Liquids

Abstract

Terminal velocities of single drops rising through infinite stagnant liquids under wide ranges of fluid properties were measured to examine the effects of initial shape deformation, surfactants and the viscosity ratio. As a result, the following conclusions were obtained: (1) the terminal velocity V_T of a drop is not affected by initial shape deformation due to strong viscous damping of shape oscillation, (2) the drop drag coefficient C_D is a function of the drop Reynolds number Re, the viscosity ratio κ and surfactant concentration, (3) surfactants increase C_D and the influence of surfactants on C_D becomes weaker as κ increases, which is consistent with the Levich's drag model, (4) the effect of κ on C_D can be evaluated by the factor in the Levich's model, [(2+3κ)/(1+κ)], even at intermediate drop Re numbers, and (5) the combination of the Levich's model and Schiller & Nauman's correlation gives good estimation of C_D of single drops in clean and fully contaminated systems under the conditions of -11.6 <log₁₀M < -0.9, 1.7×10^-1 < Re < 2×10², 1.7×10^-2 < Eo < 12.1 and 0.1 < κ < 100.