A Theoretical and Experimental Investigation of the Effect of Internal Circulation on the Drag of Spherical Droplets Falling at Terminal Velocity in Liquid Media

Abstract

Numerical solutions of the Navier-Stokes equations have been obtained for steady flow around circulating liquid spheres in liquid media in the Reynolds number range 1-50. The results are given in the form of surface vorticity and pressure distributions and drag coefficients. The computed total drag coefficients are in excellent agreement with experimental values for a number of liquid-liquid systems.

Terminal and transient drop rise velocity of single toluene droplets in water

“…In contrary to rigid particles, fluid particles have a mobile interface, and the tangential shear stress exerted by the continuous fluid on the interface leads to internal circulation patterns, provided these interfacial movements are not hindered by contaminations. The capability of interfacial movements reduces the drag and increases the particle velocity compared to a rigid sphere 1. As a consequence of the formation of an internal circulation, the mass transfer rate is significantly increased 2–4.…”

A Legendre-spectral element method for flow and heat transfer about an accelerating droplet

“…In an attempt to provide more confidence in our results, we shall turn our attention to the experimental data of Abdel-Alim and Hamielec [19] for a drop in a liquid and of Elzinga and Banchero [20] for a solid sphere. For the liquid-liquid systems, the experiments were set up in such a way that the dispersed phase is water, whereas the continuous phase is cyclohexanol and n-butyl lactate.…”

“…This phenomenon, known as Marangoni convection, is not new and has been shown to produce significant effects depending on the Marangoni number [21]. Because the information necessary for computing this dimensionless number was not given in Reference [19], it is difficult to justify whether or not such effects are indeed negligible.…”

Mass transfer to drops moving through power law fluids in the intermediate reynolds number region

“…Hamielec and Johnson (1962) and Hamielec et a1 (1963) obtained, by means of Galerkin's method, the approximate stream functions for the movement of a droplet in a viscous Newtonian fluid in the intermediate Reynolds number range (5 ,< Re' 5 40). Hamielec and co-workers (Hamielec et al, 1967;LeClair et al, 1972;Abdel-Alim and Hamielec, 1975) have numerically solved the Navier-Stokes equations for the stream functions inside and outside dispersed phases at Reynolds numbers significantly above the creeping flow regime and have applied their results to the calculation of drag coefficients. All of bhe above studies in the intermediate Reynolds number region have been for Newtonian fluids.…”