A General Correlation for the Rise Velocity of Single Gas Bubbles

Abstract

A correlation for the terminal rising velocity of a single gas bubble in an infinite Newtonian fluid is proposed. The model is an extension to high Reynolds numbers of a model developed recently by the author (Rodrigue, 2001a). This new equation, which is explicit in velocity, is able to predict the velocity for any bubble volume in any Newtonian fluid.

Theoretical study of motion of small spherical air bubbles in a uniform shear flow of water

“…3 X * and Y * are the nondimensional horizontal and vertical distances respectively defined as X Ã ¼ x b w and Y Ã ¼ y b w . It is to be noted that even though the correlation of Rodrigue [6] predicts the terminal rise velocities with an error of approximately 10%, the calculated trajectory matches well with the simulated results of Rabha and Buwa [3] (maximum deviations of 10 À1 mm) as compared to the other two models. Here it is important to mention that the models of Dijkhuizen et al [18] and Hibiki and Ishii [19] includes the effect of liquid viscosity and bubble deformation as well.…”

“…From the literature survey it was found that a general correlation for the free rise velocity of a bubble in any Newtonian liquid can be explicitly calculated by the correlation proposed by Rodrigue [6]. The correlation is given as Equations 13e16 and its comparison with the experimental results of Haberman and Morton [16] is shown in Fig.…”

“…It is shown in this study that a simple Couette flow velocity profile in combination with a general correlation for the free terminal rise velocity of the bubble in any stagnant Newtonian liquid proposed by Rodrigue [6] is sufficient to produce reliable results for the trajectories of small air bubbles. The properties of water and other relevant nondimensional numbers used in this study are shown in Table 1.…”

“…Comparison of Rodrigue[6] correlation with experiments of Haberman and Morton[16] for stagnant water.…”

Controls on the explosivity of scoria cone eruptions: Magma segregation at conduit junctions

“…The differences between the natural and experimental conditions 275 are thus large, which will affect both bubble shape and velocity. In particular, gas 276 velocity in our simulations will be underestimated by about one order of magnitude 277 because of the high Mo anticipated in volcanic systems (e.g., Rodrigue, 2004). This 278 limitation will affect both pressure calculations and mass distributions, leading to an 279 overestimation of the amount of gas that is directed into the lateral branch.…”