The effects of surface tension and tube inclination on a two-dimensional rising bubble

Abstract

The effects of surface tension σ and tube inclination β on the Froude number Fr of a large bubble rising in a two-dimensional duct is considered. It is found that there exists either one (for small σ and β > 0°) or a set (for any σ and β = 0°) of Fr-values for which the bubble has a continuous derivative at the nose. By selecting either this single Fr (or the maximum of the set), we obtain solutions in excellent agreement with both theoretical predictions and experimental results.

Taylor bubble moving in a flowing liquid in vertical channel: transition from symmetric to asymmetric shape

“…Figure 2 shows a comparison of the present VOF computations with the inviscid solutions of Couët & Strumolo (1987) and Ha Ngoc & Fabre (2004a). In the range Σ < 0.025, the bubble velocity is weakly sensitive to surface tension and the present results agree with the previous ones.…”

“…Interestingly, Birkhoff & Carter (1657) cast doubt on the Garabedian maximum velocity principle, arguing that if it was true, then the symmetric bubble would be unstable because a bubble that mounts touching one of the walls is equivalent to a bubble rising in a channel of twice the width, mounting faster than the centred one. The effect of surface tension was investigated later on, experimentally by Maneri & Zuber (1974), theoretically by Vanden-Broëck (1984), numerically by Couët & Strumolo (1987) Vanden-Broëck (1984), also motivated by the application of these concepts on descending jets falling from vertical nozzles, used the method of Birkhoff & Carter (1957) to obtain more precise estimations of the shape and velocity. It was shown that the omission of surface tension leads to an erroneous prediction of the velocity.…”

Experimental and numerical investigation of an air pocket immersed and immobilized in a horizontal water duct flow

“…The analysis of the propagation of the air pocket in a stagnant fluid was found to be in good agreement with the analytical solution of Benjamin (1968) at Bond Number growing up to infinity. Similarly, the comparison with the numerical study of Couët and Strumulo (1987) at small Froude Number (0.2-0.5) exhibited a good agreement. Renardy et al (2001) have implemented the Volume-ofFluid (VOF) method where the interface is modelled applying the piecewise linear construction (PLIC).…”

A Computational Study of Rising Plane Taylor Bubbles

“…(3.6) becomes 8) indicating that amplitudes of the coefficients a n (θ t ) for a choice of θ t = θ a will alternate in sign from odd to even n and will slowly decay to zero as n → ∞. However, in practice the series is truncated which has the following implications for our purposes here.…”

“…Approximate asymptotic analysis of Garabedian [13] puts the estimate of this speed F at an approximate value of 0.24. More recent computations [8,28] which use conformal-mapping and the Fourier collocation method have provided numerical evidence to the fact that a bubble with a stagnation point at its tip can rise at any speed F ≤ F C . Since these bubbles could be smooth or pointed, Garabedian [14] conjectured that these bubbles for values of F > F 1 are probably pointed bubbles.…”