The Drag Coefficient and the Shape for a Single Bubble Rising in Non-Newtonian Fluids

The dynamical characteristic of a single bubble rising in non-Newtonian fluid was investigated experimentally. The bubble aspect ratio and rising velocity were measured by high speed camera. The shape regimes for bubbles in non-Newtonian fluids was plotted by means of Reynolds number Re, Eötvös number Eo and Morton number Mo. The effects of bubble shape and liquid rheological property on the total bubble drag coefficient were studied. A new empirical drag coefficient correlation covering spherical bubble and deformed bubble was proposed, the predicted results shows good conformity to experimental values over a wide range of 0.05 < Re < 300.

On the lateral migration of a slightly deformed bubble rising near a vertical plane wall

Deformation-induced lateral migration of a bubble slowly rising near a vertical plane wall in a stagnant liquid is numerically and theoretically investigated. In particular, our focus is set on a situation with a short clearance c between the bubble interface and the wall. Motivated by the fact that numerically and experimentally measured migration velocities are considerably higher than the velocity estimated by the available analytical solution using the Faxén mirror image technique for a/(a + c) ≪ 1 (here a is the bubble radius), when the clearance parameter ϵ(=c/a) is comparable to or smaller than unity, the numerical analysis based on the boundary-fitted finite-difference approach solving the Stokes equation is performed to complement the experiment. The migration velocity is found to be more affected by the high-order deformation modes with decreasing ϵ. The numerical simulations are compared with a theoretical migration velocity obtained from a lubrication study of a nearly spherical drop, which describes the role of the squeezing flow within the bubble–wall gap. The numerical and lubrication analyses consistently demonstrate that when ϵ ≤ 1, the lubrication effect makes the migration velocity asymptotically μVB12/(25ϵγ) (here, VB1, μ and γ denote the rising velocity, the dynamic viscosity of liquid and the surface tension, respectively).

Nonlinear effects in the dynamics of shape and volume oscillations for a gas bubble in an external flow

This paper considers the dynamics of a gas bubble in response to either a pressure pulse or a pressure step at t = 0, both in the presence and absence of a mean flow. Our work utilizes small-deformation, domain perturbation analysis carried to second and higher order in the amplitude of deformation, ε. In the absence of a mean flow, our analysis of the small deformation problem for an initial impulsive perturbation of the bubble volume and shape is closely related to recently published work by Longuet-Higgins on the time-dependent oscillations of an initially deformed bubble in a quiescent fluid. However, in the presence of a mean flow which deforms the bubble, the bubble response to pressure changes is more complex. Specifically, the present analysis identifies a number of different mechanisms for resonant interaction between shape deformation modes and the volume or radial breathing mode of oscillation. This includes not only a fundamental change in the resonant interactions at 0(ε2) - where resonant interaction is also found in the absence of mean flow – but resonant interactions also at the level of 0(ε3/2;) which are not present without the mean flow. On the other hand, the bubble dynamics in response to a step change in the pressure distribution in a quiescent fluid exhibits similar resonant interactions at 0(ε2) to those obtained for a pressure pulse in the presence of mean flow because the bubble oscillates around a non-spherical steady-state shape owing to the non-uniform pressure distribution on the bubble surface in both the cases.