Review of potential flow solutions for velocity and shape of long isolated bubbles in vertical pipes

The motion of elongated gas bubbles in vertical pipes has been studied extensively over the past century. A number of empirical and numerical correlations have emerged out of this curiosity; amongst them, analytical solutions have been proposed. A review of the major results and resolution methods based on a potential flow theory approach is presented in this article. The governing equations of a single elongated gas bubble rising in a stagnant or moving liquid are given in the potential flow formalism. Two different resolution methods (the power series method and the total derivative method) are studied in detail. The results (velocity and shape) are investigated with respect to the surface tension effect. The use of a new multi-objective solver coupled with the total derivative method improves the research of solutions and demonstrates its validity for determining the bubble velocity. This review aims to highlight the power of analytical tools, resolution methods and their associated limitations behind often well-known and wide-spread results in the literature.

LBM modeling of solid particle dynamics in a viscous medium

This article discusses the mathematical and computer modeling of single solid particle dynamics in a viscous medium. The results of the study were obtained using a 3D numerical algorithm implemented on the basis of the D3Q19 model of the lattice Boltzmann method (LBM). The moving «liquid-solid» interface is accounted for using an interpolated bounce back (IBB) scheme. The velocity of a solid particle motion and the trajectory of a particle at Re = 1,56 are obtained. The results are in good agreement with the experimental and numerical results of other authors.

Building an open network for CO2 transport and storage

Maritime transport is emerging as an essential link in the decarbonisation chain by moving liquid carbon dioxide from the source to a safe storage location.

Magnetohydrodynamic Moving Liquid Plug Within a Microchannel: Analytical Solutions

The wide applications of plug flows in microscale in science and engineering help them attract a great deal recent interest. An analytical study is undertaken here to study the impacts of a transversely applied external uniform magnetic field affecting the motion of liquid in the plug in terms of hydrodynamic mixing properties. The well-known symmetric vortex structure occurring in a long plug with moderate aspect ratio is observed to be preserved, while the recirculation phenomenon is highly affected by the action of the magnetic field. The decelerating feature of Lorentz force on the liquid motion is illuminated by reducing the strength of the recirculating vortex moving towards the upper and lower walls. The effects of magnetic field on the flow resistance of the liquid plug as well as on the plug circulation rate and on the axial flux are also clarified. The liquid plug considered here is shown to be fully consistent with the continuous liquid flow in a channel whose exact solution is further extracted.

The Effects of Surfactant on the Evolution of a Thin Film under a Moving Liquid Drop

The effect of surfactant on the thickness of a thin film bounded by a solid surface and a moving liquid drop was investigated. We proposed a model so that parameters from the liquid drop can be stated in a parameter that acts as normal pressure to the thin film. Using the lubrication approximation, the model was reduced to a set of nonlinear partial differential equations in terms of the film thickness and surfactant concentration. Since we were interested in the role of the surfactant in lifting up the drop, we assumed that the density of the drop is higher than the density of the thin film. Numerically, the results show that the presence of the surfactant tends to delay the decrease of the film thickness insignificantly. However, when the surfactant was added into the system, it tends to significantly increase the film thickness for a certain range value of the normal pressure.