Nonuniform Collective Dissolution of Bubbles in Regular Pore Networks

Understanding the evolution of solute concentration gradients underpins the prediction of porous media processes limited by mass transfer. Here, we present the development of a mathematical model that describes the dissolution of spherical bubbles in two-dimensional regular pore networks. The model is solved numerically for lattices with up to 169 bubbles by evaluating the role of pore network connectivity, vacant lattice sites and the initial bubble size distribution. In dense lattices, diffusive shielding prolongs the average dissolution time of the lattice, and the strength of the phenomenon depends on the network connectivity. The extension of the final dissolution time relative to the unbounded (bulk) case follows the power-law function, $${B^k/\ell }$$ B k / ℓ , where the constant $$\ell$$ ℓ is the inter-bubble spacing, B is the number of bubbles, and the exponent k depends on the network connectivity. The solute concentration field is both the consequence and a factor affecting bubble dissolution or growth. The geometry of the pore network perturbs the inward propagation of the dissolution front and can generate vacant sites within the bubble lattice. This effect is enhanced by increasing the lattice size and decreasing the network connectivity, yielding strongly nonuniform solute concentration fields. Sparse bubble lattices experience decreased collective effects, but they feature a more complex evolution, because the solute concentration field is nonuniform from the outset.

Flow Structure and Deformation of Two Bubbles Rising Side by Side in a Quiescent Liquid

In the motion of two spherical bubbles rising side by side, the bubbles are known to attract each other at a high Reynolds number (Re = ρUd/μ). Furthermore, spherical bubbles kiss and bounce under certain conditions; however, deformable bubbles repel each other without kissing. This paper experimentally and numerically presents the flow structures and shape of the nonkissing repulsion of deformable bubbles. For the experimental analysis, we organized bubble behaviors by Galilei number (Ga = ρg1/2d3/2/μ) and Bond number (Bo = ρgd2/σ). The bubbles repelled each other without kissing near the unstable critical curve of a single bubble. The curvature inside the gap, which is similar to the shape of a zigzag behavior bubble, was large. For the numerical analysis, the velocity of the equatorial plane inside the gap was larger due to the potential interaction, although the velocity behind was the opposite due to the strengthened vorticity generated at the surface. Furthermore, the double-threaded wake emerged behind the interacting bubbles, and it showed that the rotation direction was repulsion regardless of whether the bubbles attracted or repelled each other. The streamline behind the bubbles in the 2D plane was from the outside to the inside.

Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

Comparison of Two Solvers for Simulation of Single Bubble Rising Dynamics: COMSOL vs. Fluent

Multiphase flows are a part of many industrial processes, where the bubble motion influences the hydrodynamic behavior of the batch. The current trend is to use numerical solvers that can simulate the movement and mutual interactions of bubbles. The aim of this work was to study how two commercial CFD solvers, COMSOL Multiphysics and Ansys Fluent, can simulate the motion of a single rising bubble in a stagnant liquid. Simulations were performed for spherical or slightly deformed bubbles (Db = 0.6, 0.8, and 1.5 mm) rising in water or in propanol. A simple 2D axisymmetric approach was used. Calculated bubble terminal velocities and bubble shape deformations were compared to both experimental data and theoretical estimations. Solver Comsol Multiphysics was able to precisely calculate the movement of smaller and larger bubbles; due to the 2D rotational symmetry, better results were obtained for small spherical bubbles. The deformation of larger bubbles was calculated sufficiently. Solver Ansys Fluent, in the setting used, failed to simulate the motion of small bubbles due to parasitic currents but allowed for modeling of the motion of larger bubbles. However, the description of the bubble velocity and shape was worse in comparison with experimental values.

Foam bubble size is significantly influenced by sclerosant concentration for polidocanol but not sodium tetradecyl sulphate

Objectives To determine the effect of liquid gas fraction (LGF), sclerosant type and concentration, and filter use on foam bubble size and count. Methods Sclerosant foam microstructure was investigated using light microscopy for a range of LGFs (1 + 2, 1 + 4 and 1 + 8), for both sodium tetradecyl sulphate (STS) and polidocanol (POL), at a range of concentrations (0.5–3%), with and without the addition of micro-filters. Foam was generated using a modified Tessari method and placed into wells for analysis by light microscopy. Foam microscopic morphology was photographically documented, and bubble diameters and counts were quantified. Results Spherical bubbles were observed at lower LGF and a trend towards polyhedral morphology was observed at the higher LGF of (1 + 8). The higher gas content in LGF led to larger but fewer bubbles. POL bubble diameters appeared to be more influenced by concentration than STS with smaller bubbles observed at higher concentrations of POL. The mean bubble diameters were slightly larger for STS than POL at the highest concentration of 3% but smaller at lower concentrations of 1% and 1.5%. Conclusions LGF is the primary determinant of bubble diameter and count. In contrast to STS, POL concentration influences the foam bubble size with smaller bubbles generated at higher concentrations of POL and larger bubbles appearing at low concentrations of this agent.

Observation of Pseudo Plume Behavior by Hydrate Sedimentary Layer Decomposition

We are focusing on the practical use of methane hydrate. For recovery and use of it as an energy resource, it is necessary to consider the possibility of clogging in the recovery pipe due to the rehydration of bubbles. The purpose of this research was to observe experimentally and evaluate theoretically the decomposition behavior of hydrate sedimentary layer and the rising behavior of bubbles generated by hydrate decomposition. Chlorodifluoromethane was used as a low pressure model gas of methane. Hydrate sedimentary layer was produced by cooling and pressurizing water in countercurrent contact with gas using a hydrate formation recovery device. The recovered hydrate was decomposed by the heating or depressurization method, without flowing water. Two theoretical rising velocities were derived from the theoretical value with using the Navier-Stokes equation or the values in consideration of the bubble shape and hydrate film existence. The experimental rising velocities of small spherical bubbles radius agreed well with the theoretical value by the Navier-Stokes equation. The relatively large elliptical bubbles showed a behavior close to the theoretical value of bubble with hydrate film. Under the pressure and temperature conditions closer to the hydrate equilibrium line, almost no generated bubbles could be identified visually.

Numerical Study of the Interaction between a Collapsing Bubble and a Movable Particle in a Free Field

This study numerically investigates the interactions between a collapsing bubble and a movable particle with a comparable size in a free field, which is associated with the microscopic mechanisms of the synergetic effects of cavitation erosion and particle abrasion on the damages of materials in fluid machineries. A new solver on OpenFOAM based on direct numerical simulations with the volume of fluid (VOF) method capturing the interface of a bubble and with the overset grid method handling the motion of the particle was developed to achieve the fluid–structure interaction (FSI). The results show that bubbles in cases with stand-off parameter χ (defined as (d0−Rp)/R0), where d0 is the initial distance between the centers of the bubble and particle, and Rp,R0 are the particle’s radius and the initial radius of the bubble respectively >1, experience spherical-shaped collapse under the influence of the approaching particle, which is attracted by the collapsing bubble. The bubbles in these cases no longer present non-spherical collapse. Additionally, a force balance model to account for the particle dynamics was established, in which the particle velocity inversely depends on the size of the particle, and approximately on the second power of the initial distance from the bubble. This analytical result accords with the numerical results and is valid for cases with χ>1 only, since it is based on the theory of spherical bubbles. These conclusions are important for further study of the interactions between a bubble and a movable particle near a rigid wall.