Interaction between two spherical bubbles rising in a viscous liquid

The three-dimensional flow around two spherical bubbles moving in a viscous fluid is studied numerically by solving the full Navier-Stokes equations. The study considers the interaction between two bubbles for moderate Reynolds numbers (50 ≤ Re ≤ 500, Re being based on the bubble diameter) and for positions described by the separation S (2.5 ≤ S ≤ 10, S being the distance between the bubble centres normalized by the bubble radius) and the angle θ (0o ≤ θ ≤ 90o ) formed between the line of centre and the direction perpendicular to the direction of the motion. We provide a general description of the interaction extending the results obtained for two bubbles moving side by side (θ = 0o ) by Legendre, Magnaudet & Mougin 2003 (J. Fluid Mech., 497,133-166) and for two bubbles moving in line (θ = 90o ) by Yuan & Prosperetti 1994 (J. Fluid Mech., 278, 325-349). Simple models based on physical arguments are given for the drag and lift forces experienced by each bubble. The interaction is the combination of three effects: a potential effect, a viscous correction (Moore correction) and a significant wake effect observed on both the drag and the transverse force of the second bubble when located in the wake of the first one

Reversal of the lift force on an oblate bubble in a weakly viscous linear shear flow

We compute the flow about an oblate spheroidal bubble of prescribed shape set fixed in a viscous linear shear flow in the range of moderate to high Reynolds numbers. In contrast to predictions based on inviscid theory, the numerical results reveal that for weak enough shear rates, the lift force and torque change sign in an intermediate range of Reynolds numbers when the bubble oblateness exceeds a critical value that depends on the relative shear rate. This effect is found to be due to the vorticity generated at the bubble surface which, combined with the velocity gradient associated with the upstream shear, results in a system of two counter-rotating streamwise vortices whose sign is opposite to that induced by the classical inviscid tilting of the upstream vorticity around the bubble. We show that this lift reversal mechanism is closely related to the wake instability mechanism experienced by a spheroidal bubble rising in a stagnant liquid

Numerical simulation of bubble generation in a T-junction

We present a numerical study of the formation of mini-bubbles in a 2D T-junction by means of the fluid dynamics numerical code JADIM. Numerical simulations were carried out for different flow conditions, giving rise to results on the behavior of bubble velocity, void fraction, bubble generation frequency and length. Numerical results are compared with existing experimental data thanks to non-dimensional analysis

Multiscale deformation of a liquid surface in interaction with a nanoprobe

The interaction between a nanoprobe and a liquid surface is studied. The surface deformation depends on physical and geometric parameters, which are depicted by employing three dimensionless parameters: Bond number Bo, modified Hamaker number Ha, and dimensionless separation distance D*. The evolution of the deformation is described by a strongly nonlinear partial differential equation, which is solved by means of numerical methods. The dynamic analysis of the liquid profile points out the existence of a critical distance D* min, below which the irreversible wetting process of the nanoprobe happens. For D* ≥ D*min, the numerical results show the existence of two deformation profiles, one stable and another unstable from the energetic point of view. Different deformation length scales, characterizing the stable liquid equilibrium interface, define the near- and the far-field deformation zones, where self-similar profiles are found. Finally, our results allow us to provide simple relationships between the parameters, which leads to determine the optimal conditions when performing atomic force microscope measurements over liquids

Shaken not stirred — On internal flow patterns in oscillating sessile drops

We use numerical (volume of fluid) simulations to study the flow in an oscillating sessile drop immersed in an ambient immiscible fluid. The drop is excited by a sinusoidal variation of the contact angle at variable frequency. We identify the eigenfrequencies and eigenmodes of the drops and analyze the internal flow fields by following the trajectories of tracer particles. The flow fields display an oscillatory component as well as a time-averaged mean component. The latter is oriented upward along the surface of the drop from the contact line towards the apex and downward along the symmetry axis. It vanishes at high and low frequencies and displays a broad maximum around f =200–300Hz. We show that the frequency dependence of the mean flow can be described in terms of Stokes drift driven by capillary waves that originate from the contact line, in agreement with recent experiments

Numerical modelling of grinding in a stirred media mill: Hydrodynamics and collision characteristics

Producing nanoparticles in dense suspensions can be achieved in a stirred media mill. However the mechanisms of fragmentation in the mill are still not fully understood and the process remains laborious because of the large amount of supplied energy. We focus on the numerical analysis of the local hydrodynamics in the mill. Based on the flow simulations we determine the parameters which control the efficiency of the collisions between grinding beads (impact velocities and orientation of the collisions). The suspension flow (grinding beads, particles, carrying fluid) is modelled with effective physical properties. We solve directly the continuity and Navier–Stokes equations for the equivalent fluid assuming that the flow is two-dimensional and steady. Depending on the Reynolds number and the non-Newtonian behaviour of the fluid, we found that the flow is composed of several toroidal vortices. The most energetic collisions are driven by the strong shear experienced by the suspension within the gap between the disc tip and the wall chamber

Experiments and modelling of a draft tube airlift reactor operated at high gas throughputs

One-dimensional modelling of global hydrodynamics and mass transfer is developed for an annulus sparged draft tube airlift reactor operating at high gas throughputs. In a first part, a specific closure law for the mean slip velocity of bubbles in the riser is proposed according for, in one hand, the collective effects on bubble rise velocity and, in the other hand, the size of the liquid recirculation in the airlift riser. This global hydrodynamics model is found towel explain the global gas volume fraction measurements in the airlift riser for a wide range of superficial gas velocity (0.6 ≤ Jg ≥10 cm sˉ¹). In a second part, mass transfer in the airlift has been studied by using the gassing-out method and a dual-tip optical probe to measure the bubble size distributions. As for bubble columns, in such airlift, the volumetric mass transfer coefficient appears to be quite proportional to the gas superficial velocity. Finally, as in Colombet et al. (2011), mass transfer at the bubble scale seems to be weakly influenced by an increase of gas volume fraction

Mass or heat transfer inside a spherical gas bubble at low to moderate Reynolds number

Mass (or heat) transfer inside a spherical gas bubble rising through a stationary liquid is investigated by direct numerical simulation. Simulations were carried out for bubble Reynolds number ranging from 0.1 to 100 and for Péclet numbers ranging from 1 to 2000. The study focuses on the effect of the bubble Reynolds number on both the interfacial transfer and the saturation time of the concentration inside the bubble. We show that the maximum velocity Umax at the bubble interface is the pertinent velocity to describe both internal and external transfers. The corresponding Sherwood (or Nusselt) numbers and the saturation time can be described by a sigmoid function depending on the Péclet number Pemax = Umaxdb/D (db and D being the bubble diameter and the corresponding diffusion coefficient)

Experiments and modelling of a draft tube airlift reactor operated at high gas throughputs

One-dimensional modelling of global hydrodynamics and mass transfer is developed for an annulus sparged draft tube airlift reactor operating at high gas throughputs. In a first part, a specific closure law for the mean slip velocity of bubbles in the riser is proposed according for, in one hand, the collective effects on bubble rise velocity and, in the other hand, the size of the liquid recirculation in the airlift riser. This global hydrodynamics model is found towel explain the global gas volume fraction measurements in the airlift riser for a wide range of superficial gas velocity (0.6 ≤ Jg ≥10 cm sˉ¹). In a second part, mass transfer in the airlift has been studied by using the gassing-out method and a dual-tip optical probe to measure the bubble size distributions. As for bubble columns, in such airlift, the volumetric mass transfer coefficient appears to be quite proportional to the gas superficial velocity. Finally, as in Colombet et al. (2011), mass transfer at the bubble scale seems to be weakly influenced by an increase of gas volume fraction

Comparison between numerical models for the simulation of moving contact lines

The aim of this study is to discus different numerically models for the simulation of moving contact lines in the context of a Volume of Fluid–Continuum Surface Force (VoF–CSF) method. We focus on the particular situation of spreading drops. We first present the numerical methods used for the simulation of moving contact line i.e. static contact angle versus dynamic contact angle, no slip condition versus slip condition. A grid and time convergence is performed for the different models. We show that the integration of the Continuum Surface Force using the finite volume method results in a grid dependence at the onset of the spreading. The static and dynamic models are compared to experiments. It is shown that the dynamic models based on the Cox’s relation for the dynamic contact angle are able to reproduce experiments while static models overestimate the spreading time and are not able to reproduce the Tanner regime. The difference between static and dynamic models is shown to increase with the Ohnesorge number