An extended volume of fluid method is developed for two-phase direct numerical simulations of systems with one viscoelastic and one Newtonian phase. A complete set of governing equations is derived by conditional volume-averaging of the local instantaneous bulk equations and interface jump conditions. The homogeneous mixture model is applied for the closure of the volume-averaged equations. An additional interfacial stress term arises in this volume-averaged formulation which requires special treatment in the finite-volume discretization on a general unstructured mesh. A novel numerical scheme is proposed for the second-order accurate finite-volume discretization of the interface stress term. We demonstrate that this scheme allows for a consistent treatment of the interface stress and the surface tension force in the pressure equation of the segregated solution approach. Because of the high Weissenberg number problem, an appropriate stabilization approach is applied to the constitutive equation of the viscoelastic phase to increase the robustness of the method at higher fluid elasticity. Direct numerical simulations of the transient motion of a bubble rising in a quiescent viscoelastic fluid are performed for the purpose of experimental code validation. The well-known jump discontinuity in the terminal bubble rise velocity when the bubble volume exceeds a critical value is captured by the method. The formulation of the interfacial stress together with the novel scheme for its discretization is found crucial for the quantitatively correct prediction of the jump discontinuity in the terminal bubble rise velocity.
Previous observations of the nontransient oscillations of rising bubbles and falling spheres in wormlike micellar fluids were limited to a single surfactant system. We present an extensive survey of rising bubbles in another system, an aqueous solution of cetylpyridinium chloride and sodium salicylate, with and without NaCl, across a range of concentrations and temperatures. Two different types of oscillation are seen in different concentration ranges, each with its own temperature dependence. Rheological data allows for the identification of these different hydrodynamic states with different …
We calculate the shape and the velocity of a bubble rising in an infinitely large and closed Hele-Shaw cell using Park and Homsy's boundary condition which accounts for the change of the three dimensional structure in the perimeter zone. We first formulate the problem in the form of a variational problem, and discuss the shape change assuming that the bubble takes elliptic shape. We calculate the shape and the velocity of the bubble as a function of the bubble size, gap distance and the inclination angle of the cell. We show that the bubble is flattened as it rises. This result is in agreement…
Shapes and paths of an air bubble rising inside a liquid are investigated experimentally. About three hundred experiments are conducted in order to generate a phase plot in the Galilei and Eotvos numbers plane, which separates distinct regimes in terms of bubble behaviour. A wide range of the Galilei and Eotvos numbers are obtained by using aqueous glycerol solutions of different concentrations as the surrounding fluid, and by varying the bubble size. The dynamics is investigated in terms of shapes, topological changes and trajectories of the bubbles. Direct numerical simulations are conducted…
We present accurate measurements of the relative motion and deformation of two large bubbles released consecutively in a quiescent liquid confined in a thin-gap cell. Though the second bubble injected is smaller, we observed that in all cases it accelerates and catches up with the leading bubble. This acceleration is related to the wake of the leading bubble which also induces significant changes in the width and curvature of the trailing bubble. On the contrary, the velocity of the leading bubble is unaltered during the whole interaction and coalescence process. Shape adaptation of the two bu…
We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Voronoï analysis enables us to quantitatively distinguish between two typical clustering configurations: preferential clustering and a grid-like structure. The bubble data is obtained from direct numerical simulations (DNS) using the front-tracking method. It is found that the bubble deformation, represented by the aspect ratio χ, plays a significant role in determining which type of clustering is realized: Nearly spherical bubbles with χ<~ 1.015 form a grid-like structure, while more d…
When a stationary bubble and a stationary droplet immersed in a liquid pool are brought in contact with each other, they form a bubble-droplet aggregate. Its equilibrium morphology and stability largely depend on the combination of different components' surface tensions, known as spreading factor. In this study, we look at the interaction between a rising bubble and a stationary droplet to better understand the dynamics of coalescence and rising as well as morphological changes for the bubble-droplet aggregate. A systematic study is conducted on the interaction processes with various bubble si…
Rising bubbles draw surface patterns: a numerical study
School of Engineering Science, University of Chinese Academy of Sciences（中国科学院大学工程科学学院）；Department of Energy and Power Engineering, Tsinghua University（清华大学能源与动力工程系）；State Key Laboratory of Nonlinear Mechanics, IMECH & UCAS（中国科学院力学研究所非线性力学国家重点实验室）
Detailed understanding of two-phase gas liquid flows is imperative for developing efficient multi-phase reactors through precise control of mixing and reaction kinetics. The bubble column is a good apparatus for elementary studies of such flows. In the current study experiments are conducted to assess the effect of liquid viscosity on flow dynamics inside a bubble column. Corn oil and water are used as the continuous media, and air was the dispersed media. The objective of this effort is to use the results for a qualitative validation of the numerical simulations.
Interface-resolved direct numerical simulations are performed to examine the combined effects of soluble surfactant and viscoelasticity on the structure of a bubbly turbulent channel flow. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is achieved through a non-linear equation of state which relates the surface tension to the surfactant concentration at the interface. The two-fluid Navier-Stokes equations are solved using a front-tracking method, augmen…
Series of experiments on turbulent bubbly channel flows observed bubble clusters near the wall which can change large-scale flow structures. To gain insights into clustering mechanisms, we study the interaction of a pair of spherical bubbles rising in a vertical channel through combined experiments and modeling. Experimental imaging identifies that pairwise bubbles of 1.0 mm diameter take two preferred configurations depending on their mutual distance: side-by-side positions for a short distance ($S<5$) and nearly inline, oblique positions for a long distance ($S>5$), where $S$ is the mutual d…
A three-field local projection stabilized finite element method is developed for computations of a 3D-axisymmetric buoyancy driven bubble rising in a liquid column in which either the bubble or the liquid column can be viscoelastic. The two-phase flow is described by the time-dependent incompressible Navier--Stokes equations, whereas the viscoelasticity is modeled by the Giesekus constitutive equation in a time-dependent domain. The arbitrary Lagrangian Eulerian~(ALE) formulation with finite elements is used to solve the governing equations in the time-dependent domain. The interface-resolved …
This work describes an experimental investigation on the mixing induced by a swarm of high Reynolds number air bubbles rising through a nearly homogeneous and isotropic turbulent flow. The gas volume fraction $α$ and the velocity fluctuations $u'_0$ of the carrier flow before bubble injection are varied, respectively, in the ranges $0\leq α\leq 0.93\%$ and 2.3 cm/s $\leq u'_0 \leq 5.5$ cm/s, resulting in a variation of the bubblance parameter $b$ in the range [0, 1.3] ($b = \frac{V_r^2 α}{{u'}_0^2}$, where $V_r$ is the relative rising velocity). Mixing in the horizontal direction can be modell…
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 small clearance $c$ between the bubble interface and the wall. Motivated by the fact that experimentally measured migration velocity (Takemura et al. (2002, J. Fluid Mech. {\bf 461}, 277)) is higher than the velocity estimated by the available analytical solution (Magnaudet et al. (2003, J. Fluid Mech. {\bf 476}, 115)) using the Faxén mirror image technique for $κ(=a/(a+c))\ll 1$ (her…
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 $a/(a+c)\ll 1$ (here $a$ is the bubble radius), when the clearance parameter $\varepsilon(= c/a)$ is com…
We investigate by direct numerical simulations the flow that rising bubbles cause in an originally quiescent fluid. We employ the Eulerian-Lagrangian method with two-way coupling and periodic boundary conditions. In order to be able to treat up to 288000 bubbles, the following approximations and simplifications had to be introduced: (i) The bubbles were treated as point-particles, thus (ii) disregarding the near-field interactions among them, and (iii) effective force models for the lift and the drag forces were used. In particular, the lift coefficient was assumed to be 1/2, independent of th…
This paper presents novel insights about the influence of soluble surfactants on bubble flows obtained by Direct Numerical Simulation (DNS). Surfactants are amphiphilic compounds which accumulate at fluid interfaces and significantly modify the respective interfacial properties, influencing also the overall dynamics of the flow. With the aid of DNS local quantities like the surfactant distribution on the bubble surface can be accessed for a better understanding of the physical phenomena occurring close to the interface. The core part of the physical model consists in the description of the sur…
This work reports an experimental characterisation of the flow properties in a homogeneous bubble swarm rising at high-Reynolds-numbers within a homogeneous and isotropic turbulent flow. Both the gas volume fraction α and the velocity fluctuations of the carrier flow before bubble injection are varied, respectively, in the ranges 0% < alpha < 0.93% and 2.3 cm/s < urms < 5.5 cm/s. The so-called bubblance parameter is used to compare the ratio of the kinetic energy generated by the bubbles to the one produced by the incident turbulence, and is varied from 0 to 1.3. Conditional measurements of th…
In this article, we present experimental and numerical techniques to investigate the transfer, transport, and reaction of a chemical species in the vicinity of rising bubbles. In the experiment, single oxygen bubbles of diameter d b = 0.55 . . . 0.85 mm are released into a measurement cell filled with tap water. The oxygen dissolves and reacts with sulfite to sulfate. Laser-induced fluorescence is used to visualize the oxygen concentration in the bubble wake from which the global mass transfer coefficient can be calculated. The ruthenium-based fluorescent dye seems to be surface active, such t…
Microbubble surface instabilities in a strain stiffening viscoelastic material
School of Engineering, Brown University（布朗大学工程学院）；Department of Mechanical Engineering, University of Michigan（密歇根大学机械工程系）；Department of Biomedical Engineering, University of Michigan（密歇根大学生物医学工程系）；Department of Biomedical Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校生物医学工程系）；Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin（德克萨斯大学奥斯汀分校航空航天工程与力学系）；Texas Materials Institute, The University of Texas at Austin（德克萨斯大学奥斯汀分校德州材料研究所）
This study aims to investigate the behavior of multicomponent fluid flows consisting of Newtonian and non-Newtonian components, especially terminal velocity of a rising bubble in a power-law fluid. A recent lattice Boltzmann (LB) model is extended using power-law scheme to be able to simulate both Newtonian and non-Newtonian fluid flows at high density and viscosity ratios. Also, a variable mobility is introduced in this study to minimize the unphysical error around small bubbles in the domain. A three-component fluid flow system is examined using a constant and variable mobility. It is shown …
The buoyancy-driven dynamics of a pair of gas bubbles released in line is investigated numerically, focusing on highly inertial conditions under which isolated bubbles follow non-straight paths. In an early stage, the second bubble always drifts out of the wake of the leading one. Then, depending on the ratios of the buoyancy, viscous and capillary forces which define the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, five distinct regimes specific to such conditions are identified, in which the two bubbles may rise independently or continue to interact and possibly collide in the end. …
Simulating the detailed movement of a rising bubble can be challenging, especially when it comes to bubble path instabilities. Free rising ellipsoidal bubbles not only move in straight lines but can describe sinusoidal, zigzag or spiraling paths. The common Euler Euler (EE) simulation techniques can no longer resolve the actual movement patterns and Direct Numerical Simulations (DNS) tend to be very costly when simulating a larger number of bubbles. A solution based on the Euler Lagrange (EL) approach is presented, where the bubbles show oscillating shape and/or instable paths while computatio…
The buoyancy-driven motion of two identical gas bubbles released in line in a liquid at rest is examined with the help of highly resolved simulations, focusing on moderately inertial regimes in which the path of an isolated bubble is vertical. Assuming first an axisymmetric evolution, equilibrium configurations of the bubble pair are determined as a function of the buoyancy-to-viscous and buoyancy-to-capillary force ratios which define the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, respectively. The three-dimensional solutions reveal that this axisymmetric equilibrium is actually ne…
Influence of a vertical-wall leading edge on bouncing and escape bubble rising regimes
Universidad de Extremadura（埃斯特雷马杜拉大学）；Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura（埃斯特雷马杜拉大学先进科学计算研究所）；Universidad de Jaén（哈恩大学）
We report the experimental study of the degassing dynamics through a thin layer of shear-thinning viscoelastic fluid (CTAB/NaSal solution), when a constant air flow is imposed at its bottom. Over a large range of parameters, the air is periodically released through series of successive bubbles, hereafter named {\it cascades}. Each cascade is followed by a continuous degassing, lasting for several seconds, corresponding to an open channel crossing the fluid layer. The periodicity between two cascades does not depend on the injected flow-rate. Inside one cascade, the properties of the overpressu…
Bubbly flows are present in various industrial processes including metallurgical processes in which gas bubbles are injected at the bottom of bulk liquid metal to stir the liquid metal and homogenize the metal. Understanding the motion of such bubbles is essential, as it has been shown that bubble flotation can remove inclusions. In this work, we have numerically studied three-dimensional dynamics of a pair of inline Argon bubbles rising in molten steel under the influence of a transverse magnetic field. We have explored the effects of two transverse magnetic field strengths (Bx = 0 and 0.2 T)…
Inertial cavitation in soft matter is an important phenomenon featured in a wide array of biological and engineering processes. Recent advances in experimental, theoretical, and numerical techniques have provided access into a world full of nonlinear physics, yet most of our quantitative understanding to date has been centered on a spherically symmetric description of the cavitation process. However, cavitation bubble growth and collapse rarely occur in a perfectly symmetrical fashion, particularly in soft materials. Predicting the onset of dynamically arising, non-spherical instabilities has …
In this paper, we have studied the three-dimensional dynamics of two equally sized air bubbles rising in a shear-thinning fluid. We have used the combined level set and volume of fluid (CLSVOF) method to track interface, maintain mass balance and estimate the interface curvature. Additionally, we have incorporated a Sharp Surface Force Method (SSF) for surface tension forces. This method significantly suppressed the spurious velocities commonly observed with the conventional volume of fluid method and the Continuum Surface Force (CSF). The algorithm is implemented in an in-house code called CU…
Surfactants in aqueous solutions self-assemble in the presence of salt, to form long, flexible worm-like micelles (WLM). WLM solutions exhibit viscoelastic properties and are used in many applications, such as for cosmetic products, drag reduction and hydraulic fracturing. The dynamics of bubbles in WLM solutions are important considerations for the stability of many of these products. In this manuscript, we investigate the thin film drainage dynamics leading up to the coalescence of bubbles in WLM solutions. The salts and surfactant type and concentrations were chosen so as to have the viscoe…
Polymer additives are commonly utilized to manipulate bubbly flows in various applications. Here, we investigate the effects of clean and contaminated bubbles driven upwards (upflow) in Newtonian and viscoelastic turbulent channel flows. Interface-resolved direct numerical simulations are performed to examine sole and combined effects of soluble surfactant and viscoelasticity using an efficient 3D finite-difference/front-tracking method. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant conc…
Bubbles rising in viscoelastic liquids may exhibit a jump discontinuity of the rise velocity as a critical bubble volume is exceeded. The phenomenon has been extensively investigated in the literature, both by means of experiments as well as via numerical simulations. The occurrence of the velocity jump has been associated with a change of the bubble shape under the formation of a pointed tip at the rear end and to the appearance of a so-called negative wake with the liquid velocity behind the bubble, pointing in the opposite direction to that in viscous Newtonian fluids. We revisit this topic…
The results of the flow structure visualization experiments conducted on the surface of a single bubble streamlined by uniform flow are presented. It is shown that, at certain critical values for bubble size, flow velocity, and contamination level, the axial symmetry of the surface flow loses its stability in a threshold manner, and the first instability mode in the form of two vortices appears. Below the threshold, the stationary flow on the bubble surface is impossible. The experimental results indicate that the assumption about the axial symmetry of the motion on the bubble surface containi…
