Small Bubble Motion in an Accelerating Liquid

1976 ◽  
Vol 43 (3) ◽  
pp. 399-403 ◽  
Author(s):  
F. A. Morrison ◽  
M. B. Stewart
Keyword(s):  
Reynolds Number ◽  
Particle Motion ◽  
Bubble Surface ◽  
Small Bubble ◽  
Bubble Motion ◽  
Bubble Behavior ◽  
Rigid Particle ◽  
Oseen Equation ◽  
Response Characteristics ◽  
Governing Relation

Low Reynolds number bubble motion in accelerating liquids is analyzed. Because of motion of the bubble surface, the flow about a bubble differs from the flow surrounding a rigid particle. A governing relation, equivalent to the Basset-Boussinesq-Oseen equation for rigid particle motion, is developed. Response characteristics of the bubble are presented. Bubble behavior is found to differ significantly from rigid particle behavior.

Bubble Trajectories and Equilibrium Levels in Vibrated Liquid Columns

1968 ◽  
Vol 90 (1) ◽  
pp. 125-132 ◽  
Author(s):  
J. M. Foster ◽  
J. A. Botts ◽  
A. R. Barbin ◽  
R. I. Vachon
Keyword(s):  
Liquid Column ◽  
Experimental Results ◽  
Small Bubble ◽  
Vibrational Amplitude ◽  
Bubble Motion ◽  
Bubble Behavior ◽  
Thermodynamic Behavior ◽  
Equilibrium Level ◽  
Bubble Pulsation ◽  
Volume Pulsation

An analysis of bubble behavior in a vertically vibrated liquid column and experimental results of equilibrium level determinations are presented. The analysis avoids the usual approximation of small bubble pulsation and predicts a nonharmonic volume pulsation; it can be used to predict bubble trajectories and equilibrium levels. The vibrational amplitude affects the bubble motion indirectly through its effect on the thermodynamic behavior of the bubble. The experimental results compare favorably with the analysis.

Shear-Induced Lift Force on a Single Bubble in Surfactant Solutions

2007 ◽  
Author(s):  
Masato Fukuta ◽  
Shu Takagi ◽  
Yoichiro Matsumoto
Keyword(s):  
Lift Force ◽  
Marangoni Effect ◽  
Surface Concentration ◽  
Bubble Surface ◽  
Single Bubble ◽  
Bubble Motion ◽  
Surfactant Solutions ◽  
Cap Model ◽  
Desorption Rate Constant ◽  
The Asymmetry

In this paper, single bubble motion in surfactant solutions is discussed. We focus on the change of the shear-induced lift force acting on a bubble when the bubble surface is contaminated by surfactant adsorption which leads the Marangoni effect. With the increase of Langmuir number corresponding to the decrease of desorption rate constant of surfactant, the lift force on a spherical bubble decreases from that on a clean bubble to near zero value. This reduction is related significantly to the asymmetry of pressure distribution on surface. Comparing the present result with our previous simulation using the stagnant cap model, the lift force of this study is larger than that of the stagnant cap model. This is because in a shear flow, the surface concentration distributes asymmetrically, and the asymmetry of the surface pressure produced by the shear appears stronger than that of the stagnant cap model.

Solid-particle motion in two-dimensional peristaltic flows

1976 ◽  
Vol 73 (1) ◽  
pp. 77-96 ◽  
Author(s):  
Tin-Kan Hung ◽  
Thomas D. Brown
Keyword(s):  
Reynolds Number ◽  
Solid Particle ◽  
Particle Motion ◽  
Particle Transport ◽  
Particle Displacement ◽  
Two Dimensional ◽  
Single Bolus ◽  
Highly Nonlinear ◽  
Neutrally Buoyant ◽  
Gap Width

Some insight into the mechanism of solid-particle transport by peristalsis is sought experimentally through a two-dimensional model study (§ 2). The peristaltic wave is characterized by a single bolus sweeping by the particle, resulting in oscillatory motion of the particle. Because of fluid-particle interaction and the significant curvature in the wall wave, the peristaltic flow is highly nonlinear and time dependent.For a neutrally buoyant particle propelled along the axis of the channel by a single bolus, the net particle displacement can be either positive or negative. The instantaneous force acting upon the particle and the resultant particle trajectory are sensitive to the Reynolds number of the flow (§ 3 and 4). The net forward movement of the particle increases slightly with the particle size but decreases rapidly as the gap width of the bolus increases. The combined dynamic effects of the gap width and Reynolds number on the particle displacement are studied (§ 5). Changes in both the amplitude and the form of the wave have significant effects on particle motion. A decrease in wave amplitude along with an increase in wave speed may lead to a net retrograde particle motion (§ 6). For a non-neutrally buoyant particle, the gravitational effects on particle transport are modelled according to the ratio of the Froude number to the Reynolds number. The interaction of the particle with the wall for this case is also explored (§ 7).When the centre of the particle is off the longitudinal axis, the particle will undergo rotation as well as translation. Lateral migration of the particle is found to occur in the curvilinear flow region of the bolus, leading to a reduction in the net longitudinal transport (§ 8). The interaction of the curvilinear flow field with the particle is further discussed through comparison of flow patterns around a particle with the corresponding cases without a particle (§ 9).

On the equation for spherical-particle motion: effect of Reynolds and acceleration numbers

1998 ◽  
Vol 367 ◽  
pp. 221-253 ◽  
Author(s):  
INCHUL KIM ◽  
SAID ELGHOBASHI ◽  
WILLIAM A. SIRIGNANO
Keyword(s):  
Reynolds Number ◽  
Spherical Particle ◽  
Particle Motion ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Navier Stokes ◽  
Fluid Density ◽  
Navier Stokes Equations ◽  
Freely Moving ◽  
New Equation

The existing model equations governing the accelerated motion of a spherical particle are examined and their predictions compared with the results of the numerical solution of the full Navier–Stokes equations for unsteady, axisymmetric flow around a freely moving sphere injected into an initially stationary or oscillating fluid. The comparison for the particle Reynolds number in the range of 2 to 150 and the particle to fluid density ratio in the range of 5 to 200 indicates that the existing equations deviate considerably from the Navier–Stokes equations. As a result, we propose a new equation for the particle motion and demonstrate its superiority to the existing equations over a range of Reynolds numbers (from 2 to 150) and particle to fluid density ratios (from 5 to 200). The history terms in the new equation account for the effects of large relative acceleration or deceleration of the particle and the initial relative velocity between the fluid and the particle. We also examine the temporal structure of the near wake of the unsteady, axisymmetric flow around a freely moving sphere injected into an initially stagnant fluid. As the sphere decelerates, the recirculation eddy size grows monotonically even though the instantaneous Reynolds number of the sphere decreases.

Bubble Motion in a Converging–Diverging Channel

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Harsha Konda ◽  
Manoj Kumar Tripathi ◽  
Kirti Chandra Sahu
Keyword(s):  
Reynolds Number ◽  
Parametric Study ◽  
Channel Wall ◽  
Two Dimensional ◽  
Bubble Motion ◽  
Diverging Channel

The migration of a bubble inside a two-dimensional converging–diverging channel is investigated numerically. A parametric study is conducted to investigate the effects of the Reynolds and Weber numbers and the amplitude of the converging–diverging channel. It is found that increasing the Reynolds number and the amplitude of the channel increases the oscillation of the bubble and promotes the migration of the bubble toward one of the channel wall. The bubble undergoes oblate–prolate deformation periodically at the early times, which becomes chaotic at the later times. This phenomenon is a culmination of the bubble path instability as well as the Segré–Silberberg effect.

Wake instability of a fixed spheroidal bubble

2007 ◽  
Vol 572 ◽  
pp. 311-337 ◽  
Author(s):  
JACQUES MAGNAUDET ◽  
GUILLAUME MOUGIN
Keyword(s):  
Reynolds Number ◽  
Body Surface ◽  
Bubble Surface ◽  
The Body ◽  
Rigid Sphere ◽  
Instability Mechanism ◽  
Aspect Ratios ◽  
Wake Instability ◽  
Vorticity Flux ◽  
Axis Length

Direct numerical simulations of the flow past a fixed oblate spheroidal bubble are carried out to determine the range of parameters within which the flow may be unstable, and to gain some insight into the instability mechanism. The bubble aspect ratio χ (i.e. the ratio of the major axis length over the minor axis length) is varied from 2.0 to 2.5 while the Reynolds number (based on the upstream velocity and equivalent bubble diameter) is varied in the range 102 ≤ Re ≤ 3 × 103. As vorticity generation at the bubble surface is at the root of the instability, theoretical estimates for the maximum of the surface vorticity and the surface vorticity flux are first derived. It is shown that, for large aspect ratios and high Reynolds numbers, the former evolves as χ8/3 while the latter is proportional to χ7/2Re−1/2. Then it is found numerically that the flow first becomes unstable for χ = χc ≈ 2.21. As the surface vorticity becomes independent of Re for large enough Reynolds number, the flow is unstable only within a finite range of Re, this range being an increasing function of χ − χc. An empirical criterion based on the maximum of the vorticity generated at the body surface is built to determine whether the flow is stable or not. It is shown that this criterion also predicts the correct threshold for the wake instability past a rigid sphere, suggesting that the nature of the body surface does not really matter in the instability mechanism. Also the first two bifurcations of the flow are similar in nature to those found in flows past rigid axisymmetric bluff bodies, such as a sphere or a disk. Wake dynamics become more complex at higher Reynolds number, until the Re−1/2-dependency of the surface vorticity flux makes the flow recover its steadiness and eventually its axisymmetry. A qualitative analysis of the azimuthal vorticity field in the base flow at the rear of the bubble is finally carried out to make some progress in the understanding of the primary instability. It is suggested that the instability originates in a thin region of the flow where the vorticity gradients have to turn almost at right angle to satisfy two different constraints, one at the bubble surface, the other within the standing eddy.

scholarly journals Modelling vertical concentration distributions of solids suspended in turbulent visco-plastic fluid

2021 ◽  
Vol 69 (3) ◽  
pp. 255-262
Author(s):  
Václav Matoušek ◽  
Andrew Chryss ◽  
Lionel Pullum
Keyword(s):  
Reynolds Number ◽  
Concentration Profile ◽  
Particle Motion ◽  
Turbulent Viscosity ◽  
Low Reynolds Number ◽  
Newtonian Fluids ◽  
Horizontal Pipe ◽  
Profile Model ◽  
Plastic Fluid ◽  
Tomographic Data

Abstract Vertical concentration distributions of solids conveyed in Newtonian fluids can be modelled using Rouse-Schmidt type distributions. Observations of solids conveyed in turbulent low Reynolds number visco-plastic carriers, suggest that solids are more readily suspended than their Newtonian counterparts, producing higher concentrations in the centre of the pipe. A Newtonian concentration profile model was adapted to include typical turbulent viscosity distributions within the pipe and particle motion calculated using non-Newtonian sheared settling. Predictions from this and the unmodified model, using the same wall viscosity, are compared with the chord averaged profile extracted from tomographic data obtained using a 50 mm horizontal pipe.

scholarly journals Dynamics and length scales in vertical convection of liquid metals

2021 ◽  
Vol 932 ◽  
Author(s):  
Lukas Zwirner ◽  
Mohammad S. Emran ◽  
Felix Schindler ◽  
Sanjay Singh ◽  
Sven Eckert ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Liquid Metals ◽  
Global Response ◽  
Response Characteristics ◽  
Aspect Ratios ◽  
Time Space ◽  
Shaped Container ◽  
Novel Method ◽  
Space Data ◽  
Rayleigh Numbers

Using complementary experiments and direct numerical simulations, we study turbulent thermal convection of a liquid metal (Prandtl number $\textit {Pr}\approx 0.03$ ) in a box-shaped container, where two opposite square sidewalls are heated/cooled. The global response characteristics like the Nusselt number ${\textit {Nu}}$ and the Reynolds number $\textit {Re}$ collapse if the side height $L$ is used as the length scale rather than the distance $H$ between heated and cooled vertical plates. These results are obtained for various Rayleigh numbers $5\times 10^3\leq {\textit {Ra}}_H\leq 10^8$ (based on $H$ ) and the aspect ratios $L/H=1, 2, 3$ and $5$ . Furthermore, we present a novel method to extract the wind-based Reynolds number, which works particularly well with the experimental Doppler-velocimetry measurements along vertical lines, regardless of their horizontal positions. The extraction method is based on the two-dimensional autocorrelation of the time–space data of the vertical velocity.

scholarly journals The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number

1993 ◽  
Vol 256 ◽  
pp. 561-605 ◽  
Author(s):  
Phillip M. Lovalenti ◽  
John F. Brady
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Stokes Flow ◽  
Slip Velocity ◽  
Hydrodynamic Force ◽  
Time Dependent ◽  
Rigid Particle ◽  
Flowing Fluid ◽  
Arbitrary Time ◽  
Unsteady Stokes Flow

The hydrodynamic force acting on a rigid spherical particle translating with arbitrary time-dependent motion in a time-dependent flowing fluid is calculated to O(Re) for small but finite values of the Reynolds number, Re, based on the particle's slip velocity relative to the uniform flow. The corresponding expression for an arbitrarily shaped rigid particle is evaluated for the case when the timescale of variation of the particle's slip velocity is much greater than the diffusive scale, a2/v, where a is the characteristic particle dimension and v is the kinematic viscosity of the fluid. It is found that the expression for the hydrodynamic force is not simply an additive combination of the results from unsteady Stokes flow and steady Oseen flow and that the temporal decay to steady state for small but finite Re is always faster than the t-½ behaviour of unsteady Stokes flow. For example, when the particle accelerates from rest the temporal approach to steady state scales as t-2.

Using surfactants to control the formation and size of wakes behind moving bubbles at order-one Reynolds numbers

2002 ◽  
Vol 453 ◽  
pp. 1-19 ◽  
Author(s):  
YANPING WANG ◽  
DEMETRIOS T. PAPAGEORGIOU ◽  
CHARLES MALDARELLI
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Continuous Phase ◽  
Bubble Surface ◽  
Surface Flow ◽  
Theoretical Research ◽  
Viscous Forces ◽  
Spherical Bubbles

A bubble translating through a continuous liquid (i.e. Newtonian) phase moves as a sphere when inertial and viscous forces are small relative to capillary forces. Spherical bubbles with stress-free interfaces do not retain wakes at their trailing ends as inertial forces become important (increasing Reynolds number). This is in contrast to translating spheres with immobile interfaces in which flow separation and wake formation occurs at order-one Reynolds number. Surfactants present in the continuous phase adsorb onto a bubble surface as it translates, and affect the interfacial mobility by creating tension gradient forces. Adsorbed surfactant is convected to the trailing end of the bubble, lowers the tension there relative to the front, and creates a tension gradient which reduces the surface flow. For low bulk concentrations of surfactant (or if kinetic exchange between bulk and surface is slow relative to convection), diffusion towards the surface is much slower than convection, and surfactant is swept into an immobile cap at the trailing end. As with solid spheres, these caps entrain wakes at order-one Reynolds number. In adsorptive bubble technologies where solutes transfer between the bubble and the continuous phase, usually through thin boundary layers around the bubble surface (high Péclet number), these wakes generally form owing to the presence of surfactant impurities. The wake presence retards the interphase transfer displacing the thin boundary layer towards the front end of the bubble; as mass transfer through the wake is much slower than through the boundary layer, the mass transfer is reduced.Our recent theoretical research has demonstrated that at low Reynolds numbers, the mobility of a surfactant-retarded bubble interface can be increased by raising the bulk concentration of a surfactant which kinetically rapidly exchanges between the surface and the bulk. At high bulk concentrations the interface saturates with surfactant, effectively removing the tension gradient. In this paper, we demonstrate theoretically that this interfacial control is still realized at order-one Reynolds numbers, and, more importantly, we show that the control can be used to manipulate the formation, size and ultimately the disappearance of a wake. This wake removal mechanism has the potential to dramatically increase the interphase transfer in adsorptive bubble technologies.

Sign in / Sign up

Export Citation Format

Share Document