The motion of a large gas bubble rising through liquid flowing in a tube

1978 ◽  
Vol 89 (3) ◽  
pp. 497-514 ◽  
Author(s):  
R. Collins ◽  
F. F. De Moraes ◽  
J. F. Davidson ◽  
D. Harrison
Keyword(s):  
Velocity Profile ◽  
Liquid Velocity ◽  
Approximate Solutions ◽  
Initial Distribution ◽  
Turbulent Velocity ◽  
Bubble Velocity ◽  
Published Data ◽  
Gas Bubble ◽  
Flowing Liquid ◽  
Bubble Rising

The theory presented here describes the motion of a large gas bubble rising through upward-flowing liquid in a tube. The basis of the theory is that the liquid motion round the bubble is inviscid, with an initial distribution of vorticity which depends on the velocity profile in the liquid above the bubble. Approximate solutions are given for both laminar and turbulent velocity profiles and have the form \begin{equation} U_s = U_c+(gD)^{\frac{1}{2}}\phi(U_c/(gD)^{\frac{1}{2}}), \end{equation}Us being the bubble velocity, Uc the liquid velocity at the tube axis, g the acceleration due to gravity, and D the tube diameter; ϕ indicates a functional relationship the form of which depends upon the shape of the velocity profile. With a turbulent velocity profile, a good approximation to (1) which is suitable for many practical purposes is \begin{equation} U_s = U_s + U_{s0}, \end{equation}Us0 being the bubble velocity in stagnant liquid. Published data for turbulent flow are known to agree with (2), so that in this case the theory supports a well-known empirical result. Our laminar flow experiments confirm the validity of (1) for low liquid velocities.

scholarly journals Determination of a Bubble Drag Coefficient during the Formation of Single Gas Bubble in Upward Coflowing Liquid

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 999
Author(s):  
Przemysław Luty ◽  
Mateusz Prończuk
Keyword(s):  
Drag Coefficient ◽  
Chemical Engineering ◽  
Liquid Velocity ◽  
Bubble Diameter ◽  
Bubble Formation ◽  
Hydraulic Drag ◽  
Gas Bubble ◽  
Flowing Liquid ◽  
Engineering Research

Bubble flow is present in many processes that are the subject of chemical engineering research. Many correlations for determination of the equivalent bubble diameter can be found in the scientific literature. However, there are only few describing the formation of gas bubbles in flowing liquid. Such a phenomenon occurs for instance in airlift apparatuses. Liquid flowing around the gas bubble creates a hydraulic drag force that leads to reduction of the formed bubble diameter. Usually the value of the hydraulic drag coefficient, cD, for bubble formation in the flowing liquid is assumed to be equal to the drag coefficient for bubbles rising in the stagnant liquid, which is far from the reality. Therefore, in this study, to determine the value of the drag coefficient of bubbles forming in flowing liquid, the diameter of the bubbles formed at different liquid velocity was measured using the shadowgraphy method. Using the balance of forces affecting the bubble formed in the coflowing liquid, the hydraulic drag coefficient was determined. The obtained values of the drag coefficient differed significantly from those calculated using the correlation for gas bubble rising in stagnant liquid. The proposed correlation allowed the determination of the diameter of the gas bubble with satisfactory accuracy.

scholarly journals Experimental Study of Single Taylor Bubble Rising in Stagnant and Downward Flowing Non-Newtonian Fluids in Inclined Pipes

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 578
Author(s):  
Yaxin Liu ◽  
Eric R. Upchurch ◽  
Evren M. Ozbayoglu
Keyword(s):  
Drift Velocity ◽  
Inclination Angle ◽  
Apparent Viscosity ◽  
Liquid Velocity ◽  
Relative Difference ◽  
Newtonian Fluids ◽  
Bubble Velocity ◽  
Velocity Correlation ◽  
Bubble Rising ◽  
Taylor Bubbles

An experimental investigation of single Taylor bubbles rising in stagnant and downward flowing non-Newtonian fluids was carried out in an 80 ft long inclined pipe (4°, 15°, 30°, 45° from vertical) of 6 in. inner diameter. Water and four concentrations of bentonite–water mixtures were applied as the liquid phase, with Reynolds numbers in the range 118 < Re < 105,227 in countercurrent flow conditions. The velocity and length of Taylor bubbles were determined by differential pressure measurements. The experimental results indicate that for all fluids tested, the bubble velocity increases as the inclination angle increases, and decreases as liquid viscosity increases. The length of Taylor bubbles decreases as the downward flow liquid velocity and viscosity increase. The bubble velocity was found to be independent of the bubble length. A new drift velocity correlation that incorporates inclination angle and apparent viscosity was developed, which is applicable for non-Newtonian fluids with the Eötvös numbers (E0) ranging from 3212 to 3405 and apparent viscosity (μapp) ranging from 0.001 Pa∙s to 129 Pa∙s. The proposed correlation exhibits good performance for predicting drift velocity from both the present study (mean absolute relative difference is 0.0702) and a database of previous investigator’s results (mean absolute relative difference is 0.09614).

scholarly journals Velocity of long bubbles transported by a liquid in horizontal channel

2010 ◽  
Vol 32 (3) ◽  
pp. 182-190
Author(s):  
Ha Ngoc Hien ◽  
Jean Fabre
Keyword(s):  
Liquid Velocity ◽  
Approximate Analytical Solution ◽  
Integral Form ◽  
Bubble Velocity ◽  
Horizontal Channel ◽  
Liquid Motion ◽  
Flowing Liquid ◽  
First Order ◽  
The Mean ◽  
Moving Liquid

The influence of flowing liquid on the motion of long bubbles in horizontal channel is studied theoretically. The method of Benjamin (1968) is extended to the case of moving liquid: the liquid is inviscid, the surface tension is ignored and the liquid motion at infinity is characterized its velocity profile. The exact solutions for the bubble velocity and the liquid film thickness are given under an integral form. An approximate analytical solution can be found when the mean liquid velocity is weak enough versus the drift velocity. Two cases are investigated: the Couette flow and the Poiseuille flow. At first order, the two cases lead to identical solutions. The influence of the velocity distribution appears only at the second order.

Linear stability of co-flowing liquid–gas jets

2001 ◽  
Vol 448 ◽  
pp. 23-51 ◽  
Author(s):  
J. M. GORDILLO ◽  
M. PÉREZ-SABORID ◽  
A. M. GAÑÁN-CALVO
Keyword(s):  
Velocity Profile ◽  
Linear Stability ◽  
Stokes Equations ◽  
Liquid Velocity ◽  
Fibre Production ◽  
Velocity Profiles ◽  
Navier Stokes ◽  
Liquid Jet ◽  
Flowing Liquid ◽  
Gas Jets

A temporal, inviscid, linear stability analysis of a liquid jet and the co-flowing gas stream surrounding the jet has been performed. The basic liquid and gas velocity profiles have been computed self-consistently by solving numerically the appropriate set of coupled Navier–Stokes equations reduced using the slenderness approximation. The analysis in the case of a uniform liquid velocity profile recovers the classical Rayleigh and Weber non-viscous results as limiting cases for well-developed and very thin gas boundary layers respectively, but the consideration of realistic liquid velocity profiles brings to light new families of modes which are essential to explain atomization experiments at large enough Weber numbers, and which do not appear in the classical stability analyses of non-viscous parallel streams. In fact, in atomization experiments with Weber numbers around 20, we observe a change in the breakup pattern from axisymmetric to helicoidal modes which are predicted and explained by our theory as having an hydrodynamic origin related to the structure of the liquid-jet basic velocity profile. This work has been motivated by the recent discovery by Gañán-Calvo (1998) of a new atomization technique based on the acceleration to large velocities of coaxial liquid and gas jets by means of a favourable pressure gradient and which are of emerging interest in microfluidic applications (high-quality atomization, micro-fibre production, biomedical applications, etc.).

Behavior of Inert Gas Bubbles in Forced Convective Liquid Metal Circuits

1976 ◽  
Vol 98 (1) ◽  
pp. 5-11 ◽  
Author(s):  
W. J. Minkowycz ◽  
D. M. France ◽  
R. M. Singer
Keyword(s):  
Liquid Metal ◽  
Bubble Dynamics ◽  
Bubble Radius ◽  
Gas Bubbles ◽  
Inert Gas ◽  
Liquid Sodium ◽  
Gas Bubble ◽  
Flowing Liquid ◽  
Argon Gas ◽  
The Core

Conservation equations are derived for the motion of a small inert gas bubble in a large flowing liquid-gas solution subjected to large thermal gradients. Terms which are of the second order of magnitude under less severe and steady-state conditions are retained, thus resulting in an expanded form of the Rayleigh equation. The bubble dynamics is a function of opposing mechanisms tending to increase or decrease bubble volume while being transported with the solution. Diffusion of inert gas between the bubble and the solution is one of the most important of these mechanisms included in the analysis. The analytical model is applied to an argon gas bubble flowing in a weak solution of argon gas in liquid sodium. Calculations are performed for these fluids under conditions typical of normal and abnormal operation of a liquid metal fast breeder reactor (LMFBR) core and the resulting bubble radius, internal gas pressure, and mass of inert gas are presented in each case. An important result obtained indicates that inert gas bubbles reaching the core inlet of an LMFBR will always grow as they traverse the core under normal and extreme abnormal conditions and that the rate of growth is quite small in all cases.

Bubble velocity profile and model of surfactant mass transfer to bubble surface

2001 ◽  
Vol 56 (23) ◽  
pp. 6605-6616 ◽  
Author(s):  
Yongqin Zhang ◽  
J.B McLaughlin ◽  
J.A Finch
Keyword(s):  
Mass Transfer ◽  
Velocity Profile ◽  
Bubble Surface ◽  
Bubble Velocity

scholarly journals Motion of large bubbles in curved channels

2007 ◽  
Vol 570 ◽  
pp. 455-466 ◽  
Author(s):  
METIN MURADOGLU ◽  
HOWARD A. STONE
Keyword(s):  
Film Thickness ◽  
Liquid Velocity ◽  
Circular Cross Section ◽  
Lubrication Theory ◽  
Bubble Velocity ◽  
Straight Tube ◽  
Curved Channel ◽  
Front Tracking Method ◽  
Curved Channels ◽  
Channel Curvature

We study the motion of large bubbles in curved channels both semi-analytically using the lubrication approximation and computationally using a finite-volume/front-tracking method. The steady film thickness is governed by the classical Landau–Levich–Derjaguin–Bretherton (LLDB) equation in the low-capillary-number limit but with the boundary conditions modified to account for the channel curvature. The lubrication results show that the film is thinner on the inside of a bend than on the outside of a bend. They also indicate that the bubble velocity relative to the average liquid velocity is always larger in a curved channel than that in a corresponding straight channel and increases monotonically with increasing channel curvature. Numerical computations are performed for two-dimensional cases and the computational results are found to be in a good agreement with the lubrication theory for small capillary numbers and small or moderate channel curvatures. For moderate capillary numbers the numerical results for the film thickness, when rescaled to account for channel curvature as suggested in the lubrication calculation, essentially collapse onto the corresponding results for a bubble in a straight tube. The lubrication theory is also extended to the motion of large bubbles in a curved channel of circular cross-section.

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