The boundary layer on a spherical gas bubble

Moore, D. W.

doi:10.1017/s0022112063000665

Cited by 450 publications

(287 citation statements)

References 4 publications

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“…An isolated spherical bubble moving with velocity v through a nearly inviscid liquid experiences a viscous drag force equal to Ϫ12 av. 32,20 We therefore express the rate of energy dissipation per unit volume of bubble suspension in terms of a scalar R diss defined by…”

Section: A Numerical Simulationsmentioning

confidence: 99%

Rheology of dense bubble suspensions

et al. 1997

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Flow of artificial microcapsules in microfluidic channels: A method for determining the elastic properties of the membrane Phys. Fluids 20, 123102 (2008) On the rest state stability of an objective fractional derivative viscoelastic fluid model J. Math. Phys. 49, 043101 (2008) Effect of surface hydrophilicity on the confined water film Appl. Phys. Lett. 91, 253110 (2007) Rheology and ultrasonic properties of Pt57.5Ni5.3Cu14.7P22.5 liquid Appl. Phys. Lett. 90, 171923 (2007) The rheological behavior of rapidly sheared bubble suspensions is examined through numerical simulations and kinetic theory. The limiting case of spherical bubbles at large Reynolds number Re and small Weber number We is examined in detail. Here, Reϭ ␥a 2 / and Weϭ ␥ 2 a 3 /s, a being the bubble radius, ␥ the imposed shear, s the interfacial tension, and and , respectively, the viscosity and density of the liquid. The bubbles are assumed to undergo elastic bounces when they come into contact; coalescence can be prevented in practice by addition of salt or surface-active impurities. The numerical simulations account for the interactions among bubbles which are assumed to be dominated by the potential flow of the liquid caused by the motion of the bubbles and the shear-induced collision of the bubbles. A kinetic theory based on Grad's moment method is used to predict the distribution function for the bubble velocities and the stress in the suspension. The hydrodynamic interactions are incorporated in this theory only through their influence on the virtual mass and viscous dissipation in the suspension. It is shown that this theory provides reasonable predictions for the bubble-phase pressure and viscosity determined from simulations including the detailed potential flow interactions. A striking result of this study is that the variance of the bubble velocity can become large compared with (␥a) 2 in the limit of large Reynolds number. This implies that the disperse-phase pressure and viscosity associated with the fluctuating motion of the bubbles is quite significant. To determine whether this prediction is reasonable even in the presence of nonlinear drag forces induced by bubble deformation, we perform simulations in which the bubbles are subject to an empirical drag law and show that the bubble velocity variance can be as large as 15␥ 2 a 2 .

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Section: A Numerical Simulationsmentioning

confidence: 99%

Rheology of dense bubble suspensions

et al. 1997

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“…Depending on the bubble Reynolds number range used, Re B can be from either HadamardRybzynski (for Re B ≤ 11) [17] or Moore's solution (for 11 < Re B ≤ 500) [18]. However, Mei et al [19] obtained an empirical correlation that matches both correlations, valid for micro-bubble Reynolds numbers presented in this study: …”

Section: Computation Of the Bubble Drag Co-efficientmentioning

confidence: 63%

Hydrodynamic drag and velocity of micro-bubbles in dilute paper machine suspensions

Haapala

Honkanen

Liimatainen

et al. 2009

Computational Methods in Multiphase Flow V

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This paper studies hydrodynamic drag forces acting on freely rising microbubbles in dilute paper machine suspensions under turbulent flow conditions. Dissolved, colloidal and numerous solid materials i.e. process chemicals, wood extractives, fillers and wood fibre fractions present in these suspensions disturb the rise of micro-bubbles increasing their drag. The aim of this study is to characterise the terminal velocities and drag coefficients of the bubbles as a function of their Reynolds number in several paper machine circulation waters, i.e. white waters, and in some model suspensions. Characterisation is performed experimentally with a high-speed CMOS camera and a submersed back-light illumination in a pressurised bubble column.Image sequences of bubbly flow are analysed with automatic image processing algorithms that measure not only the bubble size and velocity, but also the velocity of the fluid surrounding bubbles, revealing the initial slip velocity of each bubble. Bubbles are tracked in time to provide time series data for every bubble that passes the focal plane of the imaging system. Results show how some suspension properties -concentration, apparent viscosity and surface tension -affect the motion of micro-bubbles. Results also show the changes in micro-bubble formation with pressure drop and differences of bubble size distributions in a variety of suspensions and solutions. Finally, a mathematical model describing the bubble rise velocities and drag coefficients with respect to the bubble Reynolds number is developed for the investigated white waters.

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“…Blasius (1908) and Sakiadis (1961) deliberated on the flow of a Newtonian fluid past a stretchable surface at the free stream and at the wall respectively. This area of interest in the field of fluid mechanics (boundary layer theory together with heat and mass transfer) has attracted the attention of Murphy (1953), Sowerby and Cooke (1953), Moore (1963), Sawchuk and Zamir (1992), Babu et al (2015), Animasaun (2016), Motsa and Animasaun (2016a,b), Naramgari and Sulochana (2016), Sulochana et al (2016) and Sandeep et al (2016). Sandeep and Animasaun (2017) to deliberate on the boundary layer formed on spherical gas bubble, curved surface, cylinder, stagnation-point flow of a Carreau nanofluid towards a stretching/shrinking sheet, finite flat plate/sliding plate, wing of aircraft, impulsively started vertical porous surface, stagnation point flow of a micropolar fluid towards melting surface, 3-dimensional flow of Casson fluid towards a stagnation point at initial unsteady stage and final steady stage, nanofluid containing both nanoparticles and gyrotactic microorganisms due to impulsive motion flow of nanofluid, permeable stretching/shrinking sheet in the presence of suction/injection, inclined stationary/moving flat plate and over a wedge.…”

Section: Introductionmentioning

confidence: 99%

New Similarity Solution of Micropolar Fluid Flow Problem Over an Uhspr in the Presence of Quartic Kind of Autocatalytic Chemical Reaction

Animasaun¹,

Kọrikọ²

2017

Frontiers in Heat and Mass Transfer

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The motion of air (i.e fluid) in which tiny particle rotates past a pointed surface of a rocket (as in space science), over a bonnet of a car and past a pointed surface of an aircraft is of important to experts in all these fields. Geometrically, all the domains of fluid flow in all these cases can be referred to as the upper horizontal surface of a paraboloid of revolution (uhspr). Meanwhile, the solution of the corresponding partial differential equation is an open question due to unavailability of suitable similarity variable to non-dimensionalize the angular momentum equation. This article unravels the nature of skin friction coefficient, heat transfer rate, velocity, temperature, concentration of homogeneous bulk fluid and heterogeneous catalyst which exists on a stretchable surface which is neither a perfect horizontal/vertical nor inclined/cone. Theory of similarity solution was adopted to obtain the similarity variable suitable to scale the proposed angular momentum equation. These equations along with the boundary conditions are solved numerically using Runge-Kutta technique along with shooting method. The similarity variable successfully nondimensionalized and parameterized the angular momentum for boundary layer flow past uhspr. Temperature dependent dynamic viscosity parameter increases vertical velocity near a free stream but reduces micro-rotation near uhspr. Effect of thermal radiation parameter on temperature profile and heat transfer rate can be greatly influenced by thickness parameter.

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The boundary layer on a spherical gas bubble

Cited by 450 publications

References 4 publications

Rheology of dense bubble suspensions

Rheology of dense bubble suspensions

Hydrodynamic drag and velocity of micro-bubbles in dilute paper machine suspensions

New Similarity Solution of Micropolar Fluid Flow Problem Over an Uhspr in the Presence of Quartic Kind of Autocatalytic Chemical Reaction

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