Rheology of dense bubble suspensions

Abstract

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 .

On the quest for a hyperbolic effective-field model of disperse flows

“…Preliminary results in that direction have already been obtained for massless bubbles (Yurkovetsky & Brady 1996;Khang et al 1997;Spelt & Sangani 1998) but they must be extended to massive particles in a form which satisfies the energy conservation condition (2.5) before considering the hyperbolicity issue.…”

Impedance probe to measure local gas volume fraction and bubble velocity in a bubbly liquid

“…For the case of a bubble suspension in which the Reynolds number is large and the Weber number is small, a complete set of governing equations can be composed from first principles. 1,2 The extent of the validity of these theories could only be assessed if comparisons with detailed experimental measurements are performed. Hence, there is a need for accurate measurements of velocity and concentration profiles.…”

A kinetic theory for particulate systems with bimodal and anisotropic velocity fluctuations

“…The neglect of hydrodynamic interactions is a reasonable approximation when the relative velocity of interacting bubbles is large compared with their common velocity. For example, Kang et al 9 found that for sheared bubble suspensions without buoyancy, hard-sphere simulations were in close agreement with simulations of hydrodynamically interacting bubbles. Likewise, Kumaran and Koch 13 found that buoyant bubbles with different terminal velocities would encounter and separate in a manner qualitatively similar to a hard-sphere bounce ͑although the bubbles did not make actual contact͒ when the difference of velocities was larger than about 10% of the mean velocity.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] In particular, the special case of flows in which the hydrodynamic interactions among bubbles can be determined using the potential flow approximation has been extensively studied. [8][9][10]13,15 The potential flow approximation is expected to be valid when the Reynolds number based on the bubble radius and characteristic velocity is large compared with unity but the Weber number, the ratio of inertial to surface tension forces, is small enough so that the bubbles are approximately spherical, and the liquid is free of surface-active impurity. [16][17][18][19][20] This somewhat ideal case can be studied experimentally, 21,22 numerically using large scale simulations which account for the hydrodynamic interactions among bubbles, 15 and analytically using the methods of statistical mechanics 23 and kinetic theory of dense granular materials.…”