Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-04-30T19:04:52.241Z Has data issue: false hasContentIssue false
  • English
  • Français

Rheology of dilute bubble suspensions in unsteady shear flows

Published online by Cambridge University Press:  21 March 2024

K. Ohie Open the ORCID record for K. Ohie [Opens in a new window] ,
Y. Tasaka Open the ORCID record for Y. Tasaka [Opens in a new window]  and
Y. Murai Open the ORCID record for Y. Murai [Opens in a new window]
K. Ohie*
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan
Y. Tasaka
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan
Y. Murai
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan
*
†Email address for correspondence: ohie@eis.hokudai.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

The viscoelasticity of a dilute bubble suspension is theoretically derived from the constitutive equation originally for a dilute emulsion proposed by Frankel & Acrivos (J. Fluid Mech., vol. 44, issue 1, 1970, pp. 65–78). Non-dimensionalization of the original tensor equation indicates that the viscoelasticity is systematized for a given void fraction by the capillary number $Ca$ and dynamic capillary number $Cd$, representing the bubble deformability and unsteadiness of bubble deformation. Comprehensive evaluation of the viscoelasticity according to the volume fraction, $Ca$ and $Cd$ reveals that whether the viscosity increases or decreases depends on whether $Ca$ or $Cd$ exceeds a common critical value. In addition, it is indicated that the bubble suspension has the most prominent viscoelasticity when the time scale of the shear deformation is the same as the relaxation time of the suspended bubble and when the bubbles keep a spherical shape, that is, $Ca \ll 1$ and $Cd = 1$. The applicability of this theory in flow prediction was examined in a Taylor–Couette system, and experimentally good agreement was confirmed.

JFM classification

Complex Fluids: Suspensions Drops and Bubbles: Bubble dynamics Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 983 , 25 March 2024 , A39
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Choi, S.J. & Schowalter, W.R. 1975 Rheological properties of nondilute suspensions of deformable particles. Phys. Fluids 18, 420–427.CrossRefGoogle Scholar
Einstein, A. 1906 Eine neue bestimung der molekuldimensionen. Ann. Phys. 324, 289–306.CrossRefGoogle Scholar
Frankel, N.A. & Acrivos, A. 1970 The constitutive equation for a dilute emulsion. J. Fluid Mech. 44, 65–78.CrossRefGoogle Scholar
Han, C.D. & King, R.G. 1980 Measurement of the rheological properties of concentrated emulsions. J. Rheol. 24 (2), 213–237.CrossRefGoogle Scholar
Llewellin, E.W., Mader, H.M. & Wilson, S.D.R. 2002 The rheology of a bubbly liquid. Proc. R. Soc. Lond. A 458, 987–1016.CrossRefGoogle Scholar
Llewellin, E.W. & Manga, M. 2005 Bubble suspension rheology and implications for conduit flow. J. Volcanol. Geotherm. Res. 143, 205–217.CrossRefGoogle Scholar
Mackenzie, J.K. 1950 The elastic constants of a solid containing spherical holes. Proc. Phys. Soc. B 63, 2.CrossRefGoogle Scholar
Mader, H.M., Llewellin, E.W. & Mueller, S.P. 2013 The rheology of two-phase magmas: a review and analysis. J. Volcanol. Geotherm. Res. 257, 135–158.CrossRefGoogle Scholar
Mitrias, C., Jaensson, N.O., Hulsen, M.A. & Anderson, P.D. 2017 Direct numerical simulation of a bubble suspension in small amplitude oscillatory shear flow. Rheol. Acta 56, 555–565.CrossRefGoogle Scholar
Mitrou, S., Migliozzi, S., Angeli, P. & Mazzei, L. 2023 Effect of polydispersity and bubble clustering on the steady shear viscosity of semidilute bubble suspensions in Newtonian media. J. Rheol. 67 (3), 635–646.CrossRefGoogle Scholar
Morini, R., Chateau, X., Ovarlez, G., Pitois, O. & Tocquer, L. 2019 Steady shear viscosity of semi-dilute bubbly suspensions. J. Non-Newtonian Fluid Mech. 264, 19–24.CrossRefGoogle Scholar
Murai, Y. & Oiwa, H. 2008 Increase of effective viscosity in bubbly liquids from transient bubble deformation. Fluid Dyn. Res. 40, 565–575.CrossRefGoogle Scholar
Ohie, K., Yoshida, T., Tasaka, Y. & Murai, Y. 2022 Effective rheology mapping for characterizing polymer solutions utilizing ultrasonic spinning rheometry. Exp. Fluids 63 (40), 1–12.CrossRefGoogle Scholar
Ohie, K., Yoshida, T., Tasaka, Y., Sugihara-Seki, M. & Murai, Y. 2022 Rheological characterization and flow reconstruction of polyvinylpyrrolidone aqueous solutions by means of velocity profiling-based rheometry. Exp. Fluids 63 (135), 1–13.CrossRefGoogle Scholar
Pal, R. 2003 Rheological behavior of bubble-bearing magmas. Earth Planet. Sci. Lett. 207, 165–179.CrossRefGoogle Scholar
Rust, A.C. & Manga, M. 2002 Effects of bubble deformation on the viscosity of dilute suspensions. J. Non-Newtonian Fluid Mech. 104, 53–63.CrossRefGoogle Scholar
Takeda, Y. 2012 Ultrasonic Doppler Velocity Profiler for Fluid Flow. Springer Science & Business Media.CrossRefGoogle Scholar
Tan, C., Murai, Y., Liu, W., Tasaka, Y., Dong, F. & Takeda, Y. 2021 Ultrasonic Doppler technique for application to multiphase flows: a review. Intl J. Multiphase Flow 144, 103811.CrossRefGoogle Scholar
Tapia, F., Ichihara, M., Pouliquen, O. & Guazzelli, É. 2022 Viscous to inertial transition in dense granular suspension. Phys. Rev. Lett. 129, 078001.CrossRefGoogle ScholarPubMed
Tasaka, Y., Yoshida, T., Rapberger, R. & Murai, Y. 2018 Linear viscoelastic analysis using frequency-domain algorithm on oscillating circular shear flows for bubble suspensions. Rheol. Acta 57, 229–240.CrossRefGoogle Scholar
Taylor, G.I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138, 41-48.Google Scholar