The system of equations, usually employed for unsteady liquid/gas flows, has complex characteristics. This as well as other facts have led to the search for a more accurate description of effects associated with relative motion. For liquid/bubble systems the fluctuations resulting from hydrodynamic interaction between the bubbles may be taken into account in the same way as particle interactions in the theory of viscous suspensions. This is illustrated for the pressure. In a description accurate up till the third power of the void fraction two-bubble interactions are of primary importance. Numerically obtained results for the relative motion in bubble pairs are presented and interpreted with help of simplified equations from which conclusions can be drawn in an analytic way.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Batchelor GK (1970) The stress system in a suspension of force-free particles. J Fluid Mech 41: 545.
Batchelor GK (1974) Transport properties of two-phase materials with random structure. Ann Rev Fluid Mech 6: 227.
Biesheuvel A and Van Wijngaarden L (to be published).
Jeffrey DJ (1973) Conduction through a random suspension of spheres. Proc R Soc London A 335: 355.
Knibbe P (1981) Master's Thesis. Technological University Twente, The Netherlands.
Landweber L and Miloh T (1980) Unsteady Lagally theorem for multipoles and deformable bodies. J Fluid Mech 96: 33.
Voinov OV and Petrov AG (1977). On the stress tensor in a fluid containing disperse particles. PMM 41: 362.
Van Beek P (1981) An O(α)-accurate model for liquid-bubble dispersions. Appl Sc Res.
Van Wijngaarden L (1976) Hydrodynamic interaction between gas bubbles in liquid. J Fluid Mech 77: 27.
Van Wijngaarden L Jn (1980) On the mathematical modeling of two-phase flows. Proc IVth Int Meeting on water column separation, Cagliari, 1979.
About this article
Cite this article
van Wijngaarden, L. Bubble interactions in liquid/gas flows. Applied Scientific Research 38, 331–339 (1982). https://doi.org/10.1007/BF00385963
- Relative Motion
- Void Fraction
- Particle Interaction
- Accurate Description
- Hydrodynamic Interaction