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Hydrodynamic interaction between gas bubbles in liquid

  • L. Van Wijngaarden (a1) and D. J. Jeffrey (a2)


A calculation is given of the velocity which a cloud of identical gas bubbles acquires when the liquid in which the cloud is immersed is impulsively accelerated. From the results an expression follows for the effective virtual mass of a bubble in a gas-bubble/liquid mixture. Further consideration is given to that part of the momentum flux in the mixture associated with relative motion between liquid and bubbles. An expression for this quantity is derived which appears to differ from the one used in practice. It is shown that qualitative support for the expression obtained here is provided by experimental observations reported in the literature.



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Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 4, 245.
Batchelor, G. K. 1974 Transport properties of two-phase materials with random structure. Ann. Rev. Fluid Mech. 6 227.
Jeffrey, D. J. 1973 Conduction through a random suspension of spheres. Proc. Roy. Soc. A 335, 355.
Kellou, O. D. 1953 Foundations of PotendicGl Theory. Dover.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lundgren, T. S. 1972 Slow flow through stationary random beds and suspensions of spheres. J. Fluid Mech. 51, 273.
Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics. Macmillan.
Prins, C. A. 1974 Aspects of two-phase, gas liquid, separation related to nuclear steam supply systems. Delft Univ. Tech. Rep. WTHD56.
Ross, D. K. 1970 The Dirichlet boundary value problem for two non-overlapping spheres. Bull. Auatr. Math. Soc. 2, 237.
Voinov, V. V., Vomov, O. V. & Petrov, A. G. 1973 Hydrodynamic interaction between bodies in a perfect incompressible fluid and their motion in non-uniform streams. Prikl. Math. Mech. 37, 680.
Zuber, N. 1964 On the dispersed two-phase flow in the laminar flow regime. Chem. Engng Sci. 19, 897.
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Hydrodynamic interaction between gas bubbles in liquid

  • L. Van Wijngaarden (a1) and D. J. Jeffrey (a2)


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