Bifurcation with Symmetry in Multi-Phase Flows
A common approach to describe particulate flows consists in the use of (volume or ensemble) averaged equations of motion. These are coupled sets of compressible Navier-Stokes equations representing a typical wave-hierarchy problem with dissipation and expressing another hierarchy of symmetry-breaking instabilities. The general features of these hierarchies, their connection, and the details of the first two stages of instabilities are discussed.
KeywordsSolitary Wave Bifurcation Point Secondary Instability Transverse Structure Kinematic Wave
Unable to display preview. Download preview PDF.
- R. Jackson, Fluid mechanical theory, in: J.F. Davidson and D. Harrison (eds.), Fluidization ( Academic Press, London, 1971 ), pp. 65–119.Google Scholar
- J.F. Richardson, Incipient fluidization and particulate systems, in: J.F. Davidson and D. Harrison (eds.), Fluidization ( Academic Press, London, 1971 ), pp. 2664.Google Scholar
- M.F. Göz, Small Froude number asymptotics in two-dimensional two-phase flows, Phys. Rev. E 52 (1995), 3697–3710.Google Scholar
- M.F. Göz, A “complete” two-dimensional nonlinear wave equation describing the small Froude number regime of multiphase flows, in: L. Pust and F. Peterka (eds.), Proceedings of the 2nd European Nonlinear Oscillations Conference (Prague 1996), Vol. 1, 183–186.Google Scholar
- M.F. Göz, B.J. Glasser, Y.G. Kevrekidis and S. Sundaresan, Traveling waves in multi-phase flows, in: M. Rahman and C.A. Brebbia (eds.), Advances in Fluid Mechanics, Comp. Mech. Publ. ( South Hampton/Boston 1996 ), 307–316.Google Scholar
- M.F. Göz and S. Sundaresan, The growth and saturation of one-and two-dimensional disturbances in fluidized beds,submitted to J. Fluid Mech.Google Scholar
- M. F. Göz, Instabilities and the formation of wave patterns in fluidized beds, in: G. Gouesbet and A. Berlemont (eds.), Instabilities in Multiphase Flows (Plenum 1993 ), pp. 251–259.Google Scholar
- B.J. Glasser, I.G. Kevrekidis, and S. Sundaresan, Fully-developed traveling wave solutions and bubble formation in fluidized beds, to appear in J. Fluid Mech.Google Scholar
- R.H. Wilhelm and M. Kwauk, Fluidization of solid particles, Chem. Engng. Progr. 44 (1948), 201–218.Google Scholar