PHYSICA Nonlinear waves and pattern formation in multiphase flows in porous media

The paper analyzes pattern formation in initially homogeneous one-dimensional two-phase flows in porous medium. It is shown that generally these flows are unstable. The mechanism of the instabilities i associated with inertial effects. Such instabilities are of explosive type and are probably important in various engineering applications and natural phenomena. In small-amplitude finite approximation the evolution of patterns is governed by the Korteweg-de Vries-Burgers equation. Pattern formation occurs when the coefficient multiplying the Burgers term becomes negative. During nonlinear evolution a soliton with a tail is formed. The amplitude of the soliton increases while the tail decreases. These results can be regarded as a generalization f results by Harris and Crighton (1994) to the case of two-phase flows in porous medium. The obtained solution in form of soliton with a tail can be interpreted as initial phase of formation of the phase composition i homogeneities in porous media. In the case of fluidized beds this pattern can be regarded as initial phase of bubble formation in a fluidized bed of granular material. The characteristic size of bubbles and time of its formation are estimated. 1