NONLINEAR-WAVES AND PATTERN-FORMATION IN MULTIPHASE FLOWS IN POROUS-MEDIA

The paper analyzes pattern formation in initially homogeneous one-dime nsional two-phase flows in porous medium. It is shown that generally t hese hows are unstable. The mechanism of the instabilities is associat ed with inertial effects. Such instabilities are of explosive type and are probably important in various engineering applications and natura l phenomena. In small-amplitude finite approximation the evolution of patterns is governed by the Korteweg-de Vries-Burgers equation. Patter n formation occurs when the coefficient multiplying the Burgers term b ecomes negative. During nonlinear evolution a soliton with a tail is f ormed. The amplitude of the soliton increases while the tail decreases , These results can be regarded as a generalization of results by Harr is 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 interpre ted as initial phase of formation of the phase composition inhomogenei ties in porous media. In the case of fluidized beds this pattern can b e 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.