ASYMPTOTIC THEORY OF 2-PHASE GAS-SOLID FLOW-THROUGH A VERTICAL TUBE AT MODERATE PRESSURE-GRADIENT

Based on the equations, constitutive relations and boundary conditions of the kinetic theory of colliding particles in a gas-solid suspensio n, the approximate theory of the steady, developed vertical flow of a gas-particulate mixture is developed for the case of moderate gas pres sure gradient in a vertical tube. The basic equations and boundary con ditions show a singular behaviour of the solution of the problem at th e wall. The method of matched asymptotic expansions is applied to deve lop a boundary layer-type theory for the flow parameters of the partic ulate phase. The basic equations in the bulk flow are reduced to a sys tem of two ordinary integrodifferential equations for the particle-pha se concentration and mean kinetic energy of particle velocity fluctuat ions (particle-phase pseudotemperature). The distributions of the part icle concentration and velocity are found in both the bulk and the bou ndary layer. The solution shows the bifurcation of flow parameters, an d an explicit criterion is derived to identify a range of the given ma croscopic parameters corresponding to upward or downward particulate f low. The integrated parameters (total fluxes of the gas and particle p hase) are calculated.