The mixing length theory is extended to close the relevant momentum equations for two-phase turbulent flow at a first-order closure level. It is assumed that the mass fraction of the particles is on the order of unity, that the particle size is so small that the particles are fully suspended in the primary fluid, and that the relaxation time scale of the particles is sufficiently small compared with the time scale of the energy containing eddies so that the suspended particles are fully responsive to the fluctuating turbulent field. Bulk motion of the particles is treated as a secondary fluid flow with its own virtual viscosity. The proposed closure is applied to a fully developed gas-solid pipe flow in which the particles are assumed to be uniformly distributed across the pipe section. Predicted velocity profiles and the friction factors are in good agreement with available experimental data.

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