A mathematical model is worked out to treat random small-scale fluctuations of particles and a fluid in a macroscopically uniform disperse mixture. The particles are assumed large enough to ensure the interparticle exchange of momentum and energy to be effected through direct collisions, so that the particle fluctuations are nearly isotropic. The model provides for closure of equations of conservation that govern the flow of both mixture phases. Statistical properties of the fluctuations are actually studied under conditions of unidirectional flow in two extreme cases when the concentration-dependent hydraulic resistance of the particles to the relative fluid flow is either linear or quadratic in the fluid slip velocity. Overall phase volume fluxes and the hydraulic resistance coefficient happen to be sensitive to the fluctuations and differ from those specific to the same mixture without fluctuations. The particle pressure and the bulk modulus of elasticity of the dispersed phase are shown to be increasing functions of the mean concentration, which makes macroscopically uniform states of the mixture thermodynamically stable. The energy dissipation due to the collisions, however insignificant in most situations of practical importance, results in a noticeable decrease in the bulk modulus of elasticity and can therefore cause the break of stability under otherwise identical conditions.