The ‘collisional model’ for turbulent discs (Hameen-Anttila, 1991) is shown to be equivalent to the α model if the same coefficient of viscosity is adopted in both cases and if an unknown numerical coefficient in the former model is chosen appropriately. A combination of both approximations is generalized to include the behaviour of dust in the turbulent disc. If the dust grains are not too large, evolution leads to a stable final state having a non-zero temperature. Physical interpretation of the collisional model leads to a new type of turbulence, in which, if a sufficiently large element of gas is randomly displaced even in a stable disc, the resulting oscillations around the equilibrium position are maintained by the orbital energy. This effect produces an irregular wind of 10 to 100 m s−1 which is sufficient to prevent the sedimentation of dust grains on the equatorial plane.