  We propose an alternative interpretation of Markovian transport models based
on the well-mixedness condition, in terms of the properties of a random
velocity field with second order structure functions scaling linearly in the
space time increments. This interpretation allows direct association of the
drift and noise terms entering the model, with the geometry of the turbulent
fluctuations. In particular, the well known non-uniqueness problem in the
well-mixedness approach is solved in terms of the antisymmetric part of the
velocity correlations; its relation with the presence of non-zero mean helicity
and other geometrical properties of the flow is elucidated. The well-mixedness
condition appears to be a special case of the relation between conditional
velocity increments of the random field and the one-point Eulerian velocity
distribution, allowing generalization of the approach to the transport of
non-tracer quantities. Application to solid particle transport leads to a model
satisfying, in the homogeneous isotropic turbulence case, all the conditions on
the behaviour of the correlation times for the fluid velocity sampled by the
particles. In particular, correlation times in the gravity and in the inertia
dominated case, respectively, longer and shorter than in the passive tracer
case; in the gravity dominated case, correlation times longer for velocity
components along gravity, than for the perpendicular ones. The model produces,
in channel flow geometry, particle deposition rates in agreement with
experiments.
