There are many turbulent-flow phenomena for the prediction of which conventional turbulence models, such as k-epsilon, suffice.

The insufficiency of these models becomes apparent when body forces interact with fluctuating fluid properties, such as density or velocity.

Fluctuating densities can result from fluctuating temperatures, which are inevitable when heat transfer occurs in turbulent fluids.

The gravitational body force is always present; and it becomes significant whenever the gravitational acceleration times the vertical dimension exceeds the square of typical velocities.

Such phenomena need a multi-fluid model for their simulation; for only an MFM can predict "counter-gradient diffusion", eg the fact that the hotter fluids float upwards, so steepening the temperature gradient.

Swirling flows are notoriously ill-simulated by the k-epsilon model; and the reason is that this model has no means of representing the fact that faster-swirling fluids are flung outwards.

If, as in the boundary layer on a convex surface, the mean velocity is greater at the outer radii, this can be another case of counter- gradient diffusion; and it certainly results in a diminution, even if not a change of sign, of the effective viscosity.

When the surface is concave, and the mean velocity of the fluids is therefore greater at the smaller radii, the faster-moving fluids are flung towards the surface. This results in an increased momentum transfer and, if it is desired to calculate it, an enlarged effective viscosity.

Axial-flow compressors and turbines, as used in aircraft propulsion and in ground- (or sea-) level power production, are characterised by the rapid passing of one blade row behind another.

The slower-moving boundary-layer fluid from the upstream row becomes a "wake" of slower-moving fluid fragments which are distributed across the entrance plane of the downstream row.

The turbulent mixture which passes from row to row through a turbo- machine is therefore best represented as a population of fluids, with (say) axial velocity as their distinguishing characteristic.

So far, no use of MFM for the simulation of such phenomena has yet been reported; yet it seems certain that MFM will provide a better representation of turbo-machinery flows than any conventional model.

To refer to the concept discussed in section 2 of this encyclopaedia article, MFM has superior "physical plausibility" for this application.

The multi-fluid concept has even more to offer when the focus of attention is chemical reaction.

This subject is of such theoretical and practical importance that is is handled separately, in section 6.5.

There, the multi-fluid model will be seen as the culmination of a line of research which has developed from its embryonic form as the "eddy-break-up" model, through a variety of other two-fluid-model forms, to its current state of generalization.

Both chemical reactions in apparatus employed by chemical industry, and combustion as practised in the power industry, will be shown to be benefited by MFM.

wbs