### 7.11.2. MUSIG Model Advice

The MUSIG model is best applied to flows with polydispersed, medium-size bubbles. Medium-sized in this context means bubbles that are large enough to be in the distorted particle regime, but not large enough to be in the spherical cap regime. Within the distorted particle regime, the asymptotic slip velocity of such bubbles is sufficiently small relative to inertial time scales that it can be attained almost instantly. Within this assumption, it is reasonable to assume that all the bubble size groups share a common velocity field. This is the fundamental assumption in the homogeneous MUSIG model.

The assumptions used in deriving the homogeneous MUSIG model break down in the following situations:

- Small spherical bubbles, or large spherical cap bubbles. In these cases, the asymptotic slip velocity is proportional to the square root of the particle diameter.

- Liquid drops (sprays) or solid particles in a gas. In this case, not only are the asymptotic slip velocities dependent on particle size, but the particle relaxation times may be comparable to, or larger than, the inertial time scale. The MUSIG model would not predict segregation of solid particles of different sizes in a fluidized bed.

- Flows where non-drag forces are significant and depend on bubble size. For example, the lift force exerted on bubbly flows in pipes has a separating effect, moving large bubbles to the pipe center and small bubbles to the outside.

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