The paper is concerned with the flow of dispersions of gas bubbles in liquid, with bubble sizes such that the inertia forces on the bubbles are of importance to the dynamics. One-dimensional conservation equations are derived, which govern the flow when the deviations from the uniform state are small. These are used to describe the features of the propagation of void fraction disturbances, and to investigate the stability of uniform bubbly flows. The results are compared with what has been observed in experiments.

Following up ideas put forward by J.M. Ottino and colleagues, the possibility of designing a computational tool to optimize the mixing of viscous fluids in industrial devices is studied. It is shown that an efficient method to characterize and quantify a mixing process is to apply the statistical measures introduced by Danckwerts (e.g., intensity of segregation and scale of segregation) on the coarse-grained density distribution of points in Poincaré sections and advection patterns, that can be obtained by tracking the positions of marked fluid elements numerically. This method is not computationally excessively costly and, as is demonstrated here, can be applied easily to experimental dye advection studies. The model system used is the Stokes flow in a two-dimensional cavity transfer mixer: two rectangular cavities which are periodically driven by a solid wall and by the passage of the cavities over each other. This system shares with many industrial devices the complexity that the geometry of the flow is time-dependent. These changes in the geometry of the flow impose difficulties on the techniques of calculating the fluid velocity field (a boundary element method) and the advection of marked fluid elements. Ways of overcoming these difficulties are described.

Temperature distribution at the exit of the leakage gap is of interest for a number of problems. For the calculation of temperatures, the leakage flow may be considered to be a pure drag flow to a good approximation. In the Newtonian case, thermal development length may be expressed in terms of gap height as L ≈ 3/8Pe · δ;usually this is less than the available gap length. Pe is the Peclet number and δ the height of leakage gap. Therefore the existing flow may be considered fully developed. For power law fluids, numerical calculations lead to results of the same order. Martin's results therefore may be applied to the flow at the exit of the leakage gap.