Optimization of viscous mixing in a two-dimensional cavity transfer mixer

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.