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Keywords:

  • bakers transformation;
  • chaotic mixing;
  • mapping method;
  • matrices;
  • SMX mixer;
  • static mixer

Abstract

Thumbnail image of graphical abstract

Using the Mapping Method different designs of SMX motionless mixers are analyzed and optimized. The three design parameters that constitute a specific SMX design are: The number of cross-bars over the width of channel, Nx, the number of parallel cross-bars per element, Np, and the angle between opposite cross-bars θ. Optimizing Nx, somewhat surprisingly reveals that in the standard design with Np = 3, Nx = 6 is the optimum using both energy efficiency as well as compactness as criteria. Increasing Nx results in under-stretching and decreasing Nx leads to over-stretching of the interface. Increasing Np makes interfacial stretching more effective by co-operating vortices. Comparing realized to optimal stretching, we find the optimum series for all possible SMX(n) designs to obey the universal design rule Np = (2/3) Nx−1, for Nx = 3, 6, 9, 12, ….