Ghost rods adopting the role of withdrawn baffles in batch mixer designs

In batch mixers the stirring of a fluid is known to be particularly effective when the motion of the stirring rods form nontrivial braids. This motion is desirable as it generates (predictable) exponential stretching of material lines. Additionally, it has also been recognized that flow structures themselves (such as periodic islands) may adopt the role of proxy or “ghost” stirring rods. For a number of designs (which form nontrivial braids), we investigate the prevalence of ghost rods that effectively replace stationary stirring rods (baffles) as the latter are removed from the batch mixer. We show (for the case of Stokes flow) that designs with fewer baffles have comparable material stretch factors to corresponding designs with all baffles present.