Sample streamfunctions for the Childress–Soward flow (14) with values of , 0.25, 0.5, and 1.0 and .
Log-log plot of the along-channel diffusivity enhancement vs Péclet number for Childress–Soward flows with (cellular flow), 0.25, 0.5, and 1.0 (shear flow). Dotted lines indicate scalings of and for comparison.
Log-log plot of (left) unweighted mixing efficiency and macroscale- weighted mixing efficiency and (right) microscale-weighted mixing efficiency vs Péclet number Pe calculated for simulated Childress–Soward flows with monochromatic source with . Dashed lines plot the homogenization theory prediction for these mixing efficiencies (11a)–(11c). Dotted lines indicate predicted large Péclet number scalings for comparison.
Log-log plot of unweighted mixing efficiency vs Péclet number Pe for Childress–Soward flows with monochromatic source . Each figure corresponds to one of the considered flow patterns (parametrized by ), and in each figure, we examine different ratios of the scale separation parameter between the length scale of the stirring velocity field and the source. Dashed lines indicate the theoretical predictions (11a)–(11c) in the homogenization limit .
Snapshots of source function and scalar concentration at various time-steps for a stirring shear flow with no scale separation ( and ). The stirring field is unable to generate the small scales in the scalar concentration necessary for efficient mixing.
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