Diffusive mixing in continuous laminar flow systems

Abstract

If the amount of mixing required at a local position of a system is measured by the absolute value of the excess concentration in that area, then it is shown that in a batch mixer, the local efficiency of mixing, described by the fractional decrease in the amount of mixing required per unit time is given by C 3 D/δ 2, while for a continuous mixer the local efficiency of mixing, described by the fractional decrease in the amount of mixing required per unit length, is given by C 3 D/δ 2 u x . In both cases C 3 is an approximately constant factor describing the shape of the concentration distribution and of order π 2, D is the appropriate chemical diffusion coefficient, δ is the local striation thickness and u x is the velocity component along the direct line from the entrance to exit. It is also shown that the relative rate of reduction of striation thickness is given by ▪ when u l is the velocity component along a striation segment of length, dl. Application of this relation to several simple types of flow is carried out and a brief discussion of the utility of the principles to continuous laminar flow mixer design is included.