Mixing length correlation for laminar liquid mixing in wall-bounded flows

Abstract

The aim of this paper is twofold. Firstly, to examine the relationship between mixing length with respect to mixing index for two streams of liquid mixing in a two-dimensional (2D) straight plane channel. Secondly, to propose a new correlation for mixing length for a given mixing index. Although the existing analytical mixing length using LM=1 = PeH could yield accurate prediction, it is, however, restricted to only at a fully mixed condition (i.e., at mixing index M = 1). To accommodate a broad spectrum of mixing indices, a new correlation that would accurately predict the mixing length for a specific mixing index, in the range of 0.5 ≤ M ≤ 1, is proposed. As revealed in this study, this correlation is applicable to the practical range of Péclet number, for 10 ≤ Pe ≤ 1000 and would hold valid, as long as the laminar mixing flow prevails. In addition, the new correlation is applicable to liquid mixing in the mixers with different channel inlet designs (i.e., 2D Y-mixer and 2D T-mixer), and also relevant for three-dimensional (3D) straight mixers with different mixing channel aspect ratios.