Laminate Mixing in Micro-Scale Fractal-Like Merging Channel Networks

A two-dimensional model was developed to predict concentration profiles resulting from passive, or diffusive, mixing of laminated layers formed in a fractal-like merging flow network. Both uniform and parabolic velocity profiles were considered in the model. Concentration profiles were experimentally acquired near the top surface of the flow network using laser induced fluorescence. The degree of mixing was assessed from concentration profiles at the end of each channel. Although the degree of mixing from the two-dimensional model well predicts the trend of the experimental degree of mixing, the numerical model under predicts the experimental values by approximately 25 percent. This may be due in part to the presence of top and bottom walls in the experimental device. These walls tend to slow the flow in this region, thereby increasing the residence time and improving the mixing. These top and bottom walls are neglected in the two-dimensional model. For the existing flow network, the degree of mixing is provided as a function of Peclet number. The degree of mixing is further investigated by varying the number of branching levels, the width of the initial flow channels, and the total flow length for a fixed Peclet number. A nondimensional parameter is established that serves as a design tool for predicting an optimum number of branching levels for fixed values of the total flow length, initial branch width and channel depth.