Mapping approach for 3D distributive mixing simulations

A mapping approach for simulations of three-dimensional laminar distributive mixing was developed, which is an extension of a recently proposed two-dimensional technique. It offers a fast and easy way to predict long-term mixing and to compare different mixing protocols. The method requires extensive computations to create the matrices that describe the mappings, but such computations are only performed once and strongly benefit from parallelization. Once the mapping matrices are computed, they are easily used to construct different mixing protocols. The mapping used to describe the redistribution of the marker fluid is itself not computationally expensive. The CPU time required to compute the mapping matrix is of the order of days on a multi-processor machine, while the actual mapping is performed within a few seconds on a single CPU. A simple prototype mixing flow in a cubic domain was used to test the proposed mapping approach for three-dimensional mixing simulations. The reliability of the technique was confirmed by comparison of its results with the results of the adaptive front tracking. The interface shape recovered from the mapping results closely matches the surface of the same initial blob of marker fluid that was explicitely tracked in the flow. Also the comparison of the results obtained using the mappings with different spatial resolution was used to validate the mapping approach. It is demonstrated that the mapping technique can be used to compare the mixing efficiency of different protocols. For this the discrete intensity of segregation was used to characterize the overall degree of mixing. It was shown that although this parameter depends on the spatial resolution, the comparative results and revealed trends are similar for different resolutions. Thus, this mixing measure is reliable to use for comparison of the protocols. The mapping method can also be used to adjust the parameters of the selected flow protocol to achieve optimal mixing with the same energy input. The mapping technique can potentially be applied for studying fluid mixing in the systems with a more complex geometry.