(259b) The Effects of a Spatially Variant Velocity Field On Stretching: Intuitive Measures

Laminar mixing theory describes the ‘goodness’ of mixing as a function of increased surface area shared between two fluid species.  Previous work in the field attempts to describe mixing from a post processing perspective, namely as a function of stretching history, while disregarding the nature of the underlying flow.  In this work, new mathematical measures are derived which allow for the prediction of fluid body interface behavior in a flow and the exploration of the underlying flow fields itself.  This family of measures creates a more intuitive basis for the exploration interfacial growth, providing a new perspective on laminar mixing.  One set of measure relates velocity with the principal directions while the second set relates interfacial orientation with the princiapl directions. To explore the usefulness of these new measures, they are simulated in three numerical flows, steady shear, steady divergent flow, and spatially variant lid driven cavity. 

In these flow geometries, the new family of measures proves valuable for demonstration of various features underlying flow including growth regime characteristics, transition in growth regime, as well as other more flow characteristics unique to each flow type.  It has been shown that the change of mixing consistent with reorientation occurs after a rapid change in the relationship of the flow and principle directions.  The second set of measures in this family allows for interface growth and modeled to be studied more objectively.