New mathematical measures are developed for the investigation of fluid-fluid mixing in continuous laminar flows as a function of mechanisms of mixing, namely the eigenvectors of the rate of deformation tensor. Previous theoretical work in this field has shown that interfacial reorientation and chaotic advection produce improved mixing over deterministic mixing. However, these previous approaches have failed to explore the nature of the mechanisms of mixing present in the continuously spatially varying flow fields. Four new measures are presented to relate the deformation of an infinitesimal material element to the eigenvectors of the rate of deformation tensor. These expressions characterize material deformation as a function of the spatial relationship between material and the eigenvectors in a variety of general flows. The application of these measures is shown using CFD simulations for three steady flows, the Couette channel, the diverging channel, and the steady state lid driven cavity. These measures improve the understanding of mixing in the various flow field models and produce new insight into the nature of mixing in continuous flow fields.