On the dynamics of suspended microstructure in unsteady, spatially inhomogeneous, two-dimensional fluid flows

Abstract

The dynamical behaviour of stretchable, orientable microstructure suspended in a general two-dimensional fluid flow is investigated. The state of the microstructure in question is described by an axial vector; thus the microstructure may consist of axisymmetric particles, droplets of fluid, models of polymer molecules or simply a line element of the fluid itself. A quantitative measure is developed to distinguish conformation(s) (orientations and stretched lengths) of the microstructure that are robust and attractive. This leads to a strong flow criterion for microstructure suspended in unsteady, spatially inhomogeneous flows in which the effects of history-dependence are apparent. The important special case where the influence of the flow on the microstructure is time periodic is considered in some detail, owing to the fact that one can obtain additional results that concern orientation dynamics. Finally, several examples are given which illustrate the application of the present methods and the relevant innovations of the approach. Throughout the analysis, special attention is given to the robustness of the dynamics to changes in the modelling assumptions such as slight three-dimensionality or Brownian diffusion, etc. The results of the study demonstrate that using microdynamical behaviour in steady, homogeneous flows to derive macroscopic properties (such as strong flow criteria) which are then applied to problems in unsteady, spatially inhomogeneous flows can lead to incorrect results. Instead, one must account properly for effects due to the history of the flow.