Flow-Induced Alignment of Dispersed Particles: Closure Model for Particle-Fluid Interactions

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AbstractThe objective of this project is to develop a closure model for the orientation of particles in a fluid. Model predictions of low-order statistical properties, characteristic of the microstructure of suspensions, are often based on a moment equation for the particle orientation dyadic (second-order moment). The solution to this equation requires a closure model for the particle orientation tetradic (fourth-order moment) associated with particle/fluid interactions. This theoretical work will address a new closure theory for the orientation tetradic that retains the six-fold symmetry and the six-fold projection properties of the exact orientation tetradic. This fundamental research will focus on finding closure approximations of higher order tensors in terms of lower order tensors. The new representation for particle/fluid interactions will be validated for a class of simple flows (shear and extensional) by comparing second-order moment predictions with the exact behavior of the second-order moment derived from the particle orientation distribution function governed by a convective-diffusive type equation. There has been renewed interest in this field for property determination of materials that exhibit a microstructure. Standard industrial flow simulators now incorporate tensor descriptions of particle orientations, and this research may be useful in making those simulations more accurate and efficient.