ABSTRACT Proposal Number: CTS 9625347 Principal Investigator: Wedgewood This grant will support the investigation of a fundamental issue in fluid mechanics, viz., identifying the complete set of kinematic variables and rheological time derivatives that are admissible in constitutive equations. This work will be useful in the description of the mechanical behavior of fluids. It is a common requirement that constitutive equations should be frame invariant (or objective). The Rivlin-Ericksen tensors and convective derivatives that are presently employed are sufficient to satisfy objectivity, but it has been established that the vorticity can play a much less restricted role in constitutive equations than the traditional formalism allows. It is argued that it is the relative difference between the rotational state of the fluid element and its local surroundings that can cause stress in fluids with long-range molecular interactions. These arguments lead to a decomposition of the vorticity into two portions, one of which represents the rotation caused by shear deformation. The remaining portion of the vorticity is useful in defining a frame invariant time derivative. This theory was first presented as part of a network theory for polymer melts in Wedgewood and Geurts (1995a). Predictions of the theory will be tested using Brownian dynamic simulations that will indicate if polymer chain interactions can give rise to the predicted stresses. Also proposed are simulations of complex flow (e.g., the driven cavity and the four-to-one contraction) using the stochastic methods recently developed (Wedgewood and Geurts, 1995b) and established finite element methods. Finally, the evaluation of existing experimental data and the design of new flow experiments are proposed as a vital element in establishing the usefulness of the proposed theory.
