On Microdeformable Fluids: A Special Case of Microfluids.

摘要

A constitutive theory for fluids with deformable substructure is developed. the theory arises as a result of 2 physical constraints imposed on the general microfluid theory of Eringen. First an 'Onsager' type of symmetry condition is applied to the viscosity and gyroviscosity coefficient tensors. The second constraint restricts the constitutive equations so that gradients of the trace, deviator and skew part of the substructure strain rate are related to comparable elements of the stress moments. The result of these 2 constraints is a theory which is general enough to allow deforming substructure, yet contains 8 fewer gyroviscosities than the general theory. Also, restrictions on the phenomenological coefficients imposed by the Clausius-Duhem inequality are calulated. Unlike the general microfluid theory, the number of restrictions exactly equals the number of coefficients. The theory is applied to nonstationary channel flow. For the transient solution, the Clausius-Duhem conditions are just sufficient to insure the decay with time of initial disturbances. The steady solution is found to be the same form as that obtained from the general theory. (Author)