A general two-fluid theory for wormlike macromolecule suspensions

A general two-fluid continuum theory is developed for a non-dilute suspension of wormlike macromolecules dispersed in a Newtonian fluid. Individual macromolecules interact with each other and slip relative to the fluid medium. This general continuum theory is applied to the case of two-dimensional flow of a dilute macromolecule solution in simple shear in order to determine the motion and orientation of the wormlike macromolecules interacting with the fluid medium. The suspension is considered as two interacting continua; the suspending fluid medium is regarded as a classical continuum and the suspended macromolecules as a structured continuum. Each continuum has its own concentration, velocity field, and a set of conservation equations. The macromolecule phase momentum equation includes momentum exchange with the suspending fluid, and includes the macromolecule phase stress which is obtained by introducing the concept of "a structured neighborhood" to the continuum description of a collection of macromolecules.;Numerical results are presented for the motion and orientation of macromolecules entering two-dimensional laminar shear flow field. It is found that the internal macromolecule stress containing the effective macromolecule viscosity plays an important role in the momentum conservation equations and significantly affects the development of the macromolecule velocity and the alignment of the macromolecule.