CLOSED-FORM MATERIAL FUNCTIONS FOR SEMIDILUTE FIBER SUSPENSIONS

The Dinh-Armstrong constitutive equation is used to derive analytic expressions for the viscosity and the normal stress difference in shear and elongational deformation of nondilute, slender-fiber suspensions in Newtonian media. This is achieved by approximating the fourth order orientation tensor of the integral constitutive equation with the components of the Finger strain tensor according to Currie's expressions that relate the strain tensor to flow kinematics. The derived analytic expressions are in agreement with the numerical results given by Dinh-Armstrong in simple shear flow. In elongation, although the magnitude of the dimensionless viscosity at start up and steady state are identical, there is a quantitative disagreement in the values inbetween. Approximations to the fourth order orientation tensor are also derived for any two- or three-dimensional mixed flow of the same suspensions.