A constitutive model for the prediction of ellipsoidal droplet shapes and stresses in immiscible blends

We report a phenomenological constitutive model with no adjustable parameters appropriate for the transient behavior of droplets and blends. The time evolution of the droplet anisotropy tensor during droplet relaxation under quiescent conditions is described using a frame-invariant formulation that approximately imposes constancy of droplet volume. The Doi-Ohta theory [J. Chem. Phys. 95, 1242 (1991)] is then adapted to transient flows in which breakup and coalescence do not occur by replacing the Doi-Ohta relaxation terms with this relaxation description. Model predictions are compared to results of visualization of single droplets in step shear and startup of steady shear and to measurement of concentrated blend rheology in step shear and startup of steady shear. The model quantitatively described the relaxation after step strain of single droplets to axisymmetric and then to isotropic shapes. With the inclusion of the rational ellipsoidal closure for affine deformation [Wetzel and Tucker, Int. J. Multiphase Flow 25, 35 (1999)], single droplet response in startup of steady shear was also well predicted. For concentrated (phi = 0.2) blends, good agreement between experiment and theory was obtained for step strain, while in startup of steady shear the model increasingly failed as the shear rate was increased. (C) 2000 The Society of Rheology. [S0148-6055(00)00205-4].