Behavior of polymer solutions in a velocity field with parallel gradient. I. Orientation of rigid ellipsoids in a dilute solution

TLDR: In this paper, the spatial orientation of rigid ellipsoidal particles was analyzed as proceeding in a dilute solution flowing in a velocity field with parallel gradient, i.e., in a field characterized by the deformation rate tensor.

Abstract: The spatial orientation of rigid ellipsoidal particles was analyzed as proceeding in a dilute solution flowing in a velocity field with parallel gradient, i.e., in a field characterized by the deformation rate tensor: On the basis of general relations given by Jeffery, the hydrodynamic equations of motion of a single ellipsoid were obtained as Ψ = 0, φ = 0, θ = −¾qR sin 2θ, where q = ∂Vκ/∂κ is the parallel velocity gradient and R = (a2 − b2)/(a2 + b2) is the shape coefficient of ellipsoids. Considering the action of velocity field and that of Brownian motion (rotational diffusion), a distribution density function ρ(t, θ) was derived, which describes the spatial orientation of the axes of symmetry of the ellipsoids: where is the steady-state distribution. In a similar way, the axial orientation factor f0 = 1 − 3/2 sin2θ was obtained: