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

Abstract

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 = −¾ qR sin 2θ, where q = ∂V κ /∂κ is the parallel velocity gradient and R = ( a 2 − b 2 )/( a 2 + b 2 ) 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 f 0 = 1 − 3/2 sin 2 θ was obtained: