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

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<jats:title>Abstract</jats:title><jats:p>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: <jats:disp-formula> </jats:disp-formula> 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<jats:italic>qR</jats:italic> sin 2θ, where <jats:italic>q</jats:italic> = ∂V<jats:sub>κ</jats:sub>/∂κ is the parallel velocity gradient and <jats:italic>R</jats:italic> = (<jats:italic>a</jats:italic><jats:sup>2</jats:sup> − <jats:italic>b</jats:italic><jats:sup>2</jats:sup>)/(<jats:italic>a</jats:italic><jats:sup>2</jats:sup> + <jats:italic>b</jats:italic><jats:sup>2</jats:sup>) is the shape coefficient of ellipsoids. Considering the action of velocity field and that of Brownian motion (rotational diffusion), a distribution density function ρ(<jats:italic>t</jats:italic>, θ) was derived, which describes the spatial orientation of the axes of symmetry of the ellipsoids: <jats:disp-formula> </jats:disp-formula> where <jats:disp-formula> </jats:disp-formula> is the steady‐state distribution. In a similar way, the axial orientation factor <jats:italic>f</jats:italic><jats:sub>0</jats:sub> = 1 − 3/2 sin<jats:sup>2</jats:sup>θ was obtained: <jats:disp-formula> </jats:disp-formula> </jats:p>

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