Anisotropies and interactions in shear flow of macromolecular suspensions

The problem of determining the orientation distribution function for rigid particles of arbitrary shape is formulated in a general stochastic approach to consider the influence of any acting orientation mechanism, stochastic or deterministic. The effect of the various orientation mechanisms on the partial differential equation of the problem, an equation of the Fokker-Planck type, is analyzed. The question of linearity or non-linearity of the superposition of the effects due to different orientation mechanisms is examined. The orientation of rigid ellipsoidal particles in uniform shear flow is studied in detail, for different cases of acting orientation mechanisms. When only the viscous stresses act on the particles, the problem for the orientation distribution function becomes a deterministic first-order initial value problem, and its solution displays periodic behavior. In the case of macromolecules, when the Brownian influence is predominant, we examine the effect of a third orientation mechanism acting on the macromolecules in addition to the viscous stresses and the Brownian impulses. In Couette flow between concentric cylinders, the third orientation mechanism is considered to be a deterministic force field in the radial direction x, varying linearly with x. The steady state orientation distribution function is then determined to the third order, and the theory of streaming birefringence of a dilute suspension of rigid ellipsoidal macromolecules in Couette flow is generalized to include the effect of the additional influence. The direction of the isocline and the amount of birefringence are calculated to the second order. When spherical macromolecules are added to the suspension in increasing concentration, the effect of hydrodynamic interactions between the two species on the orientation of the ellipsoidal particles is examined in Couette flow. It is shown that an effect of the presence of the spheres is to decrease the drift velocity of the ellipsoids--and thus decrease the amount of birefringence--and that the effect can be described as a decrease in the effective velocity gradient. The theoretical result for this decrease is in good agreement with experimental results for sphere concentrations comparable to the concentration of ellipsoids. On the other hand, as the concentration of spheres increases, the effect of their presence on the rotational diffusion constant of the asymmetrical particles can be large enough to reverse the trend and lead to a positive variation of the amount of birefringence with sphere concentration