The purpose of the present paper is to reach some general conclusions on the motion of rigid particles in a homogeneous shear flow of a viscoelastic fluid. Under the basic assumption of nearly Newtonian slow flow, the creeping-motion equations for a second-order fluid with characteristic time constants κ0(2) and κ0(11) can be employed. It is shown that the κ0(2) contributions to the hydrodynamic force F and couple G depend upon the hydrodynamic force, couple and stresslet which act upon the particle in a Newtonian fluid (termed F(1), G(1) and S(1), respectively). Since this relation involves time derivatives of F(1) and G(1), a little reflexion is needed to realize that the modification of the classical Stokes law for steady translation in a quiescent fluid can have no κ0(2) term. Since no results of such generality are possible for the κ0(11) contributions we focus attention on transversely isotropic particles. Employing the concept of material tensors, the symmetry of such particles dictates the form these tensors adopt. This alone is sufficient to show that sedimentation in a quiescent fluid is accompanied by a change in orientation until a stable terminal orientation is attained. Depending upon the type of particle only one of the two orientations, axis of symmetry parallel or perpendicular to the external force, is stable. Another result concerns two-dimensional shear flow, for which we show that the symmetry axis has to drift through various Jeffery orbits until an equilibrium orientation is reached. While the orbits C = 0 and C = ∞ are equilibrium orbits for every transversely isotropic particle there may be a third such preferred orbit, which we denote by C*. In order for these orbits to be stable certain restrictions have to hold, showing that the orbits C = 0 and C* cannot both be stable. For the special case of a rigid tridumbbell of axis ratio s the orbit C* does not exist. If s > 1 the drift for this particle is into the orbit C = 0 while for s < 1 it is into the orbit C = ∞. This agrees qualitatively quite well with experimental results obtained for rods and disks. No quantitative comparison is possible; the particle shape influences the result quantitatively owing to its effect on the combination of the fluid parameters κ0(2) and κ0(11).
In this paper the behavior of an aqueous surfactant solution in a rotational Couette viscometer is investigated. It is shown that this behavior depends strongly upon time, upon the way in which the flow curve is obtained (with increasing or decreasing shear rate), upon the temperature, and upon the concentration of the solution. Furthermore, the results also reveal a pronounced dependence upon the size of the actual measuring system used. It is shown that the slip-velocity concept is not applicable to explain this dependence.
The hydrodynamics of bead-spring model macromolecules in nonhomogeneous flows has recently been worked out. By taking a non-infinite distance between the beads (relative to the bead size) into account a hydrodynamic driving force was found. In this paper we explore the kinetic theory consequence of that force and show that non-uniform (polymer) concentration profiles are to be expected in nonhomogeneous flows. The diffusion equation for a dilute polymer solution is derived from the continuity equation for the distribution function. Arguments, leading to a well-ordered pertubation expansion of the continuity equation are advanced and the zeroth order function of this hierarchy is studied for models with linear springs. Details for the channel flow system are worked out with special emphasis on the relation between the polymer concentration and the parameters of the system. Explicit results are presented for models with linear springs. It is shown that if the Oseen tensor is not preaveraged, inadmissible results emerge.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.