A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite-element/Newton method is presented for solving the free-boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionless value of the critical yield stress Yg below which the material acts as a solid. The computed flow fields differ appreciably from Stokes’ solution. The sphere will fall only when Yg is below 0.143 For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary-layer scalings give the correct forms of the dependence of the drag coefficient and mass-transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value of Yg there is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations For the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit.

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Laser Doppler velocimetry and flow-induced birefringence are used to measure the rate of deformation and the principal components of the refractive index tensor in a 5% polyisobutylene (PIB) solution in tetradecane (C14) flowing along the centerplane of an abrupt 3.97:1 planar contraction. The stress optical law is used to interpret the birefringence data in terms of the normal stress difference, which is used to calculate a transient elongational viscosity defined along the centerplane. These measurements are compared directly to predictions of six multimode, differential constitutive models (Oldroyd-B, White–Metzner, Acierno et al., Giesekus, Bird–DeAguiar, and Phan-Thien–Tanner) that are fit to steady and small amplitude oscillatory shear flow data for the PIB/C14 solution. The fluid exhibits slight elongational thickening followed by apparent extensional thinning at higher elongation rates. We believe that this ‘‘thinning’’ behavior is due to the decreased residence time of the polymer molecules in the high-strain-rate region as the flow rate (and maximum elongation rate) is increased. The nonlinear constitutive equations, except for the White–Metzner model, are virtually indistinguishable in their description of the dynamical response of the fluid in this experiment; however, the Phan-Thien–Tanner model gives the best quantitative fit to the data. These results point to the need for experiments in which the fluid flowing along the centerline is subjected to a greater total elongational strain.

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Under the influence of a uniform and parallel magnetic field, a ferromagnetic fiber suspended in a Newtonian fluid rotates to align with the field direction. This study examines the field-induced rotation process for an individual nonBrownian axisymmetric ellipsoid suspended in a stagnant Newtonian fluid. Theoretical predictions are derived by a perturbation analysis for the limiting case where the strength of the applied magnetic field far exceeds the saturation magnetization of the ellipsoid. Numerical calculations are performed for the more general problem of an ellipsoid with known isotropic, non-hysteretic magnetic properties, using nickel and a stainless steel as examples. The analysis encompasses materials with field-induced, nonlinear magnetic properties, distinguishing these results from the simpler cases where the particle magnetization is either independent of, or linearly dependent on, the strength of the applied external field. In this study, predictions indicate that when the ellipsoid is magnetically saturated, the particle rotation is governed by the magnetoviscous time constant, TMV = ~ls/poMs 2. It is found that the rotation rate depends strongly on the aspect ratio, a/b, of the ellipsoid, but only weakly on the dimensionless magnetization, MJHo.Key words." giber suspension,_magnetohydrodynamics, ferromagnefic particle, ellipsoid, gotation

In this paper we use the constitutive equation of Bhave et al. (1993) for rod-like, liquid-crystalline polymer solutions to analyze the isothermal, steady-state spinning of these liquids in order to understand the evolution of microstructure, predict the velocity and normal stress distributions in the filament, and examine the effect of different upstream microstructural conditions. Our analysis shows that in contrast to fiber spinning models of isotropic liquids, the velocity, structure, and stress profiles are sensitive to the choice of initial conditions. In addition we have investigated the impact of the closure approximation used in the constitutive equation of Bhave et al. on the fiber spinning problem by solving the equation for the distribution function directly; only slight changes are seen in the velocity and stress profiles. An apparent elongational viscosity defined as the ratio of normal stress difference to strain rate at the takeup compares very well with the true elongational viscosity η̄ for the model, thereby suggesting that fiber spinning flows can be used to determine η̄ for liquid-crystalline polymer solutions. Model predictions of the velocity and stress agree well with data obtained by Prilutski (1984) for HPC/acetic acid solutions. Finally, we present a linear stability analysis of the spinning problem to show the impact of viscoelasticity, inertia, gravity, and surface tension on the onset of draw resonance instabilities. The neutral stability curves obtained for dominant viscoelastic forces reflect trends in the apparent elongational viscosity. Model predictions are in qualitative agreement with the draw resonance data reported by Prilutski.