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Experimental observations and linear stability calculations are presented for the stability of torsional flows of viscoelastic fluids between two parallel coaxial disks, one of which is held stationary while the other is rotated at a constant angular velocity. Beyond a critical value of the dimensionless rotation rate, or Deborah number, the purely circumferential, viscometric base flow becomes unstable with respect to a nonaxisymmetric, time-dependent motion consisting of spiral vortices which travel radially outwards across the disks. Video-imaging measurements in two highly elastic polyisobutylene solutions are used to determine the radial wavelength, wavespeed and azimuthal structure of the spiral disturbance. The spatial characteristics of this purely elastic instability scale with the rotation rate and axial separation between the disks; however, the observed spiral structure of the secondary motion is a sensitive function of the fluid rheology and the aspect ratio of the finite disks.Very near the centre of the disk the flow remains stable at all rotation rates, and the unsteady secondary motion is only observed in an annular region beyond a critical radius, denoted R*1. The spiral vortices initially increase in intensity as they propagate radially outwards across the disk; however, at larger radii they are damped and the spiral structure disappears beyond a second critical radius, R*2. This restabilization of the base viscometric flow is described quantitatively by considering a viscoelastic constitutive equation that captures the nonlinear rheology of the polymeric test fluids in steady shearing flows. A radially localized, linear stability analysis of torsional motions between infinite parallel coaxial disks for this model predicts an instability to non-axisymmetric disturbances for a finite range of radii, which depends on the Deborah number and on the rheological parameters in the model. The most dangerous instability mode varies with the Deborah number; however, at low rotation rates the steady viscometric flow is stable to all localized disturbances, at any radial position.Experimental values for the wavespeed, wavelength and azimuthal structure of this flow instability are described well by the analysis; however, the critical radii calculated for growth of infinitesimal disturbances are smaller than the values obtained from experimental observations of secondary motions. Calculation of the time rate of change in the additional viscous energy created or dissipated by the disturbance shows that the mechanism of instability for both axisymmetric and non-axisymmetric perturbations is the same, and arises from a coupling between the kinematics of the steady curvilinear base flow and the polymeric stresses in the disturbance flow. For finitely extensible dumb-bells, the magnitude of this coupling is reduced and an additional dissipative contribution to the mechanical energy balance arises, so that the disturbance is damped at large radial positions where the mean shear rate is large.Hysteresis experiments demonstrate that the instability is subcritical in the rotation rate, and, at long times, the initially well-defined spiral flow develops into a more complex three-dimensional aperiodic motion. Experimental observations indicate that this nonlinear evolution proceeds via a rapid splitting of the spiral vortices into vortices of approximately half the initial radial wavelength, and ultimately results in a state consisting of both inwardly and outwardly travelling spiral vortices with a range of radial wavenumbers.

Experimental observations and linear stability analysis are used to quantitatively describe a purely elastic flow instability in the inertialess motion of a viscoelastic fluid confined between a rotating cone and a stationary circular disk. Beyond a critical value of the dimensionless rotation rate, or Deborah number, the spatially homogeneous azimuthal base flow that is stable in the limit of small Reynolds numbers and small cone angles becomes unstable with respect to non-axisymmetric disturbances in the form of spiral vortices that extend throughout the fluid sample. Digital video-imaging measurements of the spatial and temporal dynamics of the instability in a highly elastic, constant-viscosity fluid show that the resulting secondary flow is composed of logarithmically spaced spiral roll cells that extend across the disk in the self-similar form of a Bernoulli Spiral.Linear stability analyses are reported for the quasi-linear Oldroyd-B constitutive equation and the nonlinear dumbbell model proposed by Chilcott & Rallison. Introduction of a radial coordinate transformation yields an accurate description of the logarithmic spiral instabilities observed experimentally, and substitution into the linearized disturbance equations leads to a separable eigenvalue problem. Experiments and calculations for two different elastic fluids and for a range of cone angles and Deborah numbers are presented to systematically explore the effects of geometric and rheological variations on the spiral instability. Excellent quantitative agreement is obtained between the predicted and measured wavenumber, wave speed and spiral mode of the elastic instability. The Oldroyd-B model correctly predicts the non-axisymmetric form of the spiral instability; however, incorporation of a shear-rate-dependent first normal stress difference via the nonlinear Chilcott–Rallison model is shown to be essential in describing the variation of the stability boundaries with increasing shear rate.

To improve the mechanical properties of zein films, a commercial white zein was reacted in glacial acetic acid (HAc) with glutaraldehyde (GDA) from 0.5 to 16% by weight based on the weight of zein. Amounts of 4% or higher GDA-modified zein, when cured in a closed system, generated a gel. That gel was insoluble in organic solvents known to solubilize zein. Zein solutions cast within a silicon rubber gasket sealed onto Teflon-coated plates, when air dried, generated 0.7-0.9-mm thick films. Those films from 8% GDA-modified zein had a water vapor permeability of 5.9 Â 10 À8 g cm/Pa s m 2 . Overall, results indicate that our thicker films gave higher water vapor permeability than values reported in the literature. To achieve consistent and comparable results with differential scanning calorimetry (DSC) and dynamic mechanical analyses (DMA), film samples had to be heated to remove residual HAc. An increase in the glass transition temperatures for those films from GDA-modification of zein, observed with both DSC and DMA, was attributed to the crosslinking of zein. Physical testing of tensile bars cut from GDA-modified zein films showed minor enhancement of tensile strength, percent elongation, and Young's modulus in the 0.5% GDA-modified zein films, which increased and leveled off with 4% or higher amounts of GDA for the modifications. When the 4 to 16% GDA results are averaged, the tensile strength for the modified zein films increased 1.8-fold when compared with unmodified zein control films. On the same note, percent elongation showed a 1.8-fold increase and Young's modulus showed a 1.5-fold increase. GDA reaction with zein generated films with improved tensile strength, ductility, and stiffness when compared with respective zein control films that retained their integrity when subjected to either boiling water or extensive soaking.