Index of content:
Volume 60, Issue 2, March 2016
60(2016); http://dx.doi.org/10.1122/1.4938525View Description Hide Description
The gelation behavior of κ-carrageenan in aqueous solution was studied by microdifferential scanning calorimetry and rheology. It was found that the formation and melting of κ-carrageenan hydrogels were thermally reversible and extremely sensitive to κ-carrageenan concentration. In comparison with the crossover of G′ and G″, the extrapolation method based on multiwave oscillation and Winter–Chambon criterion were able to give more accurate critical gel temperature Tc. At the gel point, the critical relaxation exponent n was almost constant whereas the critical gel strength Sg increased with κ-carrageenan concentration. In the stable gel state, the plateau modulus Ge depended on temperature according to a power-law scaling, Ge ∝ ε2.2, where ε is the relative distance (=|T − Tc|/Tc) and independent of κ-carrageenan concentration. The presence of potassium ions shifted the formation and melting temperatures of κ-carrageenan hydrogel to higher temperatures, and the temperatures for gel formation and melting increased with increasing potassium ions' content.
60(2016); http://dx.doi.org/10.1122/1.4939098View Description Hide Description
The improved anisotropic rotary diffusion (iARD) model was previously regarded as a suitable description of anisotropic orientation states for long fibers in concentrated suspensions. However, the iARD tensor does not pass the classic rheological rule of Euclidean objectivity, namely, material frame indifference. It is hard to ignore the nonobjective effect due to the fact that different coordinate systems may yield different answers. Such an issue can be attributed to the iARD tensor related to the nonobjective velocity-gradient tensor. We therefore proposed a new iARD tensor, which depends on the square of the objective rate-of-deformation tensor. It is important to differentiate between the original Phelps–Tucker anisotropic rotary diffusiontensor and the objective iARD tensor via computing their first invariants. Furthermore, we validated this new iARD model's accuracy in predicting a distinct, broader core-shell orientation structure of injection-molded long-fiber composites through careful experimental verification.
60(2016); http://dx.doi.org/10.1122/1.4938048View Description Hide Description
The present study develops an extension of the approach pioneered by Farris [Trans. Soc. Rheol. 12, 281–301 (1968)] to model the viscosity in polydisperse suspensions. Each smaller particle size class is assumed to contribute to the suspensionviscosity through a weighting function in two ways: first, indirectly, by altering the background viscosity, and second, directly, by increasing the contribution of the larger particles to the suspensionviscosity. The weighting functions are developed in a consistent fashion as a power law with the exponent, , a function of the relative volume fraction ratio and the base, , a function of the solid particle size ratio. The model is fit to available theoretical and experimental results for the viscosity of several binary suspensions and shows good to excellent agreement depending on the functions and chosen. Once parameterized using binary suspensionviscosity data, the predictive capability to model the viscosity of arbitrary continuous size distributions is realized by representing such distributions with equivalent ternary approximations selected to match the first six moments of the actual size distribution. Model predictions of the viscosity of polydisperse suspensions are presented and compared against experimental data.
The medium amplitude oscillatory shear of semidilute colloidal dispersions. Part II: Third harmonic stress contribution60(2016); http://dx.doi.org/10.1122/1.4940946View Description Hide Description
In Paper I [J. W. Swan et al., J. Rheol. 58, 307–338 (2014)], we derived an exact theoretical description of medium amplitude oscillatory shear for a semidilute colloidal dispersion. Through solution of the Smoluchowski equation governing the spatial distribution of suspended particles in the semidilute limit, we calculated the stresses that arise from an oscillatory linear flow as an expansion in powers of the rate of deformation. Here, this is extended to calculation of the first departures from linearity in the first and third harmonics of the suspension stress driven by oscillatory deformation. The role of hydrodynamic interactions is investigated via the excluded-annulus model in which particles are given an impenetrable core with a radius larger than their hydrodynamic radius. The ratio of these length scales controls the strength of hydrodynamic interactions. The third harmonic of the suspension stress is predicted to be dominated by hydrodynamic stresses at high frequency, a result that is shown to be valid experimentally for the oscillatory shear response of concentrated near hard-sphere dispersions. The calculations anticipate recent experimental observations on model near hard-sphere colloidal dispersions, and quantitative agreement is demonstrated when the predictions are scaled appropriately to account for volume fraction effects. The first departures from linearity in harmonics of the suspension stress are separated into several material functions that are independent of the flow geometry. These functions are generated from detailed numerical solutions, while asymptotic analysis is shown to predict the values of these functions at high frequency. These exact calculations provide a basis for understanding the onset of nonlinear rheological behavior of colloidalsuspensions under dynamic oscillatory flow.
60(2016); http://dx.doi.org/10.1122/1.4941423View Description Hide Description
An asymptotic solution to the Giesekus constitutive model of polymeric fluids under homogenous, oscillatory simple shear flow at large Weissenberg number, , and large strain amplitude, , is constructed. Here, , where is the polymerrelaxation time and is the shear rate amplitude, and is a Deborah number, where is the oscillation frequency. Under these conditions, we show that the first normal stress difference is the dominant rheological signal, scaling as , where is the elastic modulus. The shear stress and second normal stress difference are of order . The polymer stress exhibits pronounced nonlinear oscillations, which are partitioned into two temporal regions: (i) A “core region,” on the time scale of , reflecting a balance between anisotropic drag and orientation of polymers in the strong flow; and (ii) a “turning region,” centered around times when the shear flow reverses, whose duration is on the hybrid time scale , in which flow-driven orientation, anisotropic drag, and relaxation are all leading order effects. Our asymptotic solution is verified against numerical computations, and a qualitative comparison with relevant experimental observations is presented. Our results can, in principle, be employed to extract the nonlinearity (anisotropic drag) parameter, α, of the Giesekus model from experimental data, without the need to fit the stress waveform over a complete oscillation cycle. Finally, we discuss our findings in relation to recent work on shear banding in oscillatory flows.