Volume 48, Issue 2, March 2004
Index of content:
Evaluation of particle migration models based on laser Doppler velocimetry measurements in concentrated suspensions48(2004); http://dx.doi.org/10.1122/1.1647560View Description Hide Description
This study compares the predictions of several “suspension temperature” models of particle migration to laser Doppler velocimetrymeasurements in a concentrated suspension of noncolloidal spheres. We compare the shear rate, concentration, and suspension temperature profiles in narrow-gap Couette flow. The models predict the observed macroscopic shear rate and concentration profiles well at moderate bulk particle concentration but diverge from one another and from the data at high concentrations. In addition, the predictions of the models compare poorly with suspensiontemperature measurements. Most of the models greatly underpredict the magnitude of the scalar temperature, capturing instead only the magnitude of the smaller two diagonal components of the temperature tensor. Also, the models do not predict the observed variation of the suspension temperature with particle concentration. Our investigation shows that both neglect of suspension temperature anisotropy and qualitative choices of model coefficients contribute to discrepancies between the model predictions and data, of which the neglect of anisotropy is more important.
Effect of confinement on dynamics and rheology of dilute DNA solutions. I. Entropic spring force under confinement and a numerical algorithm48(2004); http://dx.doi.org/10.1122/1.1648642View Description Hide Description
We present the effect of confining walls on the rheology and dynamics of dilute polymeric solutions using a self-consistent multiscale simulation technique. In Part I we formulate the mathematical problem necessary to understand and model these dynamics. Various polymermodels (the Kramers’ freely jointed bead-rod chain, FENE, worm-like, and inverse Langevin chains) are used to describe the polymer chain dynamics based on their success in previous studies [H.P. Babcock et al., Phys. Rev. Lett. 85, 2018 (2000); J. S. Hur et al., J. Rheol. 44, 713 (2000); 45, 421 (2001)]. Theoretical arguments suggest that the main consequences of confinement on chains are (a) the entropic force law is altered due to the loss of chain configurational space and (b) the viscous drag on the chain is increased due to hydrodynamic interactions with the wall. In this study, the correct entropic spring force law in the presence of confining walls is developed. In addition, an efficient multiscale simulation technique for modeling the dynamics of bead-spring models with the force law is reported.
The effect of confinement on dynamics and rheology of dilute deoxyribose nucleic acid solutions. II. Effective rheology and single chain dynamics48(2004); http://dx.doi.org/10.1122/1.1648643View Description Hide Description
In this study we use the correct entropic spring force in the gap as discussed in Part I including hydrodynamic interactions with the wall to study the effect of confinement on deoxyribose nucleic acid rheology and chain dynamics. We present results for the chain density, the velocity, and the force density of the chains, which change rapidly over the length scale of the chain size. We associate this size and dynamics in these near wall layers to the configurational dispersion layer thickness found in polymershear flowdynamics in the absence of the wall [Chopra and Larson (2002); Hur et al. (2000)]. Though such rapid variation in velocity and density profiles is localized near the wall, its effect on average mechanical properties is global and is felt even at large channel sizes beyond We determine the effective viscosity of the dilute polymer solutions using self-consistent dynamics in these confined geometries and for large gap widths determine how the viscosity asymptotically approaches its bulk value. Finally, we also study the details of individual chain dynamics under confinement: This includes the tumbling motion of a chain in shear/Poiseuille flow, and relaxation from an extended state. We find that the confinement results in two different measures of the chain relaxation time: one shorter and the other longer than the longest relaxation time in the bulk. These two relaxation times are related to dynamics perpendicular and parallel to the walls, respectively. We show that different rheological experiments are sensitive to different specific relaxation times.
48(2004); http://dx.doi.org/10.1122/1.1648644View Description Hide Description
We present a comprehensive constitutive equation to describe the convection,retraction, breakup, and coalescence of single droplets and blends of immiscible Newtonian polymeric components. The model is tested by comparing its predictions to literature data that was collected under a variety of conditions. When the strain rate is below the critical value for breakup, the model shows good agreement with literature data for single-droplet deformation for a range of flow types from simple shear to planar extension. Droplet breakup is accounted for by a term chosen to match the time evolution of anisotropy predicted by the Tomotika theory for the capillary breakup of an elongated cylinder. In start-up of fast shearing flow, the comprehensive constitutive model predicts the transient shear and first normal stress difference qualitatively, but not quantitatively, possibly because of the ad hoc way in which the model combines dropletretraction with droplet breakup. More importantly, we find that the information provided in the anisotropy tensor is alone insufficient to describe the complex behaviors of retraction and breakup concurrently. Despite this deficiency, the comprehensive model predicts a steady-state droplet size for isolated droplets that is in agreement with theoretical predictions of the Taylor theory for the critical capillary number for breakup, and correctly predicts deviations from Doi–Ohta scaling of steady-state stresses with shear rate, due to the influence of the critical film thickness at which dropletcoalescence occurs.
Convective constraint release with chain stretch: Solution of the Rouse-tube model in the limit of infinite tubes48(2004); http://dx.doi.org/10.1122/1.1645515View Description Hide Description
This article derives a constitutive equation for entangled polymer melts and solutions, including the effects of convective constraint release (CCR) and chain stretch. It uses a model for CCR based upon the conjecture that constraint release events produce local hops of the tube, giving rise to a dynamical equation similar to the Rouse model. This equation is solved in the limit of infinite tubes. Although the solution in this limit ignores chain-end effects, the method presented has the following advantages; (i) it is less computationally expensive to implement than a full “finite chain” solution, (ii) it retains separate variables for chain stretch and tube orientation, allowing for straightforward modification of the equations to include different stretch dynamics, and (iii) it allows the possibility of smoothly changing the characteristics of the tube (such as tube diameter) upon deformation. In the latter context, this article explores the consequences of possible changes to the tube characteristics (tube diameter, persistence length, and CCR hop length) in response to chain stretch. It is found that the CCR-stretch equations are highly sensitive to the nature of the tube upon deformation, and in particular to the lower lengthscale cutoff used to describe the CCR process. The effect of CCR on chain stretch is explicitly derived from the microscopic model. The behavior of the constitutive equations is described for steady states under shear and startup under steady shear (where the results are compared against experiment).
48(2004); http://dx.doi.org/10.1122/1.1645517View Description Hide Description
Shear thickening is very common in telechelic associative polymers. Yet, it is not a universal characteristic of the whole class of associative polymers. Here, more general features of associative behavior are investigated. In particular, nonlinear rheological properties have been studied for both associative hydrophobically modified ethoxylated urethanes and hydrophobically modified alkali-soluble emulsions (HASE) polymers. A known common characteristic is the failure of the Cox-Merz rule for the viscosities. The equivalent relation for the first normal stress is examined here, a parallelism with the results for the viscosities has been observed. More pronounced similarities between telechelics and the more complex HASE systems can be seen in some other nonlinear properties. The dynamic moduli display strain hardening for both moduli at intermediate strains at all but the lowest frequencies, even when no shear thickening can be detected in steady state shear flow. The linear relaxation functions differ quite strongly among associative polymers. However, they all display a specific non-linear relaxation. It includes short time strain hardening followed by strain softening starting at long relaxation times. The results indicate that the same microstructural mechanisms are responsible for the rheological behavior of both classes of associative polymer.
48(2004); http://dx.doi.org/10.1122/1.1645516View Description Hide Description
Different methods of finding the Rouse relaxation times demarcating the onset of entanglement effects, were evaluated for entangled solutions of high molecular weight polystyrene in diethyl phthalate. Five expressions were utilized, involving variously the zero shear viscosity, the storage modulus at frequencies just beyond the rubbery plateau, the terminal Andrade creep region in the retardation spectrum, and the recoverable creep compliance. Values of determined by a procedure which assumes that the deformation modes are additive in the strain were substantially larger than the Rouse times extracted from the storage modulus by assuming stress additivity.
48(2004); http://dx.doi.org/10.1122/1.1645514View Description Hide Description
The squeeze flow behavior of concentrated suspensions of spheres in both Newtonian and shear-thinning fluids is investigated experimentally. Analyzing the evolution of the squeeze force as a function of time for different controlled velocities, the suspension is found to present two main flow regimes. In the first regime the force decreases when the velocity decreases, which is expected and corresponds to a power-law fluid flow of the suspension. In the second regime the force increases when the velocity decreases which is an indication that the suspension is undergoing solid-fluid separation. It is found that the transition between the two regimes is controlled by a Peclet number defined as the ratio of the characteristic time of the fluid filtration through the porous media made up by the particles to the characteristic time of the suspensionflow. A phase diagram delimiting the flowability domain under squeeze flow conditions for each suspension can be then determined. In the present study the influence of the rheological properties of the continuous phase is particularly investigated.
48(2004); http://dx.doi.org/10.1122/1.1647559View Description Hide Description
The deformation of a viscoelasticdrop suspended in a homogeneous viscoelastic matrix is investigated. The drop and the matrix fluids are assumed to obey linear viscoelasticconstitutive equations. Small-deformation analysis is carried out on the basis of the general solution for creeping flow around a spherical drop. The corresponding stress is calculated by extending Batchelor’s approach to viscoelastic media for both small and large deformations. Good agreement was found between the model predictions and experimental results available in the literature.
Prediction of bubble growth and size distribution in polymer foaming based on a new heterogeneous nucleation model48(2004); http://dx.doi.org/10.1122/1.1645518View Description Hide Description
The cell size distribution in a thermoplastic foam to a large extent determines its mechanical and thermal properties. It is difficult to predict because of the many physical processes involved, each affected in turn by an array of factors and parameters. The two most important processes are bubble nucleation and diffusion-driven bubble growth. Neither has been thoroughly understood despite intensive and long-standing research efforts. In this work, we consider foaming by a physical blowing agent dissolved in a polymer melt that contains particulate nucleating agents. We propose a nucleationmodel based on the concept that heterogeneous nucleation originates from pre-existing microvoids on the solid particles. The nucleation rate is determined by a bubble detachment time. Once nucleated, the bubbles grow as the dissolved gas diffuses through the polymer melt into the bubbles, a process that couples mass and momentum transport. By using the Oldroyd-B constitutive equation, we explore the role of melt viscoelasticity in this process. Finally, we integrate the nucleation and growth models to predict the evolution of the bubble size distribution. A cell model is employed to simulate the effects of neighboring bubbles and the depletion of blowing agents. The latter also causes the nucleation rate to decline once growth of older bubbles is underway. Using the physical and operating parameters of a recent foam extrusion experiment, we are able to predict a cell size distribution in reasonable agreement with measurements.
48(2004); http://dx.doi.org/10.1122/1.1647561View Description Hide Description
A new model for the viscosity of misciblepolymer blends is described. It combines a mixing rule for chain relaxation, based on the double reptation concept as adopted by Tsenoglou (1989), with a calculation of the concentration dependence of the monomeric friction factors, based on the self-concentration model of Lodge and McLeish (2000). The model is successful in anticipating the experimentally observed curvatures in plots of viscosity versus composition, and the predictions are in promising agreement with the data for several systems. The model introduces no freely adjustable parameters, and all the necessary parameters may be determined from measurements on pure components.