Solution of the complete Curtiss-Bird model for polymeric liquids subjected to simple shear flow (original) (raw)
Related papers
Journal of Rheology, 2006
We consider the effects of concentration on the structural and rheological properties of dilute polymer solutions via the use of Brownian dynamics simulations. The model used here is that of Jendrejack et al. ͓J. Chem. Phys. 116, 7752-7759 ͑2002͔͒ for -phage DNA under good solvent conditions, which incorporates excluded volume and hydrodynamic interaction effects, and has been shown to quantitatively predict the nonequilibrium behavior of the molecule in the dilute limit. Our work covers the entire dilute regime, with selected investigations into the semidilute regime, as well as spanning multiple decades of both shear and extensional flow rates. In simple shear flow, as much as a 20% increase in chain extension and 30% increase in the reduced polymer viscosity is observed at the overlap concentration, as compared to the infinitely dilute case. Additionally, predicted shear viscosities are in very good agreement with experimental observations. In elongational flow, we observe much stronger concentration dependences than in shear, with a 110% increase in chain extension and 500% increase in reduced viscosity when results are compared at equivalent extension rates. Significant concentration effects are observed at concentrations as low as 10% of the overlap concentration and are largely the result of interchain hydrodynamic interactions.
Journal of Non-Newtonian Fluid Mechanics, 2003
We present new results for the low strain rate behavior of the steady-state planar shear and elongational viscometric functions of model polymer melts, computed by non-equilibrium molecular dynamics simulations. The chain lengths in our model polymer melts vary from N = 2 up to N = 100 beads, the maximum value corresponding to approximately 57 Kuhn lengths (approximately equivalent to polyethylene of molar mass 8300 g/mol). The new results allow us to more precisely evaluate the constants in the third-order fluid constitutive relation that we fitted to the results of our previous simulations. We find agreement between the values of the retarded motion expansion coefficients of terms up to second-order in the strain rate obtained from the two types of flow. This indicates that the second-order fluid model self-consistently describes the stress tensor in shear and elongational flow with a single set of material constants if the deformation rate is sufficiently small. However, we find a discrepancy between two different estimates of a third-order term when it is evaluated from the first and second planar elongational viscosities. The second-order retarded motion expansion is extended to apply to compressible fluids and the deformation rate dependence of the pressure in shear and elongational flows is obtained. The predictions are confirmed by the simulation results. The chain length dependencies of the computed zero shear rate viscosity and first normal stress coefficient agree with the predictions of the Rouse model. The second normal stress coefficient varies as the cube of the chain length and the coefficient of the quadratic term in the strain rate dependence of the shear viscosity is proportional to the sixth power of the chain length for unentangled chains. (P.J. Daivis). bead mobility that occur as the concentration [2] and chain length [1] are increased. In the limit of long (strongly entangled) chains, the reptation model incorporates a specific model for anisotropic diffusion. The stress is often (but not always) then obtained by assuming the validity of the linear stress-optical law and averaging the bond-order tensor over the single-molecule configurational distribution function.
Journal of Non-Newtonian Fluid Mechanics, 1999
The rheological and optical properties of dilute polymer solutions during the startup and subsequent relaxation in exponential shear flow are studied using Brownian dynamics simulations of freely draining, flexible bead-rod chains. We find that exponential shear flow is capable of effecting large molecular deformation for finite shear rates and strains, and furthermore, the polymer undergoes an initial stress and index of refraction relaxation that is much faster than a single exponential decay upon cessation of flow. When we compare the first normal stress difference ((11 ±(22) to the corresponding components of the index of refraction tensor, n 11 ±n 22 , we find that there is hysteresis when plotted over the course of a full startup and relaxation experiment. This is very similar to the hysteresis originally discovered by Doyle et al. [J. Non-Newtonian Fluid Mech. 76 (1998) 79±110] for uniaxial extensional flow. Moreover, the shear components of the stress and index of refraction tensors ((12 and n 12) also exhibit hysteretic behavior. However, whereas the hysteresis loop for the 11±22 component traverses up the left branch during startup and relaxes on the right branch, that for the 12 component is in the completely opposite direction, i.e. the right branch corresponds to startup and the left branch relaxation. The presence of stress-index of refraction hysteresis clearly has important implications for the stress-optic rule. We calculate the stress-optic coefficient for the startup process, and find that the normal and shear components give the same value, but that it is strongly dependent on Wi. This result is consistent with that found by Doyle et al. during the startup of steady shear flow [Doyle and Shaqfeh, Dynamic simulation of freely-draining, flexible bead-rod chains: startup of extensional and shear flow, J. Non-Newtonian Fluid Mech. 76 (1998) 43±78]. We also simulated shear flows with a linearly ramped shear rate to compare to our results for exponential shear. We find that for comparable final shear rate and time, both exponential and linear ramping shear produce very similar hysteresis effects in both the shear and normal components suggesting that there may be many unsteady shear flow capable of creating large polymer stretch and stress-birefringence hysteresis. Finally, we compare our bead-rod chain simulations to the FENE dumbbell model, and we find that while the latter can qualitatively capture the normal stress hysteresis, it predicts negligible shear stress hysteresis at equivalent shear rates and shear strains.
Rheological properties of dilute polymer solutions: An extended thermodynamic approach
Rheologica Acta, 1990
It is shown that extended irreversible thermodynamics can be used to account for the shear rate and frequency dependences of several material functions like shear viscosity, first and second normal stress coefficients, dynamic viscosity and storage modulus. Comparison with experimental data on steady shearing and small oscillatory shearing flows is performed. A good agreement between the model and experiment is reached in a wide scale of variation of the shear rate and the frequency of oscillations. The relation between the present model which includes quadratic terms in the pressure tensor and the Giesekus model is also examined.
A Monte-Carlo study of equilibrium polymers in a shear flow
European Physical Journal B, 1999
We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight
A Study of Viscoelastic Model of Polymers in Shear Flow Based on Molecular Dynamic Simulations
Medžiagotyra, 2021
In this study, the rheological properties and physical significations of an incompressible viscoelastic (inCVE) the inCVE model was investigated by employing molecular dynamics calculations. Polypropylene (PP) and polystyrene (PS) polymers were selected as candidate materials, the corresponding cell models consisting of five chains of 80 (PP) and 30 (PS) units were built successively. The energy minimization and anneal treatment were launched to optimize the unfavorable structures. The periodic boundary condition, COMPASS force field and the Velocity-Verlet algorithm were employed to calculate the shear flow behavior of chains. The sample data were collected and fitted based on the Matlab platform, and the analysis of the variance (ANOVA) method was performed to determine the validity of the model. Experimental results reveal that the inCVE model matches well with the pseudo-plastic fluids. Compared with the Ostwald-de Waele power law model and Cross model, it is effective and robust, and exhibits a three-stage rheological characteristic. Moreover, it characterizes the stress yield, activation energy, temperature dependence and viscoelastic response of polymers.
A model for the dynamics of polymers in laminar shear flows
Journal of Fluid Mechanics, 1987
A novel primitive model is proposed for the hydrodynamic behaviour of an isolated dissolved polymer molecule in a laminar shear flow. The model, in which inertial effects are neglected, allows for rotation and partial stretching of the molcule, but not for bending. Dilute solutions of flexible long-chain polymers have been experimentally observed to exhibit periodic velocity fluctuations distinct from turbulence over a broad frequency range when flowed in high-shear-rate water-table and pipe configurations. In these experiments, the frequency of the fluctuations does not increase with increasing shear rate; rather, it is lowest in the regions of the flow where the shear is the highest. A manifestation of viscous shear thickening has also been observed in these laminar flows. The proposed polymer representation appears capable of accounting for the salient features of these flows with adjustment of a single dimensionless parameter, a ratio of polymer-spring and solvent-viscosity forces.
Polymers
Numerical flow simulations play an important role in polymer processing. One of the essential prerequisites for accurate and precise flow simulations is to obtain accurate materials functions. In the framework of the generalized Newtonian fluid model, one needs to obtain shear viscosity as a function of the rate-of-shear and temperature—as determined by rheometry—and then fitted to a mathematical model. Often, many subjectively perform the fitting without paying attention to the relative quality of the estimated parameters. This paper proposes a unique iterative algorithm for fitting the rate-of-shear and temperature-dependent viscosity model under the time–temperature superposition (TTS) principle. Proof-of-concept demonstrations are shown using the five-parameter Carreau–Yasuda model and experimental data from small-amplitude oscillatory shear (SAOS) measurements. It is shown that the newly proposed iterative algorithm leads to a more accurate representation of the experimental da...