Nonlinear Flow Properties Research Articles

Coarse-grained molecular dynamics simulations of polymer melts in transient and steady shear flow

By use of nonequilibrium simulations a coarse-grained model of polyethylene, developed in our previous work [J. Chem. Phys. 115, 2846 (2001); 117, 925 (2002)], is subjected to a planar Couette flow. Both transient and steady-state nonlinear flow properties are investigated for shear rates varying from 30 to 3000 μs−1 and chain lengths varying from C80H162 to C800H1602. We report rheological data (shear viscosity, normal stress differences) and structural data (chain dimensions and the order tensor), and compare them with experimental results, where available. The locations of maxima and magnitudes of overshoots in the shear stress and normal stress difference are in agreement with experimental results. We also observe an undershoot in the transient extinction angle and a decrease of the steady-state extinction angle with shear rate, both of which are in very good agreement with recent experiments. Two rheological “rules,” the stress–optical rule and the Cox–Merz rule, are tested. It is shown that the extinction angle, as calculated from stress components, remains equal to the optical extinction angle even for high shear rates, where the stress–optical rule is no longer strictly valid.

Comparison of Original and Cross-linked Wormlike Micelles of Poly(ethylene oxide-b-butadiene) in Water: Rheological Properties and Effects of Poly(ethylene oxide) Addition

Chemical fixation can convert self-assembled amphiphilic aggregates into covalently bonded giant macromolecules that can have properties that are fundamentally different from the unreacted precursors. Following up our previous report, we here extend the comparison between pristine and cross-linked wormlike micelles prepared from a cross-linkable poly(ethylene oxide-b-butadiene) diblock copolymer. Despite retention of the overall morphology, the cross-linked wormlike micelles exhibit unusual linear and nonlinear flow properties that presumably reflect the micelle stiffening upon cross-linking. Chemical fixation also influences their responses to changes in thermodynamic conditions. To explore this point, we added nonadsorbing homo-poly(ethylene oxide) (PEO) into the otherwise stable micelle solutions as a means for creating depletion effects (that is, attractive interactions between the micelles). Experimental studies of the phase behavior and attendant macroscopic properties of the mixtures of the wormlike micelles and PEO in water indicate that, when mixed with homo-PEO, the unreacted micelles phase separate to form hexagonal arrays, due to the depletion interactions. In contrast, the cross-linked analogues, under comparable conditions, remain homogeneously dispersed, and instead form physical gels. Such gels are characterized by time-dependent rheological responses upon large deformation and no flow under small deformations. These results suggest that the addition of PEO produces depletion-induced demixing of the cross-linked wormlike micelles leading to a nonequilibrium physical gel.

Non-linear flow properties of viscoelastic surfactant solutions

This paper gives a quantitative description of the viscoelastic properties of aqueous solutions of entangled rod-shaped micelles. The experimental data are compared with the theoretical predictions of a special constitutive equation which is based on the concept of deformation-dependent tensorial mobility. In the regime of small deformations, shear stresses or shear rates, the dynamic features of the viscoelastic solutions are characterized by the equations of a simple Maxwell material. These phenomena are linked to the average lifetime of the micellar aggregates and the rheological properties are controlled by kinetic processes. At these conditions one observes simple scaling laws and linear relations between all theological quantities. At elevated values of shear stresses or deformations, however, this simple model fails and non-linear properties as normal stresses, stress overshoots or shear-thinning properties occur. All these phenomena can be described by a constitutive equation which was first proposed by H. Giesekus. The experimental results are in fairly good agreement with the theoretical predictions, and this model holds for a certain, well defined value of the mobility factor α. This parameter describes the anisotropic character of the particle motion. In transient and steady-state flow experiments we always observed α = 0.5. Especially at these conditions, the empirically observed Cox-Merz rule, the Yamamoto relation and both Gleisle mirror relations are automatically derived from the Giesekus model. The phenomena discussed in this paper are of general importance, and can be equally observed in different materials, such as polymers or proteins. The viscoelastic surfactant solutions can, therefore, be used as simple model systems for studies of fundamental principles of flow.

Shear and elongational flow properties of fluid S1 from rotational, capillary, and opposed jet rheometry

Non-linear shear and elongational flow properties of the ternary fluid S1 have been compared to those of a binary solution with similar linear viscoelastic properties. In contrast to the binary solution, fluid S1 exhibits a flow instability. The onset of this instability in rotational flow is characterized by a critical Deborah number De c = 13.5. Secondary flow causes an irreversible decrease of zero-shear viscosity. A flow-induced degradation of the dissolved polymer has been proved by different analytical methods. However, this effect is not sufficient to account for the observed reduction of η 0, and it is speculated that the irregular flow additionally gives rise to a phase separation or demixing of the originally homogeneous solution. Up to now there is no direct experimental evidence for this hypothesis. Elongational flow properties have been characterized by means of an opposing jet apparatus. Apparent elongational viscosity of fluid S1 increases strongly with increasing apparent elongation rate ⋗e and total strain ϵ. A strain-independent equilibrium value is not reached. In the case of the binary solution η E is independent of ⋗e and increases only slightly with increasing ϵ. Strong fluctuations of the force signal are observed in the case of fluid S1 when a critical flow rate is exceeded, indicating secondary flow phenomena.

Fluctuations in microvascular blood flow parameters caused by hemodynamic mechanisms

We have developed a mathematical model of microvascular network blood flow in which the nonlinear flow properties of blood and the nonuniform axial distribution of red blood cells in each vessel, as well as disproportionate cell partitioning at bifurcations, are all accounted for. The movements of red blood cells in the network are tracked; hence, the model is able to simulate temporal variations in local flow parameters in the network due to hemodynamic mechanisms. The model was applied to four rat mesenteric networks for which the topology, boundary conditions, blood velocity, and discharge hematocrit (Hctd) had been measured for each branch. Temporal variations in Hctd and blood velocity after simulation convergence were predicted. In some cases of the three vessels connected to a node, Hctd of one vessel fluctuates in a simple periodic form, Hctd of the second one oscillates in a more complex periodic form, whereas the Hctd of the third one does not oscillate at all. These variations were obtained with constant flow boundary conditions and, therefore, are due to hemodynamic factors alone. The temporal variations in flow parameters predicted by the model simulations are caused by hemorheological mechanisms and would be superimposed on variations caused by other mechanisms (e.g., vasomotion). The frequencies of the predicted fluctuations in blood velocity are in qualitative agreement with observed in vivo variations in dual-slit velocity in the arterioles of the cremaster muscle of anesthetized Golden hamster.

Physics and Modeling of Thermal Flow and Soil Mechanics in Unconsolidated Porous Media

Summary This paper describes a new formulation of nonlinear soil mechanics and multiphase thermal flow. The nonlinearities of the soil behavior and their interactions with fluid flow causing shear failure of the soil are the dominant features of the process. The numerical formulation of the coupled flow/stress solution model includes nonlinear compressibility and flow properties as functions of pressure, stress, and temperature; nonlinear, incremental, thermal poroelastic stress analysis; and shear or tensile failure and its effects on transport properties, porosity, and stress. An efficient sequential numerical scheme was developed. It is mass conservative and applicable to external coupling of existing simulators. The 1D examples show some startling new features of reservoir mechanics in unconsolidated media.

The relationship between the linear (oscillatory) and nonlinear (steady-state) flow properties of a series of polymer and colloidal systems

The Cox-Merz empirical relationship between the linear (oscillatory) and nonlinear (steady-state) viscosities has been shown to be valid for many polymeric systems. Here, we present an equivalent expression to relate the linear (G′) and nonlinear (N 1) elastic properties of viscoelastic systems. Like the Cox-Merz relationship, it uses a combination of elastic and viscous parameters. The modified form of the storage modulus is then equivalent to the Cox-Merz complex viscosity. It can be used to correlate with (half) the normal force at numerically equal circular frequency and shear rate, respectively. This new expression and the Cox-Merz rule are tested for a range of polymeric and colloidal systems. It is found that both expression work for the polymeric systems considered, but fail for the colloidal systems. In the latter, the steady state values of viscosity and elasticity are consistently low, and replacing them by the complex viscosity and our new elastic expression only makes matters worse. For polymer systems, we suggest this is a general but not universal observation, since we are aware of exceptions to the rule that polymeric systems obey the Cox-Merz rule for viscosity and our rule for elasticity. For colloidal systems we find that neither rule is obeyed for any of our systems.

Taylor vortex flow under harmonic modulation of the driving force.

Time-periodic Taylor vortex flow between two concentric cylinders is studied. With the outer cylinder at rest and the inner one rotating with angular velocity \ensuremath{\Omega}(t)=\ensuremath{\Omega}(1+\ensuremath{\Delta} cos\ensuremath{\omega}t), the stability boundary of circular Couette flow and the fully nonlinear Taylor vortices are investigated. Results are obtained by a finite-difference numerical simulation of the full Navier-Stokes equations for a radius ratio \ensuremath{\eta}=0.65 and by an analytical Galerkin approximation with four modes for arbitrary gap width. Data obtained by both methods agree very well. Modulation is found to destabilize the basic flow in agreement with earlier theoretical results. The time dependence of Taylor vortices is determined in detail and compared with recent experiments. Their response to the modulated driving is elucidated and explained by investigating various limiting behaviors and by comparison with the amplitude equation. Subharmonic response is found for large modulation amplitudes when the driving \ensuremath{\Omega}(t) becomes supercritical in both rotation directions during one period. Differences and similarities of linear and nonlinear flow properties with modulated convection in Rayleigh-B\'enard systems are discussed in detail. That low-frequency small-amplitude modulation stabilizes the basic conductive state in the latter system while it destabilizes circular Couette flow is shown to be caused by the different coupling of the driving to the secondary flow field.

Kinetic Network Model for Nonlinear Viscoelastic Properties of Entangled Monodisperse Polymers. I. Steady‐State Flow

A molecular network theory is proposed to predict the nonlinear flow properties of entangled monodisperse polymers. The rate dependence of the viscosity and normal stress coefficients is attributed to the decrease in entanglement density with increasing shear rate. The probability for the existence of entanglements at a given shear rate is determined by equating the rates of two competing processes, i.e., entanglement creation and disengagement, which in steady flow are in a state of dynamic equilibrium. The entanglement creation process is driven by thermal diffusion and is assumed to be independent of shear rate. The entanglement loss process is caused primarily by the imposed shear and is assumed to be proportional to the shear rate to a power a, a parameter that accounts for the elasticity of the medium. The final equations are algebraically simple and can be easily adapted to most engineering calculations. The theory shows excellent agreement with experimental data on both melts and concentrated solutions.

A kinetic network model for nonlinear viscoelastic flow properties of entangled monodisperse polymers

Abstract : In this work, we shall propose a kinetic network model which appears to predict the observed nonlinear viscoelastic flow properties of entangled polymer systems. The basic molecular mechanism of this model attributes the rate-dependence of viscosity and normal stress difference to the decrease in entanglement density with increasing shear rate. In a flow field, entanglements are being formed and disengaged constantly. The entanglement loss process is caused primarily by the imposed shear and is assumed to be proportional to the shear rate to a power a; where a(1) accounts for the elastic nature of the polymer. The entanglement creation process, driven by thermal diffusion, is assumed to be independent of shear rate.

Nonlinear Properties of Circular Orifices

The results of an experimental study of the nonlinear fluid flow properties of thin, square-edged, circular orifices are described. Liquids were used at low frequencies. The flow conditions considered are a sinusoidal oscillation of the fluid in the orifice and a sinusoidal oscillation with a steady flow component added. For the sinusoidal flow condition the pressure differential developed across the orifice contains higher odd harmonics. The addition of a steady flow component adds second harmonic to the pressure as well as influences the magnitude of the odd harmonics. Further, in this case, the steady pressure component is a function of the magnitude of both the sinusoidal and steady flow components. An equation descriptive of the pressure-flow relation is presented. In this equation the orifice properties are specified by three constants, two of which are the acoustic resistance and acoustic inertance as normally measured at low amplitudes of excitation. The relations derived from this equation are compared with experimental measurements.

Nonlinear Properties of Circular Orifices

The results of an experimental study of the nonlinear fluid flow properties of thin, square-edged, circular orifices are described. Liquids are used at low frequencies. The flow conditions considered are a sinusoidal oscillation of the fluid in the orifice and a sinusoidal oscillation with a steady component added. It is found that for the sinusoidal flow condition the pressure differential developed across the orifice contains higher odd harmonics. The addition of a steady flow component adds even harmonics to the pressure as well as influences the magnitude of the odd harmonics. In this case the steady pressure component is a function of the magnitude of both the sinusoidal and steady flow components. (This work was supported by the Office of Ordnance Research, Department of the Army, under Contract No. DA-23-072-ORD-583.)