A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow

In this work, we develop a new algorithm for nonequilibrium molecular dynamics of fluids under planar mixed flow, a linear combination of planar elongational flow and planar Couette flow. To date, the only way of simulating mixed flow using nonequilibrium molecular dynamics techniques was to impose onto the simulation box irreversible transformations. This would bring the simulation to an end as soon as the minimum lattice space requirements were violated. In practical terms, this meant repeating the short simulations to improve statistics and extending the box dimensions to increase the total simulation time. Our method, similar to what has already been done for pure elongational flow, allows a cuboid box to deform in time following the streamlines of the mixed flow and, after a period of time determined by the elongational field, to be mapped back and recover its initial shape. No discontinuity in physical properties is present during the mapping and the simulation can, in this way, be extended indefinitely. We also show that the most general form of mixed flow, in which the angle between the expanding (or contracting) direction and the velocity gradient axis varies, can be cast in a so-called canonical form, in which the angle assumes values that are multiples of π (when a mixed flow exists), by an appropriate choice of the field parameters.     

刚性聚合物稀溶液流变性质的计算 Ⅰ.定常流动

本文采用多棒刚杆分子模型,用Galerkin法计算了聚合物稀溶液在定常剪切流、平面拉伸流、单轴拉伸流、单轴拉伸与剪切流相组合的复杂流动的流变学性质。计算结果表明,多棒刚杆分子模型有希望成为描述聚合物稀溶液流变性质的较为完善的分子模型。本文的研究不仅可使人们用分子模型来代替连续介质本构方程进行粘弹性流体复杂流动的数值模拟,而且也为探讨描述聚合物浓溶液的分子模型提供了一种新的途径。     

Predictions of Some Internal Microstructural Models for Polymer Melts and Solutions in Shear and Elongational Flows

Summary: In this work, the behavior of some internal microstructural models with different mobility tensors has been studied for polymer melts and solutions under steady and transient simple shear and elongational flows. The time evolution equations for conformation and stress tensors in the models reviewed have their root in the Generalized Poisson bracket formalism. Two different families of conformational models have been selected for this study. The first family is based on the Modified Finitely Extensible Nonlinear Elastic (FENE‐P) energy while the second uses a Volume Preserving Conformational Rheological (VPCR) model based on the Hookean Helmholtz free energy function. Several expressions for the mobility tensor based on the previously mentioned energy functions are used to obtain the models. The sensitivity of both families of models to the choice of the mobility tensors on the prediction of material functions in the transient and steady flows is discussed. Also, effects of shear rate on the material functions in start‐up and relaxation shear flows for both models are studied. The predictions of both models are compared with experimental data taken from the literature for some polymer melts. These results show that the family of VPCR models is able to predict the steady shear and elongational flow material functions in an extended range of deformation rates whereas the family of FENE‐P models can predict the behavior of only some specified polymer melts.

Experimental data and VPCR model predictions for steady and elongational viscosity for PS [data of H. Munstedt, 1980].     

Dynamics of collapsed polymers under the simultaneous influence of elongational and shear flows

Collapsed polymers in solution represent an oft-overlooked area of polymer physics, however recent studies of biopolymers in the bloodstream have suggested that the physics of polymer globules are not only relevant but could potentially lead to powerful new ways to manipulate single molecules using fluid flows. In the present article, we investigate the behavior of a collapsed polymer globule under the influence of linear combinations of shear and elongational flows. We generalize the theory of globule-stretch transitions that has been developed for the specific case of simple shear and elongational flows to account for behavior in arbitrary flow fields. In particular, we find that the behavior of a globule in flow is well represented by a two-state model wherein the critical parameters are the transition probabilities to go from a collapsed to a stretched state P(g-s) and vice versa P(s-g). The collapsed globule to stretch transition is described using a nucleation protrusion mechanism, and the reverse transition is described using either a tumbling or a relaxation mechanism. The magnitudes of P(g-s) and P(s-g) govern the state in which the polymer resides; for P(g-s) ≈ 0 and P(s-g) ≈ 1 the polymer is always collapsed, for P(g-s) ≈ 0 and P(s-g) ≈ 0 the polymer is stuck in either the collapsed or stretched state, for P(g-s) ≈ 1 and P(s-g) ≈ 0 the polymer is always stretched, and for P(g-s) ≈ 1 and P(s-g) ≈ 1 the polymer undergoes tumbling behavior. These transition probabilities are functions of the flow geometry, and we demonstrate that our theory quantitatively predicts globular polymer conformation in the case of mixed two-dimensional flows, regardless of orientation and representation, by comparing theoretical results to Brownian dynamics simulations. Generalization of the theory to arbitrary three-dimensional flows is discussed as is the incorporation of this theory into rheological equations.     

Effect of the flow field on the rheological behavior of aqueous cetyltrimethylammonium p-toluenesulfonate solutions

It is well-known that solutions of cetyltrimethylammonium p-toluenesulfonate in water exhibit a pronounced shear-thickening phenomenon in a specific concentration range (0.1-0.8%) when they are subjected to simple-shear flows, as a consequence of flow-induced self-assembly of wormlike micelles. This work shows that a strong elongational flow field (opposed-jets flow), applied to the same solutions, does not lead to extension thickening because the extensional flow prevents or destroys micellar association. In flow through a porous medium, a substantial increase in apparent viscosity is observed beyond a critical apparent shear rate, which surpasses increases observed in simple-shear flows. This is explained as the result of a synergistic effect of shear and relatively weak elongation on the solution microstructure.     

Fluid vesicles in flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.     

An analysis of flow behavior of polymer molecules-viscoelastic functions and crystallization II

Summary A previous analysis of configurational phenomena of a macromolecule in shear and elongational flows has been extended to include predictions of viscoelastic effects. In shear flow qualitative comparisons of the viscoelastic functions show the model correctly predicts the behavior of real materials over the entire range of deformation rates that are likely to be of practical interest.In elongational flow, which provides a severe test of the generality of the model, very large viscous and orientation effects are predicted. The results for elongational flow, although disagreeing with recent theories based on network rupture arguments, are believed realistic in view of the successful predictions of the ordinary viscoelastic functions.

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Zusammenfassung Eine vorangehende Analyse der Konfigurationsphänomene eines Makromoleküls bei Scher- und Dehnungsfließen wird erweitert auf die Voraussage von viskoelastischen Effekten. Bei Scherung stellen qualitative Vergleiche der viskoelastischen Funktionen eines Modells das Verhalten des realen Materials korrekt über den ganzen Bereich der Deformationsgeschwindigkeiten dar.Beim Dehnungsfließen, das einen strengen Test der Verallgemeinerung des Modells darstellt, werden sehr hochviskose und sehr starke Orientierungseffekte vorausgesagt. Die Ergebnisse für das Dehnungsfließen dürften, obgleich sie bisherigen Theorien, die auf dem Brechen von Netzwerken basieren, widersprechen, doch als realistisch im Hinblick auf die erfolgreichen Voraussagen über die normalen viskoelastischen Funktionen angesehen werden.

     

Rheological studies on the phase separation of hydroxypropylcellulose solution systems

Phase behavior of hydroxypropylcellulose (HPC) in a mixed solvent of glycerol and water was investigated by two different rheological methods: rheooptical birefringence measurement in an elongational flow field and viscometric measurement in a shear flow field. The association process of the HPC chain during phase separation observed by the elongational flow birefringence method was also investigated by the shear viscometric method. The temperature dependence of chain rigidity was determined by measuring the intrinsic viscosity, and change in the conformation was investigated by observing elongational flow birefringence over the temperature range from the one‐phase to inside a phase boundary. The results focus on the molecular process of phase separation. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1976–1986, 2001     

Some aspects of theory and simulations of polymers in steady flows

We present a study of various properties of bead spring chains in steady flows. The Langevin equation of the normal modes of the chain is solved by Fourier transformation. From the resulting power spectrum, the autocorrelation functions of all configuration-dependent quantities can be calculated. In equilibrium, the influence of the bead masses on the short-time dynamics is discussed. The influence of different flow fields (shear, elongational and Kramers potential flow) on the mean-square chain dimension is calculated. A comparison with results obtained from non-equilibrium molecular dynamics and Monte Carlo calculations is made. Finally, the influence of shear flow on the configurational and rheological properties of cyclic polymers and on the excluded volume behavior of linear chains is examined.     

Elongational flow induced ordering in surfactant micelles and mesophases

We have used small angle neutron scattering, SANS, to investigate the elongational flow induced ordering in surfactant micelles and mesophases. Spatially resolved SANS measurements have been used to determine the distribution of orientational ordering over the flow velocity pattern in an elongational flow cell, and comparison with the effects of shear flow are made. Two different surfactant systems have been studied, the charged wormlike mixed micelles of hexaethylene monododecyl ether, C16E6/hexadecyl trimethylammonium bromide, C16TAB (3% C16E(6)/5 mol% C16TAB), and the Lalpha lamellar phase of C16E6 (50.6 wt% C16E6 at 55 degrees C), and a substantially different response is observed. The orientational distribution of the Lalpha lamellar phase of C16E6 reflects the flow velocity pattern distribution within the cell, whereas for the wormlike mixed micelles of C16E6/C16TAB this is not the case, and this is associated with the shear thinning behavior of that system.     

Analysis of mixing efficiency in polymer processing equipment

Flow patterns In various processing equipment were obtained based on 3D isothermal flow simulations. These flow patterns were further processed for mixing efficiency analysis. The dynamics of the mixing process was studied numerically by means of tracers and their trajectories In the processing equipment. Dispersive mixing efficiency was studied in terms of shear stresses and elongational flow components distributions. Distributive mixing efficiency was characterized using length stretch distributions and average values. Features of chaotic flow were also analyzed. The framework developed to analyze mixing efficiency opens the way for an unambiguous evaluation of equipment performance and for process optimization.     

Coil‐stretch transition in deformation flows

We present a novel Monte‐Carlo lattice model for the study of the coil‐stretch transition for polymer chains in deformation flows. Our results indicate that elongational flows are much more effective than shear flows in stretching polymer chains, in full agreement with experimental observation. Our model data also show that the ε˙_c∼M^−1.5 powerlaw observed experimentally for the dependence of critical flow rate on polymer molecular weight can be fully explained through a nonuniform stretching of the chain by the flow. A higher powerlaw exponent is predicted in more affine deformation cases. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2422–2428, 2000     

Effect of different matrices and nanofillers on the rheological behavior of polymer‐clay nanocomposites

In this work, a comprehensive study of the rheological behavior under shear and isothermal and nonisothermal elongational flow of low density polyethylene (LDPE) and ethylene‐vinyl acetate copolymer (EVA) based nanocomposites was reported to evaluate their “filmability”, that is, the ability of these material to be processed for film forming applications. The influence of two different kinds of organoclay – namely Cloisite 15A and Cloisite 30B – and their concentration was evaluated. The presence of filler clearly affects the rheological behavior in oscillatory state of polyolefin‐based nanocomposites but the increase of complex viscosity and the shear thinning are not dramatic. A larger strain‐hardening effect in isothermal elongational flow is shown by the nanocomposites compared to that of the pure matrix, particularly for EVA based nanocomposites. The melt strength measured under nonisothermal elongational flow increases in the presence of the nanofiller, while the drawability is only slightly lower than that measured for the neat matrix. Moreover, the rheological behavior under nonisothermal elongational flow of EVA‐based nanocomposites is similar for both nanoclays used. Differently, LDPE‐based nanocomposites show a strong dependence on the type of organoclay. Finally, the mechanical properties of the materials were measured by tensile tests. They revealed that the presence of the filler provokes, in all the cases, an increase of the rigidity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 344–355, 2010     

Single DNA molecule stretching in sudden mixed shear and elongational microflows

High-throughput stretching and monitoring of single DNA molecules in continuous elongational flow offers compelling advantages for biotechnology applications such as DNA mapping. However, the polymer dynamics in common microfluidic implementations are typically complicated by shear interactions. These effects were investigated by observation of fluorescently labeled 185 kb bacterial artificial chromosomes in sudden mixed shear and elongational microflows generated in funneled microfluidic channels. The extension of individual free DNA molecules was studied as a function of accumulated fluid strain and strain rate. Under constant or gradually changing strain rate conditions, stretching by the sudden elongational component proceeded as previously described for an ideal elongational flow (T. T. Perkins, D. E. Smith and S. Chu, Science, 1997, 276, 2016): first, increased accumulated fluid strain and increased strain rate produced higher stretching efficiencies, despite the complications of shear interactions; and second, the results were consistent with unstretched molecules predominantly in hairpin conformations. More abrupt strain rate profiles did not deliver a uniform population of highly extended molecules, highlighting the importance of balance between shear and elongational components in the microfluidic environment for DNA stretching applications. DNA sizing with up to 10% resolution was demonstrated. Overall, the device delivered 1000 stretched DNA molecules per minute in a method compatible with diffraction-limited optical sequence motif mapping and without requiring laborious chemical modifications of the DNA or the chip surface. Thus, the method is especially well suited for genetic characterization of DNA mixtures such as in pathogen fingerprinting amidst high levels of background DNA.     

Melt rheology of hyperbranched‐polystyrene synthesized with multisite macromonomer

Melt rheological behaviors of hyperbranched‐polystyrene (PS) copolymerized by dendric macromonomer technique are presented. The time–temperature superposition principle was applicable to the hyperbranched‐PS. The branched‐PS showed slightly lower zero‐shear viscosity in comparison with linear PS regardless of a presence of a number of branches expected from the dendric macromonomer technique. Although the influence of use of multimethacryloyl macromonomer in the polymerization process was marginal for linear viscoelastic regime, nonlinear shear and uniaxial elongational flows showed distinct differences between linear and branched‐PS. The strain dependence of the damping function became weak as increase of macromonomer content. The branched‐PS exhibited the growing elongational viscosity function comparing with linear PS. This prominent effect on the elongational flow behavior can be explained by the molecular architecture of the branched‐PS. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2226–2237, 2009     

A constitutive equation derived from the model of doi and edwards for concentrated polymer solutions and polymer melts

In deriving a constitutive equation from a molecular model of polymers in concentrated solutions and melts, Doi and Edwards used a mathematical approximation, the “independent alignment approximation,” which has recently been shown to produce significant error in the particular case of stress relaxation following a double-step strain in opposite direction. In the present paper, in order to examine the approximation in general cases, we derive a new constitutive equation without using the independent alignment approximation. The new equation is a nonlinear integro-differential equation and is solved numerically for several cases, i.e., steady shear and elongational flows, and the transient flows after the start of shear and elongation. It is found that, in the cases examined here, the new constitutive equation gives nearly the same results as the old one: the rheological functions calculated from the two theories differ no more than 30%. This substantiates the expectation that the independent alignment approximation does not produce drastic error as long as the flow direction is not reversed.     

Effect of ionic strength on the rheological behavior of aqueous cetyltrimethylammonium p-toluene sulfonate solutions

The influence of ionic environment on the rheological properties of aqueous cetyltrimethylammonium p-toluene sulfonate (CTAT) solutions has been studied under three different flow fields: simple shear, opposed-jets flow and porous media flow. Emphasis was placed in the experiments on a range of CTAT concentration in which wormlike micelles were formed. It is known that these solutions exhibit shear thickening in the semi-dilute regime, which has been explained in terms of the formation of shear-induced, cooperative structures involving wormlike micelles. In simple shear flow, the zero shear viscosity exhibits first an increase with salt addition followed by a decrease, while the critical shear rate for shear thickening increases sharply at low salt contents and tends to saturate at relatively high ionic strengths. The results are explained in terms of a competition between micellar growth induced by salt addition and changes in micellar flexibility caused by ionic screening effects. Dynamic light scattering results indicate that micelles grow rapidly upon salt addition but eventually achieve a constant size under static conditions. These observations suggest that the wormlike micelles continuously grow with salt addition, but, as they become more flexible due to electrostatic screening, the wormlike coils tend to adopt a more compact conformation. The trends observed in the apparent viscosities measured in porous media flows seem to confirm these hypotheses-but viscosity increases in the shear thickening region-and are magnified by micelle deformation induced by the elongational nature of the local flow in the pores. In opposed-jets flow, the solutions have a behavior that is close to Newtonian, which suggests that the range of strain rates employed makes the flow strong enough to destroy or prevent the formation of cooperative micellar structures.     

Effect of flow on solutions of rodlike molecules

A flow field imposed on a solution of rodlike particles tends to align the rods owing to friction between the fluid and the rods. The potential energy of rods in a steady-state, homogeneous, and irrotational flow is superposed on the equilibrium Gibbs free energy of the quiescent solution to obtain the total free energy. The exact lattice treatment of Flory and Ronca is used in formulating the problem. Effects of flow on the orientational distribution function of rods and phase separation are analyzed with particular reference to elongational and pure shear flows. Calculations carried out for various compositions and flow characteristics reveal the presence of a region where the order parameter is sensitive to changes in prevailing flow conditions. Experimental determination of orientation by measuring flow birefringence is discussed.     

Microfluidic flows of wormlike micellar solutions

The widespread use of wormlike micellar solutions is commonly found in household items such as cosmetic products, industrial fluids used in enhanced oil recovery and as drag reducing agents, and in biological applications such as drug delivery and biosensors. Despite their extensive use, there are still many details about the microscopic micellar structure and the mechanisms by which wormlike micelles form under flow that are not clearly understood. Microfluidic devices provide a versatile platform to study wormlike micellar solutions under various flow conditions and confined geometries. A review of recent investigations using microfluidics to study the flow of wormlike micelles is presented here with an emphasis on three different flow types: shear, elongation, and complex flow fields. In particular, we focus on the use of shear flows to study shear banding, elastic instabilities of wormlike micellar solutions in extensional flow (including stagnation and contraction flow field), and the use of contraction geometries to measure the elongational viscosity of wormlike micellar solutions. Finally, we showcase the use of complex flow fields in microfluidics to generate a stable and nanoporous flow-induced structured phase (FISP) from wormlike micellar solutions. This review shows that the influence of spatial confinement and moderate hydrodynamic forces present in the microfluidic device can give rise to a host of possibilities of microstructural rearrangements and interesting flow phenomena.     

Rheological and structural studies of liquid decane, hexadecane, and tetracosane under planar elongational flow using nonequilibrium molecular-dynamics simulations

We report for the first time rheological and structural properties of liquid decane, hexadecane, and tetracosane using nonequilibrium molecular-dynamics (NEMD) simulations under planar elongational flow (PEF). The underlying NEMD algorithm employed is the so-called p-SLLOD algorithm [C. Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. 122, 114103 (2005)]. Two elongational viscosities are measured, and they are shown not to be equal to each other, indicating two independent viscometric functions in PEF. With an appropriate definition, it is observed that the two elongational viscosities converge to each other at very low elongation rates, i.e., in the Newtonian regime. For all three alkanes, tension-thinning behavior is observed. At high elongation rates, chains appear to be fully stretched. This is supported by the result of the mean-square end-to-end distance of chains (R(ete2)) and the mean-square radius of gyration of chains (R(g2)), and further supported by the result of the intramolecular Lennard-Jones (LJ) potential energy. It is also observed that (R(ete2)) and (R(g2)) show a different trend as a function of strain rate from those in shear flow: after reaching a plateau value, (R(ete2)) and (R(g2)) are found to increase further as elongation rate increases. A minimum in the hydrostatic pressure is observed for hexadecane and tetracosane at about epsilon(msigma2/epsilon)1/2=0.02. This phenomenon is shown to be associated with the intermolecular LJ potential energy. The bond-bending and torsional energies display similar trends, but a different behavior is observed for the bond-stretching energy. An important observation common in these three bonded-intramolecular interactions is that all three modes are suppressed to a small value at high elongation rates. We conjecture that a liquid-crystal-like, nematic structure is present in these systems at high elongation rates, which is characterized by a strong chain alignment with a fully stretched conformation.