Evolution of local relaxed states and the modeling of viscoelastic fluids

We study the dynamics of bottlebrush polymer molecules in dilute solutions subjected to shear and uniaxial extensional flows using Brownian dynamics simulations with hydrodynamic interaction (HI). Bottlebrush polymers are modeled using a coarse-grained representation, consisting of a set of beads interacting pairwise via a purely repulsive potential and connected by finitely extensible nonlinear springs. We present the results for molecular stretching, stress, and solution viscosity during the startup of flow as well as under steady state as a function of side chain length while keeping the backbone length fixed. In extensional flow, the backbone fractional extension and the first normal stress difference decrease with an increase in side chain length at a fixed Weissenberg number (Wi). Using simulation results both in the presence of and in the absence of HI, we show that this is primarily a consequence of steric interaction resulting from the dense grafting of side chains. In shear flow, we observe a shear-thinning behavior in all cases, although it becomes less pronounced with increasing side chain length. Furthermore, nonmonotonicity in the backbone fractional extension is observed under shear, particularly at high Wi. We contextualize our simulation results for bottlebrush polymers with respect to existing studies in the literature for linear polymers and show that the unique dynamical features characterizing bottlebrush polymers arise on account of their additional molecular thickness due to the presence of densely grafted side chains.

Synergistic effects in flows of mixtures of wormlike micelles and hydroxyethyl celluloses with or without hydrophobic modifications

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared with diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is the generalized Taylor dispersion theory. In contrast, the dynamics and transport in orientation space remains less developed. In this work we develop a rotational Taylor dispersion theory that characterizes the long-time orientational transport of a spheroidal particle in linear flows that is constrained to rotate in the velocity-gradient plane. Similar to Taylor dispersion in position space, the orientational distribution of axisymmetric particles in linear flows at long times satisfies an effective advection–diffusion equation in orientation space. Using this framework, we then calculate the long-time average angular velocity and dispersion coefficient for both simple shear and extensional flows. Analytic expressions for the transport coefficients are derived in several asymptotic limits including nearly spherical particles, weak flow and strong flow. Our analysis shows that at long times the effective rotational dispersion is enhanced in simple shear and suppressed in extensional flow. The asymptotic solutions agree with full numerical solutions of the derived macrotransport equations and results from Brownian dynamics simulations. Our results show that the interplay between flow-induced rotations and Brownian diffusion can fundamentally change the long-time transport dynamics.

The dynamics of two dimensional polymer nematics

We examine several aspects of the dynamics of linear polymers under shear and extensional flows. We use nonequilibrium molecular dynamics (NEMD) to simulate systems under planar Couette flow (PCF) and planar extensional flow (PEF). In addition we look at several kinetic models of polymer melts, in particular the Curtiss-Bird model, for which we calculate the predictions of steady-state viscosity under PEF. To the best of our knowledge this is the first time that these results have been presented for this kinetic model. Our simulations under PEF are enabled by the use of Kraynik-Reinelt periodic boundary conditions (pbcs). We include here our observation that these pbcs are closely related to the Arnold cat map, a simple example of a dynamical map with chaotic properties. This observation enhances our understanding of this simulation technique. We compare directly under flow for the first time two commonly used coarse grained models of linear polymers. The first, a bead-spring model which uses the flexible finitely extensible nonlinear elastic potential (FENE) to bond adjacent beads. The second, a bead-rod model which uses a constraint force algorithm to fix the bond length. For this model we use the name freely jointed chain (FJC). The comparison is based on viscometric, structural and dynamical properties. We find that results for FENE and FJC systems are almost identical. Comparing results with predictions of the Curtiss-Bird model under PEF we find that values for the parameters of the Curtiss-Bird model required for a fit with the simulation data fall outside the range allowed by the Curtiss-Bird model and we conclude that assumptions of the Curtiss-Bird model deviate from dynamics observed in liquids under extensional We then focus on the self-diffusion of molecules under PEF and PCF, calculating elements of the diffusion tensor using appropriate mean-squared displacement formulae. Our interpretation of these results incorporate properties from the FENE and FJC comparison and results for the velocity autocorrelation function in these systems. We find anisotropy of diffusion more significant under PEF than under PCF. We conclude that this arises due to the significant enhancement of alignment under PEF. Our simulations represent the widest range of molecular systems under shear flow for which self-diffusion has been calculated. Results for PEF represent the first examination of self-diffusion for molecular systems under an extensional flow.

Do bending and torsional potentials affect the unraveling dynamics of flexible polymer chains in extensional or shear flows?

Numerical solution of the Fokker–Planck equation for fiber suspensions: Application to the Folgar–Tucker–Lipscomb model

The behaviors of polymer chains in simple shear flow and in flows with a large component of extension are now considered to be qualitatively different [R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, 2nd ed. (Wiley, New York, 1987), Vol. 2, Chap. 13]. To examine the extensional case, we have fractured DNA molecules in solution in steady sink (primarily extensional) flow. DNA was chosen for this study because it can be obtained as monodisperse, unique-sequence material, and because the size distribution of the fracture fragments can be obtained by gel electrophoresis. Dilute monodisperse T7 DNA (Mw=26×106) solutions were recirculated through a 0.13 mm orifice in a flat plate. The flow field upstream of the orifice closely approximated an ideal sink flow, being free of vortices under the conditions used, DNA concentrations less than 12.5 μg/mℓ and flow rates less than 0.045 cm3/s. The kinetics of the fracture at low flow rates showed an initial lag period followed by a period of first-order rate; the lag period disappeared at higher flow rates while the first-order period persisted. The fracture rate increased exponentially with the flow rate. Contrary to the classic theory by Frenkel, our experimental results showed fracture products broadly distributed in size; this anomaly was explained by a bead-spring molecular-dynamics computer simulation. The simulation showed that just prior to chain fracture the chain was aligned parallel to the flow but contained many folds, so that points of maximum stress were not usually at the molecular center. These results suggest that the residence time in the converging flow was too short for the chain to reach complete extension.

In a semi-dilute aqueous solution under certain conditions, surfactant molecules will self assemble to form wormlike micelles. The micelles are dynamic in structure since they can break and reform, providing an additional mode of relaxation. The viscoelastic properties of the wormlike micelles can be predicted using simple theological models. For many surfactant solutions the mechanical data can be related to the optical data by the stress-optical rule. From the viscoelastic data it is possible to estimate the breaking time of the micelle. The techniques of birefringence and small angle light scattering are used to study the microstructure of a surfactant solution under simple shear and extensional flow. The sample under investigation is a solution of cetyltrimethylammonium bromide and sodium salicylate in water, with a salt to surfactant ratio of 7.7. Below a critical shear rate, the birefringence increases linearly with shear rate and the stress-optical rule is valid. The SALS patterns reveal distinctive butterfly patterns indicating that scattering is a result of concentration fluctuations that moderately couple to the flow. However, above a critical shear rate the birefringence plateaus and the stress-optical rule is no longer valid. SALS patterns show both a bright streak and a butterfly pattern. The bright streak is caused by elongated structures aligned in the direction of the flow. The oriented structures occur when the characteristic time of flow is faster than the breaking time of the micelles.

In order to examine the difference between shear-induced and extensional-induced associating polymer assemblies at the molecular level, Brownian dynamics simulations with the bead-spring model were carried out for model DNA molecules with sticky spots. The radial distribution of molecules overestimates from that in the absence of flow and increases with increasing Weissenberg number in extensional flow, but slightly underestimates without regard to shear rate in shear flow. The fractional extension progresses more rapidly in extensional flow than in shear flow and the distribution of fractional extension at the formation time has a relatively sharper peak and narrower spectrum in extensional flow than in shear flow. In shear flow, the inducement of the assembly mainly results from the progress of the probability distribution of fractional extension. However, in extensional flow, the assembly is induced by both the progress of the probability distribution and increasing the values of the radial distribution.

The formation dynamics of fibrillar morphology in dilute immiscible polypropylene (PP)/polystyrene blends under simple shear flow is investigated using optical‐shear technique. Two strategies in generating fibrillar droplets under shear flow, namely temperature quench and shear jump, are studied. It is found that the shear‐induced deformation of PP droplets is closely related to the total shear strain and changes of rheological properties of components during the temperature quench or shear‐jump process. The shape evolution of fibrillar droplets under shear flow displays large deviation to the prediction of affine deformation theory based on Newtonian fluids and that of three deformation models, which consider the viscoelastic properties of components. The possible effect of droplet coalescence, breakup, and interfacial slip on the deviation between the experimental data and the prediction values for droplet deformation are discussed. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

The two-dimensional fluid dynamics of the different phases of a fatty acid monolayer (docosanoic acid) were examined. Using Brewster angle microscopy, we studied the polydomain structure of two liquid condensed phases (the L 2 and L' 2 phases) and the solid, S, phase in situ during the application of extensional flow and simple shear flow. We found that only the L2 phase deformed nearly reversibly with a liquid-like response. Nonsymmetric domain deformations were, however, found for that phase at the lowest rate of strain studied with a four-roll mill. At higher strain rates, plots of the evolution of strain against time collapsed onto a single curve so that the rate of strain was independent of roller speed. Furthermore, a critical strain y c exists above which the rate of strain shows a stepwise increase despite the constant velocity of the rollers. The two other phases, the L' 2 and S phases, experienced flow-induced reorientation of the lattice onto which the molecules are arranged. The reorientation process was accompanied by the appearance of shear bands in the monolayers at ±45° to the extension axis of both types of flow. The shear bands observed in the L' 2 phase were modeled as a plastic flow accompanying the molecular tilt reorientation developed within elastic regions of the monolayer. This model describes the time evolution of the bandwidth quite well and provides strong evidence of the existence of an additional phase within the conventional L' 2 phase region. In simple shear flow, the velocity profile for the L 2 phase across the gap of the shearing cell showed a nonlinear distribution of shear rates, which were highest at the center of the gap. Flow-induced breakup of domains was observed in the L' 2 phase subject to simple shear.

von Willebrand Factor is a mechano-sensitive protein circulating in blood that mediates platelet adhesion to subendothelial collagen and platelet aggregation at high shear rates. Its hemostatic function andthrombogenic effect, as well as susceptibility to enzymatic cleavage, are regulated by a conformational change from a collapsed globular state to a stretched state. Therefore, it is essential to account for the conformation of the vWF multimers when modeling vWF-mediated thrombosis or vWF degradation. We introduce a continuum model of vWF unfoldingthat is developed within the framework of our multi-constituent model of platelet-mediated thrombosis. The model considers two interconvertible vWF species corresponding to the collapsed and stretched conformational states. vWF unfolding takes place via two regimes: tumbling in simple shear and strong unfolding in flows with dominant extensional component. These two regimes were demonstrated in a Couette flowbetween parallel plates and anextensional flow in a cross-slotgeometry. The vWF unfolding model was then verified in several microfluidic systems designed for inducing high-shear vWF-mediated thrombosis and screening for von Willebrand Disease. The model predicted high concentration of stretched vWF in key regions where occlusive thrombosis was observed experimentally. Strong unfolding caused by the extensional flow was limited to the center axis or middle plane of the channels, whereas vWF unfolding near the channel walls relied upon the shear tumbling mechanism. The continuum model of vWF unfolding presented in this work can be employed in numerical simulations of vWF-mediated thrombosis or vWF degradation in complex geometries. However, extending the model to 3-D arbitrary flows and turbulent flows will pose considerable challenges.

Stress overshoot is one of the most important nonlinear rheological phenomena exhibited by polymeric liquids undergoing start-up shear at sufficient flow strengths. Despite considerable previous research, the fundamental molecular characteristics underlying stress overshoot remain unknown. Here, we analyze the intrinsic molecular mechanisms behind the overshoot phenomenon using atomistic nonequilibrium molecular dynamics simulations of entangled linear polyethylene melts under shear flow. Through a detailed analysis of the transient rotational chain dynamics, we identify an intermolecular collision angular regime in the vicinity of the chain orientation angle θ ≈ 20° with respect to the flow direction. The shear stress overshoot occurs via strong intermolecular collisions between chains in the collision regime at θ = 15°-25°, corresponding to a peak strain of 2-4, which is an experimentally well-known value. The normal stress overshoot appears at approximately θ = 10°, at a corresponding peak strain roughly equivalent to twice that for the shear stress. We provide plausible answers to several basic questions regarding the stress overshoot, which may further help understand other nonlinear phenomena of polymeric systems.

In order to study emulsification phenomena, devices generating well‐defined flow conditions are essential. Thus, emulsification of drop collectives under laminar shear flow is commonly performed in cylindrical Couette or Searle devices. In these devices, the flow conditions in the shear gap and in the volume underneath the rotor are often different, which can lead to inhomogeneous product properties and may complicate sample taking. Here, a novel cone‐cone shear cell is presented to study emulsification processes. The flow inside the device is examined using numerical simulations. The numerical simulations indicate that simple shear flow is realized all over the sample volume in the cone‐cone shear cell. The experimental results show that the drop breakup in the cone‐cone shear cell is equivalent to the breakup under simple shear realized in the shear gap of a conventional device, i.e., the Searle device. Critical capillary numbers are calculated from the experimental data and show breakup behavior as predicted by single‐drop experiments. Thus, the cone‐cone shear cell proved to be suitable to study emulsification mechanisms in simple shear flow.