Constraint release in entangled binary blends of linear polymers: a molecular dynamics study

We present extensive molecular dynamics simulations of the dynamics of diluted long probe chains entangled with a matrix of shorter chains. The chain lengths of both components are above the entanglement strand length, and the ratio of their lengths is varied over a wide range to cover the crossover from the chain reptation regime to tube Rouse motion regime of the long probe chains. Reducing the matrix chain length results in a faster decay of the dynamic structure factor of the probe chains, in good agreement with recent neutron spin echo experiments. The diffusion of the long chains, measured by the mean square displacements of the monomers and the centers of mass of the chains, demonstrates a systematic speed-up relative to the pure reptation behavior expected for monodisperse melts of sufficiently long polymers. On the other hand, the diffusion of the matrix chains is only weakly perturbed by the diluted long probe chains. The simulation results are qualitatively consistent with the theoretical predictions based on constraint release Rouse model, but a detailed comparison reveals the existence of a broad distribution of the disentanglement rates, which is partly confirmed by an analysis of the packing and diffusion of the matrix chains in the tube region of the probe chains. A coarse-grained simulation model based on the tube Rouse motion model with incorporation of the probability distribution of the tube segment jump rates is developed and shows results qualitatively consistent with the fine scale molecular dynamics simulations. However, we observe a breakdown in the tube Rouse model when the short chain length is decreased to around N-S = 80, which is roughly 3.5 times the entanglement spacing N-e(P) = 23. The location of this transition may be sensitive to the chain bending potential used in our simulations.

Neutron-mapping polymer flow: Scattering, flow visualization, and molecular theory

Flows of complex fluids need to be understood at both macroscopic and molecular scales, because it is the macroscopic response that controls the fluid behavior, but the molecular scale that ultimately gives rise to rheological and solid-state properties. Here the flow field of an entangled polymer melt through an extended contraction, typical of many polymer processes, is imaged optically and by small-angle neutron scattering. The dual-probe technique samples both the macroscopic stress field in the flow and the microscopic configuration of the polymer molecules at selected points. The results are compared with a recent tube model molecular theory of entangled melt flow that is able to calculate both the stress and the single-chain structure factor from first principles. The combined action of the three fundamental entangled processes of reptation, contour length fluctuation, and convective constraint release is essential to account quantitatively for the rich rheological behavior. The multiscale approach unearths a new feature: Orientation at the length scale of the entire chain decays considerably more slowly than at the smaller entanglement length.

Constriction flows of monodisperse linear entangled polymers: Multiscale modeling and flow visualization

We explore both the rheology and complex flow behavior of monodisperse polymer melts. Adequate quantities of monodisperse polymer were synthesized in order that both the materials rheology and microprocessing behavior could be established. In parallel, we employ a molecular theory for the polymer rheology that is suitable for comparison with experimental rheometric data and numerical simulation for microprocessing flows. The model is capable of matching both shear and extensional data with minimal parameter fitting. Experimental data for the processing behavior of monodisperse polymers are presented for the first time as flow birefringence and pressure difference data obtained using a Multipass Rheometer with an 11:1 constriction entry and exit flow. Matching of experimental processing data was obtained using the constitutive equation with the Lagrangian numerical solver, FLOWSOLVE. The results show the direct coupling between molecular constitutive response and macroscopic processing behavior, and differentiate flow effects that arise separately from orientation and stretch. (c) 2005 The Society of Rheology.

Dietary quality and encephalization in platyrrhine primates.

The high energetic costs of building and maintaining large brains are thought to constrain encephalization. The 'expensive-tissue hypothesis' (ETH) proposes that primates (especially humans) overcame this constraint through reduction of another metabolically expensive tissue, the gastrointestinal tract. Small guts characterize animals specializing on easily digestible diets. Thus, the hypothesis may be tested via the relationship between brain size and diet quality. Platyrrhine primates present an interesting test case, as they are more variably encephalized than other extant primate clades (excluding Hominoidea). We find a high degree of phylogenetic signal in the data for diet quality, endocranial volume and body size. Controlling for phylogenetic effects, we find no significant correlation between relative diet quality and relative endocranial volume. Thus, diet quality fails to account for differences in platyrrhine encephalization. One taxon, in particular, Brachyteles, violates predictions made by ETH in having a large brain and low-quality diet. Dietary reconstructions of stem platyrrhines further indicate that a relatively high-quality diet was probably in place prior to increases in encephalization. Therefore, it is unlikely that a shift in diet quality was a primary constraint release for encephalization in platyrrhines and, by extrapolation, humans.

Hierarchical modeling of entangled polymers

We demonstrate that it is possible to link multi-chain molecular dynamics simulations with the tube model using a single chain slip-links model as a bridge. This hierarchical approach allows significant speed up of simulations, permitting us to span the time scales relevant for a comparison with the tube theory. Fitting the mean-square displacement of individual monomers in molecular dynamics simulations with the slip-spring model, we show that it is possible to predict the stress relaxation. Then, we analyze the stress relaxation from slip-spring simulations in the framework of the tube theory. In the absence of constraint release, we establish that the relaxation modulus can be decomposed as the sum of contributions from fast and longitudinal Rouse modes, and tube survival. Finally, we discuss some open questions regarding possible future directions that could be profitable in rendering the tube model quantitative, even for mildly entangled polymers

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

Effects of compressibility and heat release on entrainment processes in mixing layers

Characteristics of the process of entrainment in plane mixing layers, and the changes with compressibility and heat release, were studied using temporal DNS with simultaneous fluid packet tracking. Convective Mach numbers of the simulations are 0.15, 0.7 and 1.1. The Reynolds number is quite high (between 11 000 and 37 000 based on layer width and velocity difference), and is above the mixing transition. The study agrees with recent findings in round jets: first, engulfed fluid volume and its growth rate are both very small compared with the volume of the turbulent region and its growth rate, respectively. Secondly, most often, the process occurs close to the turbulent-nonturbulent boundaries. A new finding is that both compressibility and heat release retard the entrainment process so that it takes an O(1) time for vorticity or scalar levels to grow even after growth has been initiated. This delay is manifested as the fall in mixing layer growth rates as compressibility and heat release levels increase.

Cumulus clouds and convective boundary layers: a tropical perspective on two turbulent shear flows

This paper is a review prepared for the second Marseille Colloquium on the mechanics of turbulence, held in 2011, 50 years after the first. The review covers recent developments in our understanding of the large-scale dynamics of cumulus cloud flows and of the atmospheric boundary layer in the low-wind convective regime that is often encountered in the tropics. It has recently been shown that a variety of cumulus cloud forms and life cycles can be experimentally realized in the laboratory, with the transient diabatic plume taken as the flow model for a cumulus cloud. The plume is subjected to diabatic heating scaled to be dynamically similar to heat release from phase changes in clouds. The experiments are complemented by exact numerical solutions of the Navier-Stokes-Boussinesq equations for plumes with scaled off-source heating. The results show that the Taylor entrainment coefficient first increases with heating, reaches a positive maximum and then drops rapidly to zero or even negative values. This reduction in entrainment is a consequence of structural changes in the flow, smoothing out the convoluted boundaries in the non-diabatic plume, including the tongues engulfing the ambient flow. This is accompanied by a greater degree of mixedness in the core flow because of lower dilution by the ambient fluid. The cloud forms generated depend strongly on the history of the diabatic heating profile in the vertical direction. The striking effects of heating on the flow are attributable to the operation of the baroclinic torque due to the temperature field. The mean baroclinic torque is shown to peak around a quasi-cylindrical sheet situated midway between the axis of the flow and the edges. This torque is shear-enhancing and folds down the engulfment tongues. The increase in mixedness can be traced to an explosive growth in the enstrophy, triggered by a strong fluctuating baroclinic torque that acts as a source, especially at the higher wave numbers, thus enhancing the mixedness. In convective boundary layers field measurements show that, under conditions prevailing in the tropics, the eddy fluxes of momentum and energy do not follow the Monin-Obukhov similarity. Instead, the eddy momentum flux is found to be linear in the wind speed at low winds; and the eddy heat flux is, to a first approximation, governed by free convection laws, with wind acting as a small perturbation on a regime of free convection. A new boundary layer code, based on heat flux scaling rather than wall-stress scaling, shows promising improvements in predictive skills of a general circulation model.

Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms-(1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are colocated. Regions in the space of parameters characterizing the base flow velocity profile, i.e., shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on understanding prior experimental studies of combustion instability in backward facing step combustors and hydrodynamic instability in other flows such as heated jets and bluff body stabilized flames is discussed.

ABSOLUTE/CONVECTIVE INSTABILITY TRANSITION IN A BACKWARD FACING STEP COMBUSTOR: FUNDAMENTAL MECHANISM AND INFLUENCE OF DENSITY GRADIENT

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms - (1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are co-located. Regions in the space of parameters characterizing the base flow velocity profile, i.e. shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on prior observations of flow instability in other flows such as heated jets and bluff-body stabilized flames is discussed.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model

For data assimilation in numerical weather prediction, the initial forecast-error covariance matrix Pf is required. For variational assimilation it is particularly important to prescribe an accurate initial matrix Pf, since Pf is either static (in the 3D-Var case) or constant at the beginning of each assimilation window (in the 4D-Var case). At large scales the atmospheric flow is well approximated by hydrostatic balance and this balance is strongly enforced in the initial matrix Pf used in operational variational assimilation systems such as that of the Met Office. However, at convective scales this balance does not necessarily hold any more. Here we examine the extent to which hydrostatic balance is valid in the vertical forecast-error covariances for high-resolution models in order to determine whether there is a need to relax this balance constraint in convective-scale data assimilation. We use the Met Office Global and Regional Ensemble Prediction System (MOGREPS) and a 1.5 km resolution version of the Unified Model for a case study characterized by the presence of convective activity. An ensemble of high-resolution forecasts valid up to three hours after the onset of convection is produced. We show that at 1.5 km resolution hydrostatic balance does not hold for forecast errors in regions of convection. This indicates that in the presence of convection hydrostatic balance should not be enforced in the covariance matrix used for variational data assimilation at this scale. The results show the need to investigate covariance models that may be better suited for convective-scale data assimilation. Finally, we give a measure of the balance present in the forecast perturbations as a function of the horizontal scale (from 3–90 km) using a set of diagnostics. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

The role of convective parameterization in the simulation of a cyclone over the South Atlantic

Numerical simulations are carried out to examine the role of the Kuo and Kain-Fritsch (KF) cumulus parameterization schemes and dry dynamics on a cyclone development, in a weak baroclinic atmosphere, over subtropical South Atlantic Ocean. The initial phase of the cyclone development is investigated with a coarse horizontal mesh (75 km) and when the cyclone reaches the mature stage two different horizontal resolutions are used (75 and 25 km). The best performance simulation for the cyclone initial phase occurs when the Kuo convective scheme is applied, and this may be attributed to a greater diabatic warming in the troposphere. On the other hand, the dry simulation is not capable of simulating the correct location and intensity of the cyclone in its initial phase. During the mature phase, a cyclone over deepening occurs in the Kuo scheme experiment associated with larger latent heat release in a deep vertical column. The presence of downdraft currents in the KF scheme, which acts to cool and dry the lower levels, is essential to stabilize the atmosphere and to reproduce the nearest observation cyclone deepening rate. The largest cyclone deepening is found in the Kuo scheme high resolution experiment. This suggests that the KF convective scheme is less sensitive to the horizontal grid resolution. It was also revealed that the diabatic processes are crucial to simulate the observed features of this marine cyclone over subtropical region.