Effect of enhanced dissipation by shear flows on transient relaxation and probability density function in two dimensions

We report a non-perturbative study of the effects of shear flows on turbulence reduction in a decaying turbulence in two dimensions. By considering different initial power spectra and shear flows (zonal flows, streamers and zonal flows, and streamers combined), we demonstrate how shear flows rapidly generate small scales, leading to a fast damping of turbulence amplitude. In particular, a double exponential decrease in the turbulence amplitude is shown to occur due to an exponential increase in wavenumber. The scaling of the effective dissipation time scale se, previ- ously taken to be a hybrid time scale se / s2=3sg, is shown to depend on types of shear flow as X well as the initial power spectrum. Here, sX and sg are shearing and molecular diffusion times, respectively. Furthermore, we present time-dependent Probability Density Functions (PDFs) and discuss the effect of enhanced dissipation on PDFs and a dynamical time scale s(t), which repre- sents the time scale over which a system passes through statistically different states

Cloud microphysical effects of turbulent mixing and entrainment

Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence time scales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered.Comment: 17 pages, 10 Postscript figures (figures 3,4,6,7,8 and 10 are in reduced quality), to appear in Theoretical Computational Fluid Dynamic

Shear-thinning in dense colloidal suspensions and its effect on elastic instabilities: from the microscopic equations of motion to an approximation of the macroscopic rheology

In the vicinity of their glass transition, dense colloidal suspensions acquire elastic properties over experimental timescales. We investigate the possibility of a visco-elastic flow instability in curved geometry for such materials. To this end, we first present a general strategy extending a first-principles approach based on projections onto slow variables (so far restricted to strictly homogeneous flow) in order to handle inhomogeneities. In particular, we separate the advection of the microstructure by the flow, at the origin of a fluctuation advection term, from the intrinsic dynamics. On account of the complexity of the involved equations, we then opt for a drastic simplification of the theory, in order to establish its potential to describe instabilities. These very strong approximations lead to a constitutive equation of the White-Metzner class, whose parameters are fitted with experimental measurements of the macroscopic rheology of a glass-forming colloidal dispersion. The model properly accounts for the shear-thinning properties of the dispersions, but, owing to the approximations, the description is not fully quantitative. Finally, we perform a linear stability analysis of the flow in the experimentally relevant cylindrical (Taylor-Couette) geometry and provide evidence that shear-thinning strongly stabilises the flow, which can explain why visco-elastic instabilities are not observed in dense colloidal suspensions

Shear-induced anisotropic decay of correlations in hard-sphere colloidal glasses

Spatial correlations of microscopic fluctuations are investigated via real-space experiments and computer simulations of colloidal glasses under steady shear. It is shown that while the distribution of one-particle fluctuations is always isotropic regardless of the relative importance of shear as compared to thermal fluctuations, their spatial correlations show a marked sensitivity to the competition between shear-induced and thermally activated relaxation. Correlations are isotropic in the thermally dominated regime, but develop strong anisotropy as shear dominates the dynamics of microscopic fluctuations. We discuss the relevance of this observation for a better understanding of flow heterogeneity in sheared amorphous solids.Comment: 6 pages, 4 figure

Nonlinear rheology of colloidal dispersions

Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.Comment: Review articl

Understanding Dynamics of Polymers Under Confinement: A Molecular Dynamics and Neutron Scattering Study

The current study probes the structure, dynamics, and rheological behavior of associating polymers including ionomers in melts and solutions as well as conjugated polymers confined into nanoparticles, using molecular dynamics (MD) simulations and neutron scattering techniques. The study focuses on two families of associative polymers, ion containing macromolecules and conjugated polymers. Polymers that consist of ionizable groups along their backbone found uses in a broad range of applications. Examples include light weight energy storage and generation systems, and biomedical applications, where the polymers act as ion exchange membranes, and actuators. The ionic groups tend to form clusters that are in the core of many of the applications. Understanding the relationship of cluster properties and the structure and dynamics of ionizable polymers is crucial to optimize current applications and develop new materials with controlled transport, mechanical stability, and desired response to external stimuli. The first part of the study focuses on understanding the structure and dynamics of polystyrene sulfonate melts as the distribution of the ionizable groups varies with random, precise (number of carbons between ionizable groups is exact), and blocky distributions along the backbone, using atomistic MD simulations. We find that the shape and size distribution of clusters as well as the number of unique chains associated with each cluster are affected by the distribution of the ionic groups. The dynamics of the polymer and the mobility of the counterions are affected by both the number and size of the clusters as well as the number of polymer chains associated with each cluster. Following the understanding of the effects of the clusters on polymer melts, the study proceeds to probe the effects of nonlinear elongational flow on associating polymer melts, which are processed into viable materials under elongational flows. This effort contains two components a coarse grain, and an atomistic MD studies. We find that the response of the melts to elongational flows results from the evolution of both the ionic clusters and Van der Waals domains. The coarse grain study shows that clusters break and reform continuously as the chain stretches heterogeneously in the presence of elongational flow. The atomistic study provides details regarding the effect of chain and cluster rearrangements on the response to the flow. Following melts studies, the work probed the segmental motion of slightly sulfonated polystyrene in cyclohexane solutions using the quasi-elastic neutron scattering technique. We find constraint dynamics at larger length scales however the polymer remains mobile on smaller length scales. Adding a small amount of alcohol is enough to release the constraints within the ionic clusters and results in an increase in segmental polymer motion on all length scales. The last part of the study focused on understanding the effects of the number of rigid luminescent polymer molecules, their chemistries, and initial orientation, on the structure and dynamics of soft nanoparticles (referred to as “polydots”). We find that increasing the number of chains confined affects the internal conformation of the polymer chains where side chains substituting the polymer backbone affect the polydots’ shape and stability. Similar to a single macromolecule polydots, these NPs exhibit a glass-like dynamics with relaxation times in a range of microseconds

Nonlinear rheological properties of dense colloidal dispersions close to a glass transition under steady shear

The nonlinear rheological properties of dense colloidal suspensions under steady shear are discussed within a first principles approach. It starts from the Smoluchowski equation of interacting Brownian particles in a given shear flow, derives generalized Green-Kubo relations, which contain the transients dynamics formally exactly, and closes the equations using mode coupling approximations. Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses arise from a competition between a slowing down of structural relaxation, because of particle interactions, and enhanced decorrelation of fluctuations, caused by the shear advection of density fluctuations. The integration through transients approach takes account of the dynamic competition, translational invariance enters the concept of wavevector advection, and the mode coupling approximation enables to quantitatively explore the shear-induced suppression of particle caging and the resulting speed-up of the structural relaxation. Extended comparisons with shear stress data in the linear response and in the nonlinear regime measured in model thermo-sensitive core-shell latices are discussed. Additionally, the single particle motion under shear observed by confocal microscopy and in computer simulations is reviewed and analysed theoretically.Comment: Review submited to special volume 'High Solid Dispersions' ed. M. Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009); some figures slightly cu