27 research outputs found
Hard discs under steady shear: comparison of Brownian dynamics simulations and mode coupling theory
Brownian dynamics simulations of bidisperse hard discs moving in two
dimensions in a given steady and homogeneous shear flow are presented close to
and above the glasstransition density. The stationary structure functions and
stresses of shear-melted glass are compared quantitatively to parameter-free
numerical calculations of monodisperse hard discs using mode coupling theory
within the integration through transients framework. Theory qualitatively
explains the properties of the yielding glass but quantitatively
overestimatesthe shear-driven stresses and structural anisotropies.Comment: 1. The original Phil. Trans. R. Soc. contains an error in the caption
of the y-axes of the upper left panel in figure 9: There's a factor
\dot{\gamma} missing in the denominato
Density Functional approach to Nonlinear Rheology
We present a density functional based closure of the pair Smoluchowski
equation for Brownian particles under shear flow. Given an equilibrium free
energy functional as input the theory provides first-principles predictions for
the flow-distorted pair correlation function and associated rheological
quantities over a wide range of volume fractions and flow rates. Taking
two-dimensional hard-disks under shear flow as an illustrative model we
calculate the pair correlation function, viscosity and normal stress difference
under both steady and start-up shear
Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation
We analyze the slow, glassy structural relaxation as measured through
collective and tagged-particle density correlation functions obtained from
Brownian dynamics simulations for a polydisperse system of quasi-hard spheres
in the framework of the mode-coupling theory of the glass transition (MCT).
Asymptotic analyses show good agreement for the collective dynamics when
polydispersity effects are taken into account in a multi-component calculation,
but qualitative disagreement at small when the system is treated as
effectively monodisperse. The origin of the different small- behaviour is
attributed to the interplay between interdiffusion processes and structural
relaxation. Numerical solutions of the MCT equations are obtained taking
properly binned partial static structure factors from the simulations as input.
Accounting for a shift in the critical density, the collective density
correlation functions are well described by the theory at all densities
investigated in the simulations, with quantitative agreement best around the
maxima of the static structure factor, and worst around its minima. A
parameter-free comparison of the tagged-particle dynamics however reveals large
quantiative errors for small wave numbers that are connected to the well-known
decoupling of self-diffusion from structural relaxation and to dynamical
heterogeneities. While deviations from MCT behaviour are clearly seen in the
tagged-particle quantities for densities close to and on the liquid side of the
MCT glass transition, no such deviations are seen in the collective dynamics.Comment: 23 pages, 26 figure
Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time
The shear modulus G of two glass-forming colloidal model systems in d=3 and
d=2 dimensions is investigated by means of, respectively, molecular dynamics
and Monte Carlo simulations. Comparing ensembles where either the shear strain
gamma or the conjugated (mean) shear stress tau are imposed, we compute G from
the respective stress and strain fluctuations as a function of temperature T
while keeping a constant normal pressure P. The choice of the ensemble is seen
to be highly relevant for the shear stress fluctuations mu_F(T) which at
constant tau decay monotonously with T following the affine shear elasticity
mu_A(T), i.e. a simple two-point correlation function. At variance,
non-monotonous behavior with a maximum at the glass transition temperature T_g
is demonstrated for mu_F(T) at constant gamma. The increase of G below T_g is
reasonably fitted for both models by a continuous cusp singularity, G(T) is
proportional to (1-T/T_g)^(1/2), in qualitative agreement with some recent
replica calculations. It is argued, however, that longer sampling times may
lead to a sharper transition. The additive jump discontinuity predicted by
mode-coupling theory and other replica calculations thus cannot ultimately be
ruled out
Nonlinear response of dense colloidal suspensions under oscillatory shear: Mode-coupling theory and FT-rheology experiments
Using a combination of theory, experiment and simulation we investigate the
nonlinear response of dense colloidal suspensions to large amplitude
oscillatory shear flow. The time-dependent stress response is calculated using
a recently developed schematic mode-coupling-type theory describing colloidal
suspensions under externally applied flow. For finite strain amplitudes the
theory generates a nonlinear response, characterized by significant higher
harmonic contributions. An important feature of the theory is the prediction of
an ideal glass transition at sufficiently strong coupling, which is accompanied
by the discontinuous appearance of a dynamic yield stress. For the oscillatory
shear flow under consideration we find that the yield stress plays an important
role in determining the non linearity of the time-dependent stress response.
Our theoretical findings are strongly supported by both large amplitude
oscillatory (LAOS) experiments (with FT-rheology analysis) on suspensions of
thermosensitive core-shell particles dispersed in water and Brownian dynamics
simulations performed on a two-dimensional binary hard-disc mixture. In
particular, theory predicts nontrivial values of the exponents governing the
final decay of the storage and loss moduli as a function of strain amplitude
which are in excellent agreement with both simulation and experiment. A
consistent set of parameters in the presented schematic model achieves to
jointly describe linear moduli, nonlinear flow curves and large amplitude
oscillatory spectroscopy
Density functional approach to nonlinear rheology
We present a density-functional–based closure of the pair Smoluchowski equation for Brownian particles under shear flow. Given an equilibrium free-energy functional as input, the theory provides first-principles predictions for the flow-distorted pair correlation function and associated rheological quantities over a wide range of volume fractions and flow rates. Taking two-dimensional hard disks under shear flow as an illustrative model, we calculate the pair correlation function, viscosity and normal-stress difference under both steady and start-up shear