265 research outputs found
Effect of aspect ratio on transverse diffusive broadening: A lattice Boltzmann study
We study scaling laws characterizing the inter-diffusive zone between two
miscible fluids flowing side by side in a Y-shape laminar micromixer using the
lattice Boltzmann method. The lattice Boltzmann method solves the coupled 3D
hydrodynamics and mass transfer equations and incorporates intrinsic features
of 3D flows related to this problem. We observe the different power law regimes
occurring at the center of the channel and close to the top/bottom wall. The
extent of the inter-diffusive zone scales as square root of the axial distance
at the center of the channel. At the top/bottom wall, we find an exponent 1/3
at early stages of mixing as observed in the experiments of Ismagilov and
coworkers [Appl. Phys. Lett. 76, 2376 (2000)]. At a larger distance from the
entrance, the scaling exponent close to the walls changes to 1/2 [J.-B. Salmon
et al J. Appl. Phys. 101, 074902 (2007)]. Here, we focus on the effect of
finite aspect ratio on diffusive broadening. Interestingly, we find the same
scaling laws regardless of the channel's aspect ratio. However,the point at
which the exponent 1/3 characterizing the broadening at the top/bottom wall
reverts to the normal diffusive behavior downstream strongly depends on the
aspect ratio. We propose an interpretation of this observation in terms of
shear rate at the side walls. A criterion for the range of aspect ratios with
non-negligible effect on diffusive broadening is also provided.Comment: 19 pages, 7 figure
Shear localization in a model glass
Using molecular dynamics simulations, we show that a simple model of a glassy
material exhibits the shear localization phenomenon observed in many complex
fluids. At low shear rates, the system separates into a fluidized shear-band
and an unsheared part. The two bands are characterized by a very different
dynamics probed by a local intermediate scattering function. Furthermore, a
stick-slip motion is observed at very small shear rates. Our results, which
open the possibility of exploring complex rheological behavior using
simulations, are compared to recent experiments on various soft glasses.Comment: 4 pages, 4 figures (5 figure files
Fluctuating Multicomponent Lattice Boltzmann Model
Current implementations of fluctuating lattice Boltzmann equations (FLBE)
describe single component fluids. In this paper, a model based on the continuum
kinetic Boltzmann equation for describing multicomponent fluids is extended to
incorporate the effects of thermal fluctuations. The thus obtained fluctuating
Boltzmann equation is first linearized to apply the theory of linear
fluctuations, and expressions for the noise covariances are determined by
invoking the fluctuation-dissipation theorem (FDT) directly at the kinetic
level. Crucial for our analysis is the projection of the Boltzmann equation
onto the ortho-normal Hermite basis. By integrating in space and time the
fluctuating Boltzmann equation with a discrete number of velocities, the FLBE
is obtained for both ideal and non-ideal multicomponent fluids. Numerical
simulations are specialized to the case where mean-field interactions are
introduced on the lattice, indicating a proper thermalization of the system.Comment: 30 pages, 6 figure
Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids
We introduce thermal fluctuations in the lattice Boltzmann method for
non-ideal fluids. A fluctuation-dissipation theorem is derived within the
Langevin framework and applied to a specific lattice Boltzmann model that
approximates the linearized fluctuating Navier-Stokes equations for fluids
based on square-gradient free energy functionals. The obtained thermal noise is
shown to ensure equilibration of all degrees of freedom in a simulation to high
accuracy. Furthermore, we demonstrate that satisfactory results for most
practical applications of fluctuating hydrodynamics can already be achieved
using thermal noise derived in the long wavelength-limit.Comment: 15 pages, 5 figure
Roughness gradient induced spontaneous motion of droplets on hydrophobic surfaces: A lattice Boltzmann study
The effect of a step wise change in the pillar density on the dynamics of
droplets is investigated via three-dimensional lattice Boltzmann simulations.
For the same pillar density gradient but different pillar arrangements, both
motion over the gradient zone as well as complete arrest are observed. In the
moving case, the droplet velocity scales approximately linearly with the
texture gradient. A simple model is provided reproducing the observed linear
behavior. The model also predicts a linear dependence of droplet velocity on
surface tension. This prediction is clearly confirmed via our computer
simulations for a wide range of surface tensions.Comment: 6 pages, 8 figure
Amorphous silica between confining walls and under shear: a computer simulation study
Molecular dynamics computer simulations are used to investigate a silica melt
confined between walls at equilibrium and in a steady-state Poisseuille flow.
The walls consist of point particles forming a rigid face-centered cubic
lattice and the interaction of the walls with the melt atoms is modelled such
that the wall particles have only a weak bonding to those in the melt, i.e.
much weaker than the covalent bonding of a Si-O unit. We observe a pronounced
layering of the melt near the walls. This layering, as seen in the total
density profile, has a very irregular character which can be attributed to a
preferred orientational ordering of SiO4 tetrahedra near the wall. On
intermediate length scales, the structure of the melt at the walls can be well
distinguished from that of the bulk by means of the ring size distribution.
Whereas essentially no structural changes occur in the bulk under the influence
of the shear fields considered, strong structural rearrangements in the ring
size distribution are present at the walls as far as there is a slip motion.
For the sheared system, parabolic velocity profiles are found in the bulk
region as expected from hydrodynamics and the values for the shear viscosity as
extracted from those profiles are in good agreement with those obtained in pure
bulk simulations from the appropriate Green-Kubo formula.Comment: 23 pages of Late
Diffuse interface models of solidification with convection: The choice of a finite interface thickness
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original formulation of this problem is restricted to transport by diffusion, we consider here the case of melt convection. Using an analysis of the coupled phase field-fluid dynamic equations, we show here that such a thin interface limit does also exist if transport contains both diffusion and convection. This prediction is tested by comparing simulation studies, which make use of the thin-interface condition, with an analytic sharp-interface theory for dendritic tip growth under convection. © 2020, The Author(s)
Profile blunting and flow blockage in a yield stress fluid: A molecular dynamics study
The flow of a simple glass forming system (a 80:20 binary Lennard-Jones
mixture) through a planar channel is studied via molecular dynamics
simulations. The flow is driven by an external body force similar to gravity.
Previous studies show that the model exhibits both a static [Varnik et al. J.
Chem. Phys. 120, 2788 (2004)] and a dynamic [F. Varnik and O. Henrich Phys.
Rev. B 73, 174209 (2006)] yield stress in the glassy phase. \blue{These
observations are corroborated by the present work, where we investigate how the
presence of a yield stress may affect the system behavior in a Poiseuille-type
flow geometry.} In particular, we observe a blunted velocity profile across the
channel: A relatively wide region in the channel center flows with a constant
velocity (zero shear rate) followed by a non linear change of the shear rate as
the walls are approached. The observed velocity gradients are compared to those
obtained from the knowledge of the shear stress across the channel and the
flow-curves (stress versus shear rate), the latter being determined in our
previous simulations of homogeneous shear flow. Furthermore, using the value of
the (dynamic) yield stress known from previous simulations, we estimate the
threshold body force for a complete arrest of the flow. Indeed, a blockage is
observed as the imposed force falls below this threshold value. Small but
finite shear rates are observed at stresses above the dynamic but below the
static yield stress. We discuss the possible role of the \blue{stick-slip like
motion} for this observation.Comment: 22 pages, 8 figure
Flow curves of colloidal dispersions close to the glass transition: Asymptotic scaling laws in a schematic model of mode coupling theory
The flow curves, viz. the curves of stationary stress under steady shearing,
are obtained close to the glass transition in dense colloidal dispersions using
asymptotic expansions in a schematic model of mode coupling theory. The shear
thinning of the viscosity in fluid states and the yielding of glassy states is
discussed. At the transition between fluid and shear-molten glass, simple and
generalized Herschel-Bulkley laws are derived with power law exponents that can
be computed for different particle interactions from the equilibrium structure
factor.Comment: 14 pages, 14 figures, 4 tables, Eur. Phys. J. E (submitted
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