1,694 research outputs found
Mesoscopic modeling of heterogeneous boundary conditions for microchannel flows
We present a mesoscopic model of the fluid-wall interactions for flows in
microchannel geometries. We define a suitable implementation of the boundary
conditions for a discrete version of the Boltzmann equations describing a
wall-bounded single phase fluid. We distinguish different slippage properties
on the surface by introducing a slip function, defining the local degree of
slip for mesoscopic molecules at the boundaries. The slip function plays the
role of a renormalizing factor which incorporates, with some degree of
arbitrariness, the microscopic effects on the mesoscopic description. We
discuss the mesoscopic slip properties in terms of slip length, slip velocity,
pressure drop reduction (drag reduction), and mass flow rate in microchannels
as a function of the degree of slippage and of its spatial distribution and
localization, the latter parameter mimicking the degree of roughness of the
ultra-hydrophobic material in real experiments. We also discuss the increment
of the slip length in the transition regime, i.e. at O(1) Knudsen numbers.
Finally, we compare our results with Molecular Dynamics investigations of the
dependency of the slip length on the mean channel pressure and local slip
properties (Cottin-Bizonne et al. 2004) and with the experimental dependency of
the pressure drop reduction on the percentage of hydrophobic material deposited
on the surface -- Ou et al. (2004).Comment: 21 pages, 10 figure
A note on the stability of slip channel flows
We consider the influence of slip boundary conditions on the modal and
non-modal stability of pressure-driven channel flows. In accordance with
previous results by Gersting (1974) (Phys. Fluids, 17) but in contradiction
with the recent investigation of Chu (2004) (C.R. Mecanique, 332), we show that
slip increases significantly the value of the critical Reynolds number for
linear instability. The non-modal stability analysis however reveals that the
slip has a very weak influence on the maximum transient energy growth of
perturbations at subcritical Reynolds numbers. Slip boundary conditions are
therefore not likely to have a significant effect on the transition to
turbulence in channel flows
The Johnson-Segalman model with a diffusion term in Couette flow
We study the Johnson-Segalman (JS) model as a paradigm for some complex
fluids which are observed to phase separate, or ``shear-band'' in flow. We
analyze the behavior of this model in cylindrical Couette flow and demonstrate
the history dependence inherent in the local JS model. We add a simple gradient
term to the stress dynamics and demonstrate how this term breaks the degeneracy
of the local model and prescribes a much smaller (discrete, rather than
continuous) set of banded steady state solutions. We investigate some of the
effects of the curvature of Couette flow on the observable steady state
behavior and kinetics, and discuss some of the implications for metastability.Comment: 14 pp, to be published in Journal of Rheolog
Molecular transport and flow past hard and soft surfaces: Computer simulation of model systems
The properties of polymer liquids on hard and soft substrates are
investigated by molecular dynamics simulation of a coarse-grained bead-spring
model and dynamic single-chain-in-mean-field (SCMF) simulations of a soft,
coarse-grained polymer model. Hard, corrugated substrates are modelled by an
FCC Lennard-Jones solid while polymer brushes are investigated as a
prototypical example of a soft, deformable surface. From the molecular
simulation we extract the coarse-grained parameters that characterise the
equilibrium and flow properties of the liquid in contact with the substrate:
the surface and interface tensions, and the parameters of the hydrodynamic
boundary condition. The so-determined parameters enter a continuum description
like the Stokes equation or the lubrication approximation.Comment: 41 pages, 13 figure
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