135 research outputs found
Convective Nonlinearity in Non-Newtonian Fluids
In the limit of infinite yield time for stresses, the hydrodynamic equations
for viscoelastic, Non-Newtonian liquids such as polymer melts must reduce to
that for solids. This piece of information suffices to uniquely determine the
nonlinear convective derivative, an ongoing point of contention in the rheology
literature.Comment: 4 page
Influence of Sedimentation on Convective Instabilities in Colloidal Suspensions
We investigate theoretically the bifurcation scenario for colloidal
suspensions subject to a vertical temperature gradient taking into account the
effect of sedimentation. In contrast to molecular binary mixtures, here the
thermal relaxation time is much shorter than that for concentration
fluctuations. This allows for differently prepared ground states, where a
concentration profile due to sedimentation and/or the Soret effect has been
established or not. This gives rise to different linear instability behaviors,
which are manifest in the temporal evolution into the final, generally
stationary convective state. In a certain range above a rather high barometric
number there is a coexistence between the quiescent state and the stationary
convective one, allowing for a hysteretic scenario.Comment: to appear in Int. J. Bif. Chao
Hydrodynamics of topological defects in nematic liquid crystals
We show that back-flow, the coupling between the order parameter and the
velocity fields, has a significant effect on the motion of defects in nematic
liquid crystals. In particular the defect speed can depend strongly on the
topological strength in two dimensions and on the sense of rotation of the
director about the core in three dimensions.Comment: 4 pages including two figure
Shear induced instabilities in layered liquids
Motivated by the experimentally observed shear-induced destabilization and
reorientation of smectic A like systems, we consider an extended formulation of
smectic A hydrodynamics. We include both, the smectic layering (via the layer
displacement u and the layer normal p) and the director n of the underlying
nematic order in our macroscopic hydrodynamic description and allow both
directions to differ in non equilibrium situations. In an homeotropically
aligned sample the nematic director does couple to an applied simple shear,
whereas the smectic layering stays unchanged. This difference leads to a finite
(but usually small) angle between n and p, which we find to be equivalent to an
effective dilatation of the layers. This effective dilatation leads, above a
certain threshold, to an undulation instability of the layers. We generalize
our earlier approach [Rheol. Acta, vol.39(3), 15] and include the cross
couplings with the velocity field and the order parameters for orientational
and positional order and show how the order parameters interact with the
undulation instability. We explore the influence of various material parameters
on the instability. Comparing our results to recent experiments and molecular
dynamic simulations, we find a good qualitative agreement.Comment: 15 pages, 12 figures, accepted for publication in PR
Faraday waves on a viscoelastic liquid
We investigate Faraday waves on a viscoelastic liquid. Onset measurements and
a nonlinear phase diagram for the selected patterns are presented. By virtue of
the elasticity of the material a surface resonance synchronous to the external
drive competes with the usual subharmonic Faraday instability. Close to the
bicriticality the nonlinear wave interaction gives rise to a variety of novel
surface states: Localised patches of hexagons, hexagonal superlattices,
coexistence of hexagons and lines. Theoretical stability calculations and
qualitative resonance arguments support the experimental observations.Comment: 4 pages, 4figure
Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection
Patterns forming spontaneously in extended, three-dimensional, dissipative
systems are likely to excite several homogeneous soft modes (
hydrodynamic modes) of the underlying physical system, much more than quasi
one- and two-dimensional patterns are. The reason is the lack of damping
boundaries. This paper compares two analytic techniques to derive the patten
dynamics from hydrodynamics, which are usually equivalent but lead to different
results when applied to multiple homogeneous soft modes. Dielectric
electroconvection in nematic liquid crystals is introduced as a model for
three-dimensional pattern formation. The 3D pattern dynamics including soft
modes are derived. For slabs of large but finite thickness the description is
reduced further to a two-dimensional one. It is argued that the range of
validity of 2D descriptions is limited to a very small region above threshold.
The transition from 2D to 3D pattern dynamics is discussed. Experimentally
testable predictions for the stable range of ideal patterns and the electric
Nusselt numbers are made. For most results analytic approximations in terms of
material parameters are given.Comment: 29 pages, 2 figure
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