372 research outputs found
Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment
We derive the hydrodynamic equations for nematic liquid crystals lying on
curved substrates. We invoke the Lagrange-Rayleigh variational principle to
adapt the Ericksen-Leslie theory to two-dimensional nematics in which a
degenerate anchoring of the molecules on the substrate is enforced. The only
constitutive assumptions in this scheme concern the free-energy density, given
by the two-dimensional Frank potential, and the density of dissipation which is
required to satisfy appropriate invariance requirements. The resulting
equations of motion couple the velocity field, the director alignment and the
curvature of the shell. To illustrate our findings, we consider the effect of a
simple shear flow on the alignment of a nematic lying on a cylindrical shell
Influence of the Extrinsic Curvature on 2D Nematic Films
Nematic interfaces are thin fluid films, ideally two-dimensional, endowed
with an in-plane degenerate nematic order. In this letter we examine a
generalisation of the classical Plateau problem to an axisymmetric nematic
interface bounded by two coaxial parallel rings. The equilibrium interface
shape results from the competition between surface tension, which favours the
minimization of the interface area, and the nematic elasticity which instead
promotes the alignment of the molecules along a common direction. We find two
classes of equilibrium solutions with intrinsically uniform alignments: one in
which the molecules are aligned along the meridians, the other along parallels.
Depending on two parameters, one geometric and the other constitutive, the
Gaussian curvature of the equilibrium interface may be negative, vanishing or
positive. The stability of these equilibrium configurations is investigated
Flow of fluids with pressure- and shear-dependent viscosity down an inclined plane
In this paper we consider a fluid whose viscosity depends on both the mean normal stress and the shear rate flowing down an inclined plane. Such flows have relevance to geophysical flows. In order to make the problem amenable to analysis, we consider a generalization of the lubrication approximation for the flows of such fluids based on the development of the generalization of the Reynolds equation for such flows. This allows us to obtain analytical solutions to the problem of propagation of waves in a fluid flowing down an inclined plane. We find that the dependence of the viscosity on the pressure can increase the breaking time by an order of magnitude or more than that for the classical Newtonian fluid. In the viscous regime, we find both upslope and downslope travelling wave solutions, and these solutions are quantitatively and qualitatively different from the classical Newtonian solutions
Braginskii magnetohydrodynamics for arbitrary magnetic topologies: coronal applications
We investigate single-fluid magnetohydrodynamics (MHD) with anisotropic viscosity,
often referred to as Braginskii MHD, with a particular eye to solar coronal applications.
First, we examine the full Braginskii viscous tensor in the single-fluid limit. We pay
particular attention to how the Braginskii tensor behaves as the magnetic field strength
vanishes. The solar corona contains a magnetic field with a complex and evolving
topology, so the viscosity must revert to its isotropic form when the field strength is zero,
e.g. at null points. We highlight that the standard form in which the Braginskii tensor
is written is not suitable for inclusion in simulations as singularities in the individual
terms can develop. Instead, an altered form, where the parallel and perpendicular tensors
are combined, provides the required asymptotic behaviour in the weak-field limit. We
implement this combined form of the tensor into the Lare3D code, which is widely used
for coronal simulations. Since our main focus is the viscous heating of the solar corona,
we drop the drift terms of the Braginskii tensor. In a stressed null point simulation,
we discover that small-scale structures, which develop very close to the null, lead to
anisotropic viscous heating at the null itself (that is, heating due to the anisotropic
terms in the viscosity tensor). The null point simulation we present has a much higher
resolution than many other simulations containing null points so this excess heating is
a practical concern in coronal simulations. To remedy this unwanted heating at the null
point, we develop a model for the viscosity tensor that captures the most important
physics of viscosity in the corona: parallel viscosity for strong field and isotropic viscosity
at null points. We derive a continuum model of viscosity where momentum transport,
described by this viscosity model, has the magnetic field as its preferred orientation.
When the field strength is zero, there is no preferred direction for momentum transport
and viscosity reverts to the standard isotropic form. The most general viscous stress
tensor of a (single-fluid) plasma satisfying these conditions is found. It is shown that
the Braginskii model, without the drift terms, is a specialization of the general model.
Performing the stressed null point simulation with this simplified model of viscosity
reveals very similar heating profiles compared to the full Braginskii model. The new
model, however, does not produce anisotropic heating at the null point, as required.
Since the vast majority of coronal simulations use only isotropic viscosity, we perform the
stressed null point simulation with isotropic viscosity and compare the heating profiles
to those of the anisotropic models. It is shown than the fully isotropic viscosity can
over-estimate the viscous heating by an order of magnitude
Stability analysis of the Rayleigh-B enard convection for a fluid with temperature and pressure dependent viscosity
Li-ion batteries monitoring for electrified vehicles applications
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