1,607 research outputs found
Steady base states for non-Newtonian granular hydrodynamics
We study in this work steady laminar flows in a low density granular gas
modelled as a system of identical smooth hard spheres that collide
inelastically. The system is excited by shear and temperature sources at the
boundaries, which consist of two infinite parallel walls. Thus, the geometry of
the system is the same that yields the planar Fourier and Couette flows in
standard gases. We show that it is possible to describe the steady granular
flows in this system, even at large inelasticities, by means of a
(non-Newtonian) hydrodynamic approach. All five types of Couette-Fourier
granular flows are systematically described, identifying the different types of
hydrodynamic profiles. Excellent agreement is found between our classification
of flows and simulation results. Also, we obtain the corresponding non-linear
transport coefficients by following three independent and complementary
methods: (1) an analytical solution obtained from Grad's 13-moment method
applied to the inelastic Boltzmann equation, (2) a numerical solution of the
inelastic Boltzmann equation obtained by means of the direct simulation Monte
Carlo method and (3) event-driven molecular dynamics simulations. We find that,
while Grad's theory does not describe quantitatively well all transport
coefficients, the three procedures yield the same general classification of
planar Couette-Fourier flows for the granular gasComment: 33 pages, 11 figures; v2: improved version accepted for publication
in J. Fluid Mec
Molecular hydrodynamics of the moving contact line in two-phase immiscible flows
The ``no-slip'' boundary condition, i.e., zero fluid velocity relative to the
solid at the fluid-solid interface, has been very successful in describing many
macroscopic flows. A problem of principle arises when the no-slip boundary
condition is used to model the hydrodynamics of immiscible-fluid displacement
in the vicinity of the moving contact line, where the interface separating two
immiscible fluids intersects the solid wall. Decades ago it was already known
that the moving contact line is incompatible with the no-slip boundary
condition, since the latter would imply infinite dissipation due to a
non-integrable singularity in the stress near the contact line. In this paper
we first present an introductory review of the problem. We then present a
detailed review of our recent results on the contact-line motion in immiscible
two-phase flow, from MD simulations to continuum hydrodynamics calculations.
Through extensive MD studies and detailed analysis, we have uncovered the slip
boundary condition governing the moving contact line, denoted the generalized
Navier boundary condition. We have used this discovery to formulate a continuum
hydrodynamic model whose predictions are in remarkable quantitative agreement
with the MD simulation results at the molecular level. These results serve to
affirm the validity of the generalized Navier boundary condition, as well as to
open up the possibility of continuum hydrodynamic calculations of immiscible
flows that are physically meaningful at the molecular level.Comment: 36 pages with 33 figure
Modulated rotating waves in the magnetized spherical Couette system
We present a study devoted to a detailed description of modulated rotating
waves (MRW) in the magnetized spherical Couette system. The set-up consists of
a liquid metal confined between two differentially rotating spheres and
subjected to an axially applied magnetic field. When the magnetic field
strength is varied, several branches of MRW are obtained by means of three
dimensional direct numerical simulations (DNS). The MRW originate from parent
branches of rotating waves (RW) and are classified according to Rand's (Arch.
Ration. Mech. Anal 79:1-37, 182) and Coughling & Marcus (J. Fluid Mech.
234:1-18,1992) theoretical description. We have found relatively large
intervals of multistability of MRW at low magnetic field, corresponding to the
radial jet instability known from previous studies. However, at larger magnetic
field, corresponding to the return flow regime, the stability intervals of MRW
are very narrow and thus they are unlikely to be found without detailed
knowledge of their bifurcation point. A careful analysis of the spatio-temporal
symmetries of the most energetic modes involved in the different classes of MRW
will allow in the future a comparison with the HEDGEHOG experiment, a
magnetized spherical Couette device hosted at the Helmholtz-Zentrum
Dresden-Rossendorf.Comment: Contains 3 tables and 8 figures. Published in the Journal of
Nonlinear Scienc
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