128 research outputs found
Dynamics of aeolian sand ripples
We analyze theoretically the dynamics of aeolian sand ripples. In order to
put the study in the context we first review existing models. We argue on the
local character of sand ripple formation. Using a hydrodynamical model we
derive a nonlinear equation for the sand profile. We show how the
hydrodynamical model may be modified to recover the missing terms that are
dictated by symmetries. The symmetry and conservation arguments are powerful in
that the form of the equation is model-independent. We then present an
extensive numerical and analytical analysis of the generic sand ripple
equation. We find that at the initial stage the wavelength of the ripple is
that corresponding to the linearly most dangerous mode. At later stages the
profile undergoes a coarsening process leading to a significant increase of the
wavelength. We find that including the next higher order nonlinear term in the
equation, leads naturally to a saturation of the local slope. We analyze both
analytically and numerically the coarsening stage, in terms of a dynamical
exponent for the mean wavelength increase. We discuss some future lines of
investigations.Comment: 22 pages and 10 postscript figure
Influence of uniaxial stress on the lamellar spacing of eutectics
Directional solidification of lamellar eutectic structures submitted to
uniaxial stress is investigated. In the spirit of an approximation first used
by Jackson and Hunt, we calculate the stress tensor for a two-dimensional
crystal with triangular surface, using a Fourier expansion of the Airy
function. crystal with triangular surface in contact with its melt, given that
a uniaxial external stress is applied. The effect of the resulting change in
chemical potential is introduced into the standard model for directional
solidification of a lamellar eutectic. This calculation is motivated by an
observation, made recently [I. Cantat, K. Kassner, C. Misbah, and H.
M\"uller-Krumbhaar, Phys. Rev. E, in press] that the thermal gradient produces
similar effects as a strong gravitational field in the case of dilute-alloy
solidification. Therefore, the coupling between the Grinfeld and the
Mullins-Sekerka instabilities becomes strong, as the critical wavelength of the
former instability gets reduced to a value close to that of the latter.
Analogously, in the case of eutectics, the characteristic length scale of the
Grinfeld instability should be reduced to a size not extremely far from typical
lamellar spacings. In a Jackson-Hunt like approach we average the undercooling,
including the stress term, over a pair of lamellae. Following Jackson and Hunt,
we assume the selected wavelength to be determined by the minimum undercooling
criterion and compute its shift due to the external stress. we realize the
shifting of the wavelength by the application of external stress. In addition,
we find that in general the volume fraction of the two solid phases is changed
by uniaxial stress. Implications for experiments on eutectics are discussed.Comment: 8 pages RevTex, 6 included ps-figures, accepted for Phys. Rev.
The fluctuation energy balance in non-suspended fluid-mediated particle transport
Here we compare two extreme regimes of non-suspended fluid-mediated particle
transport, transport in light and heavy fluids ("saltation" and "bedload",
respectively), regarding their particle fluctuation energy balance. From direct
numerical simulations, we surprisingly find that the ratio between collisional
and fluid drag dissipation of fluctuation energy is significantly larger in
saltation than in bedload, even though the contribution of interparticle
collisions to transport of momentum and energy is much smaller in saltation due
to the low concentration of particles in the transport layer. We conclude that
the much higher frequency of high-energy particle-bed impacts ("splash") in
saltation is the cause for this counter-intuitive behavior. Moreover, from a
comparison of these simulations to Particle Tracking Velocimetry measurements
which we performed in a wind tunnel under steady transport of fine and coarse
sand, we find that turbulent fluctuations of the flow produce particle
fluctuation energy at an unexpectedly high rate in saltation even under
conditions for which the effects of turbulence are usually believed to be
small
Energy Dissipation and Trapping of Particles Moving on a Rough Surface
We report an experimental, numerical and theoretical study of the motion of a
ball on a rough inclined surface. The control parameters are , the diameter
of the ball, , the inclination angle of the rough surface and ,
the initial kinetic energy. When the angle of inclination is larger than some
critical value, , the ball moves at a constant average
velocity which is independent of the initial conditions. For an angle , the balls are trapped after moving a certain distance. The
dependence of the travelled distances on , and . is
analysed. The existence of two kinds of mechanisms of dissipation is thus
brought to light. We find that for high initial velocities the friction force
is constant. As the velocity decreases below a certain threshold the friction
becomes viscous.Comment: 8 pages RevTeX, 12 Postscript figure
Porous silicon formation and electropolishing
Electrochemical etching of silicon in hydrofluoride containing electrolytes
leads to pore formation for low and to electropolishing for high applied
current. The transition between pore formation and polishing is accompanied by
a change of the valence of the electrochemical dissolution reaction. The local
etching rate at the interface between the semiconductor and the electrolyte is
determined by the local current density. We model the transport of reactants
and reaction products and thus the current density in both, the semiconductor
and the electrolyte. Basic features of the chemical reaction at the interface
are summarized in law of mass action type boundary conditions for the transport
equations at the interface. We investigate the linear stability of a planar and
flat interface. Upon increasing the current density the stability flips either
through a change of the valence of the dissolution reaction or by a nonlinear
boundary conditions at the interface.Comment: 18 pages, 8 figure
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