61 research outputs found
Dynamics of fluctuations in a fluid below the onset of Rayleigh-B\'enard convection
We present experimental data and their theoretical interpretation for the
decay rates of temperature fluctuations in a thin layer of a fluid heated from
below and confined between parallel horizontal plates. The measurements were
made with the mean temperature of the layer corresponding to the critical
isochore of sulfur hexafluoride above but near the critical point where
fluctuations are exceptionally strong. They cover a wide range of temperature
gradients below the onset of Rayleigh-B\'enard convection, and span wave
numbers on both sides of the critical value for this onset. The decay rates
were determined from experimental shadowgraph images of the fluctuations at
several camera exposure times. We present a theoretical expression for an
exposure-time-dependent structure factor which is needed for the data analysis.
As the onset of convection is approached, the data reveal the critical
slowing-down associated with the bifurcation. Theoretical predictions for the
decay rates as a function of the wave number and temperature gradient are
presented and compared with the experimental data. Quantitative agreement is
obtained if allowance is made for some uncertainty in the small spacing between
the plates, and when an empirical estimate is employed for the influence of
symmetric deviations from the Oberbeck-Boussinesq approximation which are to be
expected in a fluid with its density at the mean temperature located on the
critical isochore.Comment: 13 pages, 10 figures, 52 reference
Inconsistency of a dissipative contribution to the mass flux in hydrodynamics
The possibility of dissipative contributions to the mass flux is considered
in detail. A general, thermodynamically consistent framework is developed to
obtain such terms, the compatibility of which with general principles is then
checked--including Galilean invariance, the possibility of steady rigid
rotation and uniform center-of-mass motion, the existence of a locally
conserved angular momentum, and material objectivity. All previously discussed
scenarios of dissipative mass fluxes are found to be ruled out by some
combinations of these principles, but not a new one that includes a smoothed
velocity field v-bar. However, this field v-bar is nonlocal and leads to
unacceptable consequences in specific situations. Hence we can state with
confidence that a dissipative contribution to the mass flux is not possible.Comment: 18 pages; submitted to Phys. Rev.
Generalized Casimir forces in non-equilibrium systems
In the present work we propose a method to determine fluctuation induced
forces in non equilibrium systems. These forces are the analogue of the well
known Casimir forces, which were originally introduced in Quantum Field theory
and later extended to the area of Critical Phenomena. The procedure starts from
the observation that many non equilibrium systems exhibit long-range
correlations and the associated structure factors diverge in the long
wavelength limit. The introduction of external bodies into such systems in
general modifies the spectrum of these fluctuations and leads to the appearance
of a net force between these bodies. The mechanism is illustrated by means of a
simple example: a reaction diffusion equation with random noises.Comment: Submitted to Europhysics Letters. 7 pages, 2 figure
Fractal fronts of diffusion in microgravity
Spatial scale invariance represents a remarkable feature of natural phenomena. A ubiquitous example is represented by miscible liquid phases undergoing diffusion. Theory and simulations predict that in the absence of gravity diffusion is characterized by long-ranged algebraic correlations. Experimental evidence of scale invariance generated by diffusion has been limited, because on Earth the development of long-range correlations is suppressed by gravity. Here we report experimental results obtained in microgravity during the flight of the FOTON M3 satellite. We find that during a diffusion process a dilute polymer solution exhibits scale-invariant concentration fluctuations with sizes ranging up to millimetres, and relaxation times as large as 1,000 s. The scale invariance is limited only by the finite size of the sample, in agreement with recent theoretical predictions. The presence of such fluctuations could possibly impact the growth of materials in microgravity
Fluctuating hydrodynamics and correlation lengths in a driven granular fluid
Static and dynamical structure factors for shear and longitudinal modes of
the velocity and density fields are computed for a granular system fluidized by
a stochastic bath with friction. Analytical expressions are obtained through
fluctuating hydrodynamics and are successfully compared with numerical
simulations up to a volume fraction . Hydrodynamic noise is the sum
of external noise due to the bath and internal one due to collisions. Only the
latter is assumed to satisfy the fluctuation-dissipation relation with the
average granular temperature. Static velocity structure factors
and display a general non-constant behavior with two plateaux
at large and small , representing the granular temperature and the
bath temperature respectively. From this behavior, two different
velocity correlation lengths are measured, both increasing as the packing
fraction is raised. This growth of spatial order is in agreement with the
behaviour of dynamical structure factors, the decay of which becomes slower and
slower at increasing density.Comment: 24 pages, 8 figure
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