33 research outputs found
The minimum or natural rate of flow and droplet size ejected by Taylor cone-jets: physical symmetries and scaling laws
Long Wavelength Instability for Uniform Shear Flow
Uniform Shear Flow is a prototype nonequilibrium state admitting detailed
study at both the macroscopic and microscopic levels via theory and computer
simulation. It is shown that the hydrodynamic equations for this state have a
long wavelength instability. This result is obtained first from the
Navier-Stokes equations and shown to apply at both low and high densities.
Next, higher order rheological effects are included using a model kinetic
theory. The results are compared favorably to those from Monte Carlo
simulation.Comment: 12 pages, including 2 figure
The onset of electrospray: the universal scaling laws of the first ejection
The disintegration of liquid drops with low electrical conductivity and subject to an electric field
is investigated both theoretically and experimentally. This disintegration takes place through the
development of a conical cusp that eventually ejects an ultrathin liquid ligament. A first tiny drop is
emitted from the end of this ligament. Due to its exceptionally small size and large electric charge per
unit volume, that drop has been the object of relevant recent studies. In this paper, universal scaling
laws for the diameter and electric charge of the first issued droplet are proposed and validated both
numerically and experimentally. Our analysis shows how charge relaxation is the mechanism that
differentiates the onset of electrospray, including the first droplet ejection, from the classical steady
cone-jet mode. In this way, our study identifies when and where charge relaxation and electrokinetic
phenomena come into play in electrospray, a subject of live controversy in the field.Ministerio de Economía y Competitividad DPI2013-4648
The second and third Sonine coefficients of a freely cooling granular gas revisited
In its simplest statistical-mechanical description, a granular fluid can be
modeled as composed of smooth inelastic hard spheres (with a constant
coefficient of normal restitution ) whose velocity distribution
function obeys the Enskog-Boltzmann equation. The basic state of a granular
fluid is the homogeneous cooling state, characterized by a homogeneous,
isotropic, and stationary distribution of scaled velocities, .
The behavior of in the domain of thermal velocities ()
can be characterized by the two first non-trivial coefficients ( and
) of an expansion in Sonine polynomials. The main goals of this paper are
to review some of the previous efforts made to estimate (and measure in
computer simulations) the -dependence of and , to report new
computer simulations results of and for two-dimensional systems,
and to investigate the possibility of proposing theoretical estimates of
and with an optimal compromise between simplicity and accuracy.Comment: 12 pages, 5 figures; v2: minor change
Navier-Stokes transport coefficients of -dimensional granular binary mixtures at low density
The Navier-Stokes transport coefficients for binary mixtures of smooth
inelastic hard disks or spheres under gravity are determined from the Boltzmann
kinetic theory by application of the Chapman-Enskog method for states near the
local homogeneous cooling state. It is shown that the Navier-Stokes transport
coefficients are not affected by the presence of gravity. As in the elastic
case, the transport coefficients of the mixture verify a set of coupled linear
integral equations that are approximately solved by using the leading terms in
a Sonine polynomial expansion. The results reported here extend previous
calculations [V. Garz\'o and J. W. Dufty, Phys. Fluids {\bf 14}, 1476 (2002)]
to an arbitrary number of dimensions. To check the accuracy of the
Chapman-Enskog results, the inelastic Boltzmann equation is also numerically
solved by means of the direct simulation Monte Carlo method to evaluate the
diffusion and shear viscosity coefficients for hard disks. The comparison shows
a good agreement over a wide range of values of the coefficients of restitution
and the parameters of the mixture (masses and sizes).Comment: 6 figures, to be published in J. Stat. Phy
Stability of Uniform Shear Flow
The stability of idealized shear flow at long wavelengths is studied in
detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for
small shear rates is given to identify the origin and universality of an
instability at any finite shear rate for sufficiently long wavelength
perturbations. The analysis is extended to larger shear rates using a low
density model kinetic equation. Direct Monte Carlo Simulation of this equation
is computed with a hydrodynamic description including non Newtonian rheological
effects. The hydrodynamic description of the instability is in good agreement
with the direct Monte Carlo simulation for , where is the mean
free time. Longer time simulations up to are used to identify the
asymptotic state as a spatially non-uniform quasi-stationary state. Finally,
preliminary results from molecular dynamics simulation showing the instability
are presented and discussed.Comment: 25 pages, 9 figures (Fig.8 is available on request) RevTeX, submitted
to Phys. Rev.
Measurement of relaxation times in extensional flow of weakly viscoelastic polymer solutions
The characterization of the extensional rheology of polymeric solutions is important in several applications and industrial processes. Filament stretching andcapillary breakup rheometers have been developed to characterize the extensional properties of polymeric solutions,mostly for high-viscosity fluids. However, for low concentration polymer solutions, the measurements are difficultusing available devices, in terms of the minimum viscosity and relaxation times that can be measured accurately.In addition, when the slow retraction method is used, solvent evaporation can affect the measurements for volatilesolvents. In this work, a new setup was tested for filament breakup experiments using the slow retraction method,high-speed imaging techniques, and an immiscible oil bathto reduce solvent evaporation and facilitate particle trackingin the thinning filament. Extensional relaxation times abovearound 100 μs were measured with the device for dilute andsemi-dilute polymer solutions. Particle tracking velocimetrywas also used to measure the velocity in the filament andthe corresponding elongation rate, and to compare with thevalues obtained from the measured exponential decay of thefilament diameter
Diffusion of impurities in a granular gas
Diffusion of impurities in a granular gas undergoing homogeneous cooling
state is studied. The results are obtained by solving the Boltzmann--Lorentz
equation by means of the Chapman--Enskog method. In the first order in the
density gradient of impurities, the diffusion coefficient is determined as
the solution of a linear integral equation which is approximately solved by
making an expansion in Sonine polynomials. In this paper, we evaluate up to
the second order in the Sonine expansion and get explicit expressions for
in terms of the restitution coefficients for the impurity--gas and gas--gas
collisions as well as the ratios of mass and particle sizes. To check the
reliability of the Sonine polynomial solution, analytical results are compared
with those obtained from numerical solutions of the Boltzmann equation by means
of the direct simulation Monte Carlo (DSMC) method. In the simulations, the
diffusion coefficient is measured via the mean square displacement of
impurities. The comparison between theory and simulation shows in general an
excellent agreement, except for the cases in which the gas particles are much
heavier and/or much larger than impurities. In theses cases, the second Sonine
approximation to improves significantly the qualitative predictions made
from the first Sonine approximation. A discussion on the convergence of the
Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.