57,199 research outputs found
Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton's theory to empirical models
The aim of this study is to derive accurate models for quantities
characterizing the dynamics of droplets of non-vanishing viscosity in
capillaries. In particular, we propose models for the uniform-film thickness
separating the droplet from the tube walls, for the droplet front and rear
curvatures and pressure jumps, and for the droplet velocity in a range of
capillary numbers, , from to and inner-to-outer viscosity
ratios, , from , i.e. a bubble, to high viscosity droplets.
Theoretical asymptotic results obtained in the limit of small capillary number
are combined with accurate numerical simulations at larger . With these
models at hand, we can compute the pressure drop induced by the droplet. The
film thickness at low capillary numbers () agrees well with
Bretherton's scaling for bubbles as long as . For larger viscosity
ratios, the film thickness increases monotonically, before saturating for
to a value times larger than the film thickness of a
bubble. At larger capillary numbers, the film thickness follows the rational
function proposed by Aussillous \& Qu\'er\'e (2000) for bubbles, with a fitting
coefficient which is viscosity-ratio dependent. This coefficient modifies the
value to which the film thickness saturates at large capillary numbers. The
velocity of the droplet is found to be strongly dependent on the capillary
number and viscosity ratio. We also show that the normal viscous stresses at
the front and rear caps of the droplets cannot be neglected when calculating
the pressure drop for
A novel weight function for RMS stress intensity factor determination in surface cracks
This paper discusses the problem of stress intensity factor determination in
surface cracks. In particular, the concept of root mean square stress intensity factors (RMS
SIF) is discussed for the general class of semi-elliptical surface cracks. The weight
function SIF derivation method is considered problems with the existing techniques are
highlighted, and a novel technique for the derivation of the RMS SIF weight functions for
surface cracks is presented and results are compared with numerical solutions for a variety
of loadings and geometries
A connection between the Camassa-Holm equations and turbulent flows in channels and pipes
In this paper we discuss recent progress in using the Camassa-Holm equations
to model turbulent flows. The Camassa-Holm equations, given their special
geometric and physical properties, appear particularly well suited for studying
turbulent flows. We identify the steady solution of the Camassa-Holm equation
with the mean flow of the Reynolds equation and compare the results with
empirical data for turbulent flows in channels and pipes. The data suggests
that the constant version of the Camassa-Holm equations, derived under
the assumptions that the fluctuation statistics are isotropic and homogeneous,
holds to order distance from the boundaries. Near a boundary, these
assumptions are no longer valid and the length scale is seen to depend
on the distance to the nearest wall. Thus, a turbulent flow is divided into two
regions: the constant region away from boundaries, and the near wall
region. In the near wall region, Reynolds number scaling conditions imply that
decreases as Reynolds number increases. Away from boundaries, these
scaling conditions imply is independent of Reynolds number. Given the
agreement with empirical and numerical data, our current work indicates that
the Camassa-Holm equations provide a promising theoretical framework from which
to understand some turbulent flows.Comment: tex file, 29 pages, 4 figures, Physics of Fluids (in press
Applicability of a Representation for the Martin's Real-Part Formula in Model-Independent Analyses
Using a novel representation for the Martin's real-part formula without the
full scaling property, an almost model-independent description of the
proton-proton differential cross section data at high energies (19.4 GeV - 62.5
GeV) is obtained. In the impact parameter and eikonal frameworks, the extracted
inelastic overlap function presents a peripheral effect (tail) above 2 fm and
the extracted opacity function is characterized by a zero (change of sign) in
the momentum transfer space, confirming results from previous model-independent
analyses. Analytical parametrization for these empirical results are introduced
and discussed. The importance of investigations on the inverse problems in
high-energy elastic hadron scattering is stressed and the relevance of the
proposed representation is commented. A short critical review on the use of
Martin's formula is also presented.Comment: Two comments and one reference added at the end of Subsec. 3.3; 23
pages, 9 figures; to be published in Int. J. Mod. Phys.
A two-species continuum model for aeolian sand transport
Starting from the physics on the grain scale, we develop a simple continuum
description of aeolian sand transport. Beyond popular mean-field models, but
without sacrificing their computational efficiency, it accounts for both
dominant grain populations, hopping (or "saltating") and creeping (or
"reptating") grains. The predicted stationary sand transport rate is in
excellent agreement with wind tunnel experiments simulating wind conditions
ranging from the onset of saltation to storms. Our closed set of equations thus
provides an analytically tractable, numerically precise, and computationally
efficient starting point for applications addressing a wealth of phenomena from
dune formation to dust emission.Comment: 23 pages, 9 figure
Modeling and control of a plastic film manufacturing web process
This paper is concerned with the modelling of aplastic film manufacturing process and the development and implementation of a model-based Cross-Directional (CD) controller. The model is derived from first-principles and some empirical relationships. The final validated nonlinear model could provide a useful off-line platform for developing control and monitoring algorithms.A new controller is designed which has a similar structureto that of Internal Model Control (IMC) with the addition ofan observer whose gain is designed to minimise process andmodel mis-match. The observer gain is obtained by solving amulti-objective optimisation problem through the application of a genetic algorithm. The controller is applied to the nonlinear model and simulation results are presented demonstrating improvements that can be achieved by the proposed controller over two existing CD controllers
Nonequilibrium Thermodynamics of Porous Electrodes
We reformulate and extend porous electrode theory for non-ideal active
materials, including those capable of phase transformations. Using principles
of non-equilibrium thermodynamics, we relate the cell voltage, ionic fluxes,
and Faradaic charge-transfer kinetics to the variational electrochemical
potentials of ions and electrons. The Butler-Volmer exchange current is
consistently expressed in terms of the activities of the reduced, oxidized and
transition states, and the activation overpotential is defined relative to the
local Nernst potential. We also apply mathematical bounds on effective
diffusivity to estimate porosity and tortuosity corrections. The theory is
illustrated for a Li-ion battery with active solid particles described by a
Cahn-Hilliard phase-field model. Depending on the applied current and porous
electrode properties, the dynamics can be limited by electrolyte transport,
solid diffusion and phase separation, or intercalation kinetics. In
phase-separating porous electrodes, the model predicts narrow reaction fronts,
mosaic instabilities and voltage fluctuations at low current, consistent with
recent experiments, which could not be described by existing porous electrode
models
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