65 research outputs found
The movement of water droplets in clouds around the nose of an atmospheric research aircraft
The dynamic interaction between droplets and the airflow around the hemispherical nose of an aircraft was evaluated. The effect of the aircraft nose on droplet sampling for cloud research is explained. The proportion of different droplet sizes and their concentration at each point around the aircraft nose were determined. In a cloud, interaction between droplets is negligible. Each particle acts, for the calculation of the forces applied to it, as if it is alone in the air. The airflow carrying the droplets, on the average, is not influenced by their presence. The trajectory of each droplet was studied separately after calculating dry airflow. Concentrations were found with a Lagrangian method, using two trajectories computed directly close to one another. Theory confirms that to within 3% experimentally measured concentrations are representative of those in a cloud
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
We propose a mathematical derivation of Brinkman's force for a cloud of
particles immersed in an incompressible fluid. Our starting point is the Stokes
or steady Navier-Stokes equations set in a bounded domain with the disjoint
union of N balls of radius 1/N removed, and with a no-slip boundary condition
for the fluid at the surface of each ball. The large N limit of the fluid
velocity field is governed by the same (Navier-)Stokes equations in the whole
domain, with an additional term (Brinkman's force) that is (minus) the total
drag force exerted by the fluid on the particle system. This can be seen as a
generalization of Allaire's result in [Arch. Rational Mech. Analysis 113
(1991), 209-259] who treated the case of motionless, periodically distributed
balls. Our proof is based on slightly simpler, though similar homogenization
techniques, except that we avoid the periodicity assumption and use instead the
phase-space empirical measure for the particle system. Similar equations are
used for describing the fluid phase in various models for sprays
Transport Phenomena and Structuring in Shear Flow of Suspensions near Solid Walls
In this paper we apply the lattice-Boltzmann method and an extension to
particle suspensions as introduced by Ladd et al. to study transport phenomena
and structuring effects of particles suspended in a fluid near sheared solid
walls. We find that a particle free region arises near walls, which has a width
depending on the shear rate and the particle concentration. The wall causes the
formation of parallel particle layers at low concentrations, where the number
of particles per layer decreases with increasing distance to the wall.Comment: 14 pages, 14 figure
Sedimentation and Flow Through Porous Media: Simulating Dynamically Coupled Discrete and Continuum Phases
We describe a method to address efficiently problems of two-phase flow in the
regime of low particle Reynolds number and negligible Brownian motion. One of
the phases is an incompressible continuous fluid and the other a discrete
particulate phase which we simulate by following the motion of single
particles. Interactions between the phases are taken into account using locally
defined drag forces. We apply our method to the problem of flow through random
media at high porosity where we find good agreement to theoretical expectations
for the functional dependence of the pressure drop on the solid volume
fraction. We undertake further validations on systems undergoing gravity
induced sedimentation.Comment: 22 pages REVTEX, figures separately in uudecoded, compressed
postscript format - alternatively e-mail '[email protected]' for
hardcopies
Numerical calculation of singular integrals related to Hankel transform
AbstractThe singular integral S = ∫0∞ f(x)e−x J0(ωx) dx, related to the Hankel transform of order 0, is calculated numerically by using an integral expression for the Bessel function of order zero, J0. With the assumptions that the function f(x) is bounded and is analytic in some complex domain, the double integral obtained in this way is calculated by a combination of changes of variables and Gauss methods using Laguerre, Chebyshev and Legendre polynomials. The singular integral S′ = ∫0∞ f(x)e−x J1(ωx) dx is derived from S. The subroutines written in FORTRAN run very fast on a personal computer and give a relative precision better than 5 × 10−6
Collision and size evolution of drops in homogeneous isotropic turbulence
International audienceThis paper is devoted to the study of the evolution of the spectrum in a cloud due tocollisions between drops
Interaction of elastic bodies via surface forces. 1. Power-law attraction
We study theoretically the effect of finite elasticity on the attractive power-law interaction of two solids separated by a thin liquid (or gas) film. A new asymptotic technique is developed to determine the deformed shape of the surfaces and to calculate the elasticity contribution to the total force, i.e., an additional term present between the deformed bodies. Both the deformation and the elasticity contribution are found to be nonnegligible well before contact is reached, although they are of much shorter range than the surface force that caused them. This range can be characterized by a reference elasticity length, which depends on elastic constants and size of the solids, as well as on the attractive force that led to deformation. The total force vs separation profile for elastic surfaces is found to depend on how the measurements are made, namely, how the separation is detected: it can lead to either less or more attractive force compared with the case of rigid surfaces
Interaction of elastic bodies via surface forces 2. Exponential decay
Our goal is to study theoretically the effect of deformation on the exponentially decaying interaction of two elastic solids separated by a thin liquid film. The deformed shape of the surfaces and the contribution of the elasticity to the total force, i.e., an additional term present between elastic bodies, are calculated from continuum elastic theory via a new asymptotic technique. Both the deformation and the contribution of the elasticity to the force are found to be significant on the length scale over which the surface force acts. The surface deformation is exponentially decaying with a decay length equal to that of the original surface interaction. It is especially important for large and/or rapidly changing force. The contribution of the elasticity is also exponentially decaying, but with half the decay length. Its strength depends on the elastic constants and size of the solids and on the magnitude and gradient of the original surface force. Depending on how the separation is detected, it can appear either as an attractive or as a repulsive contribution to the force. Our results open the possibility of recalculating the measured force to the interaction free energy
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