Droplet Size Distribution Function Research Articles

Cirrus Cloud Simulation Using Explicit Microphysics and Radiation. Part I: Model Description

Abstract A mesoscale 2D/3D cloud model complex with explicit account for the water and ice cloud microphysics and radiative processes is described. The model has several versions suitable for the simulation of various cloud types, including, of particular concern in the current version, cirrus clouds. Model computations are based on the two kinetic equations for droplet and crystal size distribution functions, with division of droplet and crystal size spectra into 30 bins from 1 μm to 3.5 mm, and with account for the various mechanisms of cloud condensation and ice nuclei activation, condensation–deposition, and coalescence–accretion growth. These equations are solved along with supersaturation and radiative transfer equations for longwave and solar radiation. Simple yet accurate analytical expressions are presented for the scattering and absorption coefficients, and the single-scattering albedo. This allows detailed calculations of the optical and radiative characteristics of clouds (i.e., fluxes, diverg...

Computer simulation study of phase separation in a binary mixture with a glass-forming component

We present a computer simulation study of spinodal decomposition with one of the two phases freezing in a glassy state during phase separation. As a model we used the Cahn-Hilliard equation with a concentration-dependent mobility coefficient which decreases rapidly with increasing concentration of the glass-forming component. We solved the Cahn-Hilliard equation numerically for two dimensions. The domain growth depends crucially on the volume fraction of the glassy phase. For high volume fractions, when the glassy phase forms a percolating matrix, a novel coarsening mechanism is discovered, which arises from the migration and coalescence of liquid droplets within the glassy matrix. Various quantities characterizing the time-dependent domain pattern, like droplet size distribution, one- and two-point distribution function and structure factor of the concentration field, are computed. We checked the validity of the dynamic scaling hypothesis.

Prediction of drop size distributions in sprays using the maximum entropy formalism: the effect of satellite formation

The droplet size distribution function for sprays is derived using the maximum entropy formalism (MEF) to link the end stage of the atomization process to an intermediate state, characterized by unstable liquid cylinders. The probability density function, PDF, for droplet diameter, δ, is mainly governed by conservation of mass and the energy equation. Many of the small droplets are supposedly created together with a much larger droplet, i.e. are supposed to be satellites. A dual PDF, f1(δ,δ∗), represents the number of satellites of diameter δ corresponding to a central or primary drop with diameter δ∗. The representation space is extended with the primary droplet diameter δ∗ and the MEF is applied to derive the function f1. The physical constraints are first related to parts of the liquid cylinders only, and some higher moments of the primary size distribution function, f0(δ∗), have to be known in order to be able to apply the MEF. Some problems inherent in the application of this formalism are examined. Without invoking fitting parameters or ad-hoc constraints the predicted PDFs are close to measured ones.

Physical properties of a sprinkler water spray

AbstractThis paper reports an experimental study on the physical properties of a sprinkler water spray. The mass flux density, shape of spray pattern, size distribution and velocity of water droplets discharged from two types of 15 mm orifice sprinkler heads were measured. Three operating flow conditions of the sprinkler system, including one specified for the Ordinary Hazard class under the LPC rules for sprinkler design, were set. The sprinkler head was installed above finished floor levels of either 2 m or 2.2 m. The median droplet size was found to be related to the water pressure and the orifice diameter of the sprinkler head as proposed by Dundas. The droplet size distribution function can be fitted by a Rosin–Rammler function.

Modeling of the initial droplet size distribution function in the spray formed by impinging jets

Modeling of the initial droplet size distribution function in the spray formed by impinging jets

Effect of elastic bending energy on the emulsification failure in a microemulsion

Small-angle neutron scattering experiments have been carried out to study the phase stability of a very dilute water-in-oil microemulsion. At the fixed water to surfactant molar ratio of ω = 30, we observed a decrease in the microemulsion droplet radius and an increase in the polydispersity when the dispersed-phase volume fraction, φ, was dilute to less than 1%. Upon further dilution to below 0.1%, the droplets disappeared. This suggested that in the concentration range, 0.1% ⩽ φ ⩽ 1.0%, a single-phase microemulsion was unstable, and a phase separation, known as the emulsification failure, occurred. To understand the interesting phase behavior, we have formulated an analytic solution for the droplet size distribution function for a two-phase microemulsion based on the theory of Borkvec et al. ( J. Colloid Interface Sci. 131, 366 (1989)). We found that the distribution function attained a simple Gaussian form, and the width of the distribution function was inversely proportional to the renormalized elastic bending energy of the microemulsion droplets. Other features predicted by the theory were also in good agreement with the small-angle neutron scattering measurements.

Calculated Characteristics of Droplet Size and Velocity Distributions in liquid sprays

AbstractPredictions of the droplet size and velocity distributions in sprays under isothermal conditions are reported. The calculations are based on the maximum entropy formalism, complying with the conservation laws of liquid mass, momentum and energy. This theoretical approach considers only the macroscopic quantities about the atomization processes, without resorting to the details of the liquid breakup processes such as the onset and growth of instabilities. The derived joint droplet size and velocity distribution function depends on the Weber number as well as the liquid mass, momentum and energy source terms.These parameters represent the conditions under which the atomization occurs. The droplet velocity distributions are truncated Gaussian distributions for any specific sizes. The nondimensional Sauter mean diameter decreases slightly with the Weber number and then approaches an asymptotic constant. The calculated values of D21/D30 are very close to unity which agrees with the experimental observations. The computations also show that the atomization efficiency is very low; less than 2.6 percent.

The time dependent behavior of the ostwald ripening for the finite volume fraction

On the basis of the theory of Tokuyama and Kawasaki on the Ostwald ripening, we investigate the time dependent behavior from the late stage into the scaling region. We calculate numerically the transient behavior of the droplet size distribution function and the average droplet radius for various initial conditions. Moreover we compare the obtained results with the experiments in which the transient behavior of the Al-Li, Ni-Al and Ni-Si alloy systems were investigated for various ageing temperatures. The present theoretical results are in good agreement with these experimental results.

Computer modelling of Ostwald ripening

On the basis of the multiparticle diffusion equation in the Ostwald ripening, we construct a new effective model by using three simplifications: 1. (1) explicit consideration of the screening effect of the diffusion field, 2. (2) the dimensional reduction, 3. (3) the expansion in the volume fraction. We simulate this model for various values of the volume fraction, and obtain the droplet size distribution functions, coarsening rates, the standard deviations and the skewness of the distribution function, which are compared with those of the earlier theories and the recent direct computer simulations of the multiparticle diffusion equation. The present results are in good agreement with those of the theory by Tokuyama and Kawasaki, which have pointed out the importance of the soft-collision processes.

Finite volume fraction effects on Ostwald ripening

We investigate the effect of a finite droplet volume fraction on the Ostwald ripening on the basis of the statistical theory recently developed by us. The theory takes into account both the competitive growth and soft-collision effect of droplets arising from statistical correlations among them. The Lifshitz-Slyozov-Wagner scaling law is found to hold. The scaled droplet size distribution function and the average droplet size are determined self-consistently, up to order Q 1 2 , Q being the volume fraction, by numerically solving the kinetic equation of the theory for long times. The results are in excellent agreement with those of the computer by Voorhees and Glicksman within the data scatter, which is not the case if soft-collision processes are omitted as in all the previous theories.

Numerical simulation of diffusion-controlled droplet growth: Dynamical correlation effects.

Diffusion-controlled coarsening (Ostwald ripening) of precipitated solutions is studied by numerical simulation. An algorithm is devised which exploits the screening of solute concentration fields, thereby removing the restriction to small systems of previous work. Simulation of the coarsening of 5000 droplets at 10% volume fraction reveals long-ranged dynamical correlations which broaden the droplet size-distribution function and increase the coarsening-rate coefficient.

Kinetic equations for Ostwald ripening

A new viewpoint on the kinetics of Ostwald ripening is presented by studying the kinetic equation recently derived for the late stage of phase separation. It is shown that the average droplet radius grows as t 1 3 and the number density of droplets decays as t -1. An important effect of a soft (distant) collision on coarsening is discussed. Thus the relative droplet size distribution function is found to obey a second-order differential equation. The coarsening rate is also expressed in terms of the distribution function, leading to a dependence on the volume fraction of the minority phase.

A high resolution infrared radiative transfer scheme to study the interaction of radiation with cloud

AbstractThis paper describes a high resolution radiative transfer scheme which calculates infrared fluxes and heating rates in a cloudy atmosphere. It is intended as a research tool for use in studies of the role of radiation in the physics of fog and layer cloud. The spectrum is split into five bands and allowance is made for molecular absorption by the water vapour 6.3 μm band and the rotation band beyond 20 μm, the 15 μm carbon dioxide band, the 9.6 μm ozone band, and the continuum absorption by water vapour in the 10 μm atmospheric window. The strong absorption by cloud water droplets is calculated directly from the droplet size distribution function. The scheme has been run with a model stratocumulus cloud included, using data based on tethered balloon observations at Cardington. A large cooling rate of 8.7 K per hour is shown to exist at the cloud top.

The Effect of Heat Transfer Coefficient, Local Wet Bulb Temperature and Droplet Size Distribution Function on the Thermal Performance of Sprays

Energy balance considerations indicate that the droplet heat transfer coefficient, local wet bulb temperature, and droplet size distribution function are the basic parameters affecting spray system thermal performance. Within the range of available experimental data, results indicate that the Ranz-Marshall correlation gives an agreement to within ±5.0 percent of measured droplet temperatures at the pond surface for a medium wind range of between 2.5 and 5 m/s. The local wet bulb temperature is taken as the arithmetic mean of the initial and final wet bulb temperatures. For wind speeds greater than 3.5 m/s, the local wet bulb can be taken as the ambient. The modified log normal distribution of Mugele and Evans provides the best description of the droplet size distribution. Further, through the introduction of a correction term, the Spray Energy Release (SER) can be deduced from single droplet information.

Diffusing droplet model for Rayleigh linewidth studies on critical fluids

Measurements of the intensity autocorrelation of light scattered from diffusing micropheres suspended in a normal fluid show that if the particle radii satisfy the condition $l\ensuremath{\lesssim}{\ensuremath{\lambda}}_{0}$ where ${\ensuremath{\lambda}}_{0}$ is the wavelength of the incident light, and if the suspension is polydisperse (a finite-width particle-size distribution), the experimental diffusion constant displays a dependence upon the scattered wave number $k$ which is qualitatively the same as that for a critical fluid system in the nonhydrodynamic ($k\ensuremath{\xi}\ensuremath{\gtrsim}1$) regime. These experimental observations have led us to propose a model of a critical fluid in which the order-parameter fluctuations are considered as spherical molecular clusters, or droplets, performing Brownian motion in a normal host fluid. The droplets are assumed to have a Gaussian index of refraction spacial profile, and a particle-size distribution $N(l)$ characterizing the suspension determined from the requirement that the scattered light intensity be of the modified Ornstein-Zernike form. In a first approximation, the droplets are assumed to diffuse without changing size for times of the order of the characteristic diffusion time. The intensity-autocorrelation function of light scattered by our model system of diffusing droplets is evaluated, and the effective Rayleigh linewidth is found to agree to within a constant factor of order 1 with the ansatz for the critical part of the Rayleigh linewidth chosen by Perl and Ferrell. The resulting line-shape function is nearly Lorentzian, except in the wings where experimental detection of a departure from Lorentzian behavior becomes extremely difficult. Our droplet-size distribution is very similar to that which results from the static droplet model of Fisher which has been applied successfully to describe static critical phenomena in fluids below the critical temperature. In the diffusing droplet model, the $k$ dependence of the diffusion constant extracted from light-scattering measurements on critical fluids is seen to be an artifact introduced by the light-scattering process, and introduces no new physical information concerning the critical fluid behavior which is not contained in the droplet-size distribution function.

Comments on “Empirical Fog Droplet Size Distribution Functions with Finite Limits”

Comments on “Empirical Fog Droplet Size Distribution Functions with Finite Limits”

Empirical Fog Droplet Size Distribution Functions with Finite Limits

Abstract The Deirmendjian-Chu-Hogg fog droplet size distribution function N (a) = Caα exp[-(α / γ)aγ] restricts the parameters α and γ to he positive. We outline a procedure for calculating realistic fog distributions, including appropriate normalization, and show that actual distributions are described by both positive and negative α and γ.