James D. Felske

Refractive indices of soot particles deduced from in-situ laser light scattering measurements☆

Classical and dynamic laser light scattering data are obtained for a fuel-rich premixed methane/oxygen flat flame. Particle size distribution is determined directly from the dynamic light scattering measurements. Particle number density and complex refractive index are then inferred from classical scattering and extinction data by introducing a relation between the real and imaginary parts of the complex electrical permittivity.

Mechanistic Model for Aluminum Particle Ignition and Combustion in Air

A mechanistic model for the ignition and combustion of an isolated aluminum particle burning in air is presented. The model consists of two stages, ignition and combustion. In the ignition stage, melting and heterogeneous surface reactions (HSR) are assumed to occur until a predefined transition temperature of the oxide is attained. In the combustion stage, a quasi-steady state diffusion flame is assumed, and a new conserved scalar formulation is presented that accounts for the deposition of metal oxide on the surface of the molten aluminum. A system of nonlinear ordinary differential equations that describes each stage self-consistently with the gas-phase analysis is developed. Representative results are presented for a range of ambient temperature conditions and compared to experimental measurements. Predictions of overall burn rates, particle velocity, and flame radius show good agreement with experimental data. Also discussed is the extension of the conserved scalar approach to include a more generalized oxidizing environment as well as HSR from nitride reactions during the quasi-steady burning stage.

The effect of soot particle optical inhomogenity and agglomeration on the analysis of light scattering measurements in flames

Abstract Computations have been performed for homogeneous and radially inhomogeneous spheres plus agglomerated structures composed of spherical primary units. The ranges of refractive index and particle size considered are typical of soot in flames. The effects of uncertainty in the refractive index and neglect of its radial distribution on inferring spherical particle sizes and concentrations from in situ light-scattering measurements are delineated. A framework is established for computing various scattering characteristics of agglomerated particles in terms of the scattering functions for spherical particles. The results achieved for agglomerates indicate that mean values of the particle concentration, number of units in an agglomerate and overall agglomerate size may be inferred from light-scattering data.

Analytical solution for Stokes flow inside an evaporating sessile drop: Spherical and cylindrical cap shapes

Exact analytical solutions are derived for the Stokes flows within evaporating sessile drops of spherical and cylindrical cap shapes. The results are valid for all contact angles. Solutions are obtained for arbitrary evaporative flux distributions along the free surface as long as the flux is bounded at the contact line. Specific results and computations are presented for evaporation corresponding to uniform flux and to purely diffusive gas phase transport into an infinite ambient. Wetting and nonwetting contact angles are considered with the flow patterns in each case being illustrated. For the spherical cap with evaporation controlled by vapor phase diffusion, when the contact angle lies in the range 0≤θc<π/2, the mass flux of vapor becomes singular at the contact line. This condition requires modification when solving for the liquid-phase transport. Droplets in all of the above categories are considered for the following two cases: the contact lines are either pinned or free to move during evaporation....

Determination of refractive indices of Mie scatterers from Kramers–Kronig analysis of spectral extinction data

Kramers–Kronig relations for semiconducting particles are established for a set of functions related to the scattering amplitude function in the forward direction. It is shown that some of these relationships allow subtractive Kramers–Kronig relations to be formed that are independent of any material constants. As a consequence, the refractive-index spectra can be determined without requiring the value of the index to be known at any frequency a priori. The approach is to use the optical theorem to establish the spectrum of one part of a complex function from the measured data. Its Kramers–Kronig counterpart is then computed, thereby establishing the values of two functions at each frequency. Since the dependence of each of the functions on the refractive index is known from the Mie theory, the real and imaginary parts of the index are then determined by simultaneous solution of the two functions at each frequency. Calculations are presented based on simulated data for combustion-generated hydrocarbon soot particles, and the influence of various types of experimental error on data inversion is investigated.

The range of validity of the Rayleigh limit for computing mie scattering and extinction efficiencies

Abstract For the small particle limit for scattering by either absorbing or dielectric spheres, values of the size parameter are determined below which various approximate expressions for the scattering and extinction efficiencies are accurate to within 1%. Simple, analytical criteria for ensuring 1% accuracy are given in terms of the size parameter and the complex refractive index. A much broader range of refractive indices is considered than has been studied previously.

Gray gas weighting coefficients for arbitrary gas-soot mixtures

Abstract A method is developed for determining the gray gas weighting coefficients for gas-soot mixtures from the coefficients which separately model the soot behavior and the behavior of the gases. Representations for both the emissivity and absorptivity are achieved. The approach is shown to be accurate over wide ranges of temperature, pathlength and soot concentration.

A technique for determining the spectral refractive indices, size, and number density of soot particles from light scattering and spectral extinction measurements in flames

Abstract A technique is presented that allows the spectral refractive indices, size, and number density of soot particles in flames to be inferred from a combination of single-wavelength light scattering and multiwavelength extinction measurements. In contrast to previous schemes for inferring optical properties, the present approach does not require the introduction of a model for the spectral dispersion of the refractive index; it employs Kramers-Kronig theory instead. When applied to spherical particles, the only approximations involved are the usual ones associated with using Kramers-Kronig theory to analyze actual data, that is, for those spectral regions where experimental data are not obtainable, extrapolations and interpolations must be made. The particles, however, may be of any size, including Rayleigh-size (for which it is particularly difficult to simultaneously infer particle size, concentration, and complex refractive index). The approach requires a combination of static (elastic) and dynamic (quasielastic) laser light scattering measurements plus measurements of the spectral transmittance. Closure is achieved in data analysis by the introduction of an exact (model-independent) Kramers-Kronig dispersion theory for scattering amplitude functions. The influence of various spectral extrapolation schemes (required because of the finite spectral width of the transmittance data) is thoroughly investigated.

Analytical solution for inviscid flow inside an evaporating sessile drop.

Inviscid flow within an evaporating sessile drop is analyzed. The field equation E;{2}psi=0 is solved for the stream function. The exact analytical solution is obtained for arbitrary contact angle and distribution of evaporative flux along the free boundary. Specific results and computations are presented for evaporation corresponding to both uniform flux and purely diffusive gas phase transport into an infinite ambient. Wetting and nonwetting contact angles are considered, with flow patterns in each case being illustrated. The limiting behaviors of small contact angle and droplets of hemispherical shape are treated. All of the above categories are considered for the cases of droplets whose contact lines are either pinned or free to move during evaporation.

Radiative transport in a planar medium exposed to azimuthally unsymmetric incident radiation

An analytical solution is developed for the radiation field engendered by illuminating an absorbing/anisotropically scattering planar medium with an azimuthally unsymmetric incident flux. The boundaries of the medium are allowed to possess both specular and diffuse reflection characteristics. The problem is mathematically reduced to solving a system of azimuthally independent equations which may be analyzed by many existing techniques. A solution scheme is formulated in terms of singular eigenfunctions and solved using a modified FN method. Computations are performed for the azimuthally symmetric case of irradiation by parallel rays at oblique incidence. Several different phase functions are considered and results are presented for the discrete eigenvalues, the heat flux distributions within the medium, the reflectance and transmittance of the slab and the angular distribution of the intensities at the boundaries.