In many materials processing and manufacturing situations such as steel, aluminum, ceramics and glass, gas bubbles can form in liquid and solid phases. The presence of such bubbles affects the thermophysical properties and radiation characteristics of the two-phase system and hence the transport phenomena. This paper presents a general formulation of the radiation characteristics of semitransparent media containing large gas bubbles (bubble radius is much larger than the wavelength of radiation). Sample calculations for the spectral absorption and extinction coefficients and single scattering albedo of soda-lime silicate glass containing bubbles are discussed. Particular attention is paid to the effect of the volumetric void fraction and the bubble size distribution. Results clearly show that the presence of bubbles strongly affects the radiation characteristics of the semitransparent media containing entrapped gas bubbles, particularly if bubbles, void fractions, and spectral absorption coefficient of the continuous phase are small.

# Your search: "author:"Viskanta, Raymond""

## filters applied

## Type of Work

Article (11) Book (0) Theses (0) Multimedia (0)

## Peer Review

Peer-reviewed only (11)

## Supplemental Material

Video (0) Audio (0) Images (0) Zip (0) Other files (0)

## Publication Year

## Campus

UC Berkeley (0) UC Davis (0) UC Irvine (0) UCLA (11) UC Merced (0) UC Riverside (0) UC San Diego (0) UCSF (0) UC Santa Barbara (0) UC Santa Cruz (0) UC Office of the President (0) Lawrence Berkeley National Laboratory (0) UC Agriculture & Natural Resources (0)

## Department

## Journal

## Discipline

## Reuse License

## Scholarly Works (11 results)

This paper is the second part of a study on bubble transport, growth and shrinkage in three-dimensional gravity driven flow. Sample calculations with applications to glass melting furnaces are presented. First, a consistent set of thermophysical properties of the most common composition [74 SiO2-16 Na2O-10 CaO (mol.%)] of soda-lime silicate glass or similar compositions over the temperature range of 1000 to 2000 K is reported. The population balance equation is solved for the bubble density function using the backward method of characteristics. The zeroth to third order moments, i.e, number of bubbles, average radius, molar gas fraction, interfacial area, and void fraction are computed by numerical integration. Results for both transient and steady state operations are presented and analysed. Two cases are considered (1) bubbles containing only CO2 and (2) bubbles containing a diffusing gas (O2) and a non-diffusing gas (CO2). The feasibility of such complex calculation is demonstrated and is in qualitative agreement with reported results.

This paper is concerned with semi-batch foams generated by injecting gas bubbles in a vertical column containing a liquid phase at rest. Its aim is to better understand the physical mechanisms responsible for foam formation at the liquid free surface and to predict the superficial gas velocity for onset of foaming. The model for predicting the onset of foaming is derived from the one-dimensional drift-flux model for gravity driven flow in the absence of wall shear. The analysis is based on experimental data reported in the literature and covers a wide range of physico-chemical properties, bubble sizes and shapes, and flow regimes. It identifies the inhibition of coalescence between rising bubbles and bubbles at rest at the free surface as a key mechanism responsible for the onset of foaming. A semi-empirical correlation for high viscosity fluids has been developed and good agreement with experimental data is found.

This paper presents a new numerical method for solving the population balance equation using the modified method of characteristics. Aggregation and break-up are neglected but the density function variations in the three dimensional space and its dependence on the external fields are accounted for. The method is an intepretation of the Lagrangian approach. Based on a pre-specified grid, it follows the particles backward in time as opposed to forward in the case of traditional method of characteristics. Unlike the direct marching method, the inverse marching method uses a fixed grid thus, making it compatible with other numerical schemes (e.g., finite-volume, finite elements) that may be used to solve other coupled equations such as the mass, momentum, and energy equations. The numerical solutions are compared with the exact analytical solutions for simple one-dimensional flow cases. Very good agreement between the numerical and the theoretical solutions has been obtained confirming the validity of the numerical procedure and the associated computer program.

This paper is the second part (Part II) of a parametric study of the flow and thermal structure in glass melting furnaces with a throat. The effects of the following parameters are discussed: (i) the batch velocity, (ii) the melting temperature, (iii) the submerged depth of the batch, (iv) the wall heat losses, and (v) the thickness of glass melt containing gas bubbles under the batch. The study indicates that the partially submerged batch and heat losses through the refractories have a strong impact on both the longitudinal and spanwise flow patterns of the molten glass. These physical phenomena must be accounted for if one wants to realistically simulate the natural convection circulation of the molten glass in the bath.

This paper presents a study of the flow and thermal structures in the molten glass bath of a typical glass melting furnace with a throat but without air bubblers or electric boosting. Different separate effects on the flow structure of the glass melt are simulated, but only the glass melt is considered. The net heat flux distribution is imposed at the combustion space/glass melt interface, and its effects on the flow and thermal structures of the glass melt are analyzed in a systematic manner by changing the heat flux distribution while keeping the total heat input to the glass bath constant. The main purpose of the work is to evaluate the capability of the furnace operators to control the glass flow and temperature fields by adjusting the firing in the combustion space. The physical phenomena affecting the flow structure in the glass melt are analyzed and discussed in detail. The major results of the study indicate that (i) the heat flux distribution has no significant effect on the flow structure of the glass melt under the batch blanket where several Rayleigh-Benard cells develop in the spanwise direction, (ii) a heat flux gradient in the longitudinal direction is required to generate two recirculation loops in the direction, and (iii) steep heat flux gradient in the refining part of the tank increase significantly the size of the refining recirculation loop near the front wall.

This paper presents an approach for predicting the thickness of isothermal foams produced by blowing gas in a liquid solution under steady-state conditions. The governing equation for the transient foam thickness has been non-dimensionalized, and two dimensionless numbers have been identified to describe the formation and stability of this type of foam: \Pi_1 = {Re}/{Fr} and \Pi_2 = Ca H_{\infty}/r_0. Physical interpretation of the dimensionless numbers has been proposed, a power-law type relation has been assumed between \Pi_1 and \Pi_2 (i.e., \Pi_2=K \Pi^n_1). Experimental data available in the literature have been used to determine the empirical parameters of the correlation K and n. The experimental conditions cover a wide range of viscosity, density, surface tension, gas superficial velocity, and average bubble radius. The model is valid for foams formed from high viscosity liquids bubbled with nitrogen, air, helium, hydrogen, and argon injected through single, multi-orifice nozzles or porous medium. Comparison between the correlation developed and the experimental data yields reasonable agreements (within 35% error), given the broadness of the bubble radius distribution around the mean value, the uncertainty of the experimental data and of the thermophysical properties. Predictions have been found to be very sensitive to the average bubble radius. A more refined model is still needed which should be supported by a careful experimental studies. Finally, suggestions are given to extend the present work to foams generated from low viscosity solutions.

The objective of this paper is to present an engineering model based on fundamentally sound but simplified treatment of mass diffusion phenomena for practical predictions of the effective diffusion coefficient of gases through closed-cell foams. A special attention was paid to stating all assumptions and simplifications that define the range of applicability of the proposed model. The model developed is based on the electrical circuit analogy, and on the first principles. The analysis suggests that the effective diffusion coefficient through the foam can be expressed as a product of the geometric factor and the gas diffusion coefficient through the foam membrane. Validation against experimental data available in the literature gives satisfactory results. Discrepancies between the model predictions and experimental data have been observed for gases with high solubility in the condensed phase for which Henry's law does not apply. Finally, further experimental data concerning both the foam morphology and the diffusion coefficient in the membrane are needed to fully validate the model.

This paper presents a simple, experimentally validated approach to analyze the transient formation of a foam layer produced by injecting gas bubbles in a foaming solution. Based on experimental observations, three different regimes in the transient growth of the foam have been identified as a function of the superficial gas velocity. A model based on the mass conservation equation for the gas phase in the foam combined with three different models for the average porosity is proposed. It is shown that for practical calculations a constant average porosity equal to 0.82 can be used. The model predictions show very good agreement with experimental data for low superficial gas velocity and provide an upper limit of the foam thickness for intermediate and large superficial gas velocities. The paper discusses the physical mechanisms that may occur during the foam formation and the effects of the superficial gas velocity on the foam dynamics. The present analysis speculates several mechanisms for the bursting of the bubbles at the top of the foams and proposes the framework for more fundamental and detailed studies.

We report experimental measurement of radiation characteristics of fused quartz containing bubbles over the spectral region from 1.67 to 3.5 microm. The radiation characteristics were retrieved by an inverse method that minimizes the quadratic difference between the measured and the calculated spectral bidirectional transmittance and reflectance for different sample thicknesses. The theoretical spectral transmittances and reflectances were computed by solving the one-dimensional radiative transfer equation by the discrete-ordinates method for a nonemitting, homogeneous, and scattering medium. The results of the inversion were shown to be independent of the sample thickness for samples thicker than 3 mm and clearly demonstrate that bubbles have an effect on the radiation characteristics of fused quartz.