U.S. DEPARTMENT OF AGRICULTURE • FOREST SERVICE • FOREST PRODUCTS LABORATORY • MADISON, WIS. In Cooperation with the University of Wisconsin

U.S. FOREST SERVICE

RESEARCH NOTE

FPL-0137 JUNE 1966

LIGHT-TRANSMlTTlNG AND LIGHT-SCATTERING PROPERTIES OF SMOKE

The FOREST SERVICE of the U.S. DEPARTMENT OF AGRICULTURE is dedicated to the principle of mul­tiple use management of the Nation's forest resources for sustained yields of wood, water, forage, wildlife, and recreation. Through forestry research, cooperation with the States and private forest owners, and management of the National Forests and National Grasslands, it strives - as directed by Congress - to provide increasingly greater service to a growing Nation.

LIGHT-TRANSMITTING AND LIGHT-SCATTERING

PROPERTIES OF SMOKE1

By

Gene E. Wampfler Physical Science Aid

Forest Products Laboratory,2 Forest Service U.S. Department of Agriculture

Summary

A study was made of the light-transmitting and light-scattering properties of smoke to learn more about methods of measuring smoke density. The study was done in two parts; the first consisted of a literature survey to determine what is known about light transmission and light scattering in smoke systems. In term of light transmission measurements it was learned that the Beer-Lambert law applies to smoke, but that light-scattering theories may not apply well because of the complexity of the equations for such polydisperse system as smoke.

The second phase of the study involved experimental work which supported some of the findings described in the literature for optical measurements of smoke, specifically the application of the Beer and Lambert laws. The purpose of this work was to become familiar with the apparatus, with methods of optical measurement, and with the problems involved in smoke density measurements.

The results of these two phases of work allowed observations and suggestions on methods and apparatus to be used in making smoke density measurements.

1 This study was performed as a part of the Forest Products Laboratory Summer Student Training Program, under the general direction of J. J. Brenden and H. W. Elckner, Fire Research Project.

2 Maintained at Madison, Wls., in cooperation with the University of Wisconsin.

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Introduction

Building codes sometimes require a performance rating of construction materials to indicate their relative fire hazard. Such ratings may measure rate of flame spread, resistance to fire penetration, heat contribution, and amount of smoke produced. The smoke rating is an important one because smoke seriously hinders vision in evacuating buildings and in controlling the fires. An accurate smoke density rating on construction materials would allow the builder to choose materials that would produce the least amount of smoke and to plan safer fire escape routes.

Unfortunately, smoke density ratings are usually empirical and not at all quantitative. Many ratings are suited only to the conditions under which they were obtained and give no universal expression of the hazard of smoke in obscuring vision.

The simplest and most widely used method of measuring smoke density is based on light transmission through a smoke path. In this method, a light source and a light receptor are located on opposite sides of the smoke path. The light receptor is connected to a meter which is calibrated to read 100 percent transmission when there is no smoke. When smoke passes between the light source and light receptor, the amount of smoke is read in terms of percent transmission of the light through the smoke path.

Many techniques for measuring smoke are available and a large amount of literature has been published in this field. A literature survey was made to discover just how much was known about smoke density measurements and to discover whether any of the methods being used could be further developed or improved. The optical measurement of smoke is the most promising method because of convenience and sensitivity and depends on the theories of light transmittance and light scattering. Therefore these two theories were also investigated. Later, experimental work was done to get practical working experience with actual optical measurements of smoke system and the problems involved, and to determine the applicability of the Beer-Lambert law for such systems.

Before proceeding with further discussion of smoke systems, a definition of smoke will be helpful. Smokes are generally defined as gaseous disperse system formed by combustion, condensation, or pulverization. The main

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criterion is particle size: 3

most smoke particles fall in the range of 0.1 to 5 microns in diameter (6). Experimental work has indicated that the average particle diameter for wood smoke is about 0.2 to 0.4 micron (5).

Particulate system, such as smoke, are subject to many physical phe­nomena such as electrification, coagulation, and diffusion. Precise theories have been worked out and applied to such phenomena. Of particular interest here are the optical properties of smoke systems which include light trans­mittance and light scattering.

Theory of Light Transmittance

The theory of light transmittance deals mainly with an exponential relation­ship between the attenuation and concentration of light and the length of the smoke chamber through which it passes. The Lambert law is based on the assumption that a change in the length of the chamber, 1, will produce a cor­responding change in the intensity of the transmitted light, I:

Integration of this equation followed by application of appropriate limits for light intensity from I --the initial intensity, to I--the final intensity, results o in the Lambert law:

The constant k is known as the extinction coefficient and is a measure of the space rate of attenuation due to absorption as energy propagates from its source (11). The law was extended by Beer to include an expression for con­centration, c. The Beer-Lambert law thus became:

3 Underlined numbers In parentheses refer to Literature Cited at the end of this report. Other articles pertinent to light scattering and smoke are listed under the heading Additional References.

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The expression log10(Io/I) is the optical density, D; the expression kcl is the

extinction, and the term I/Io is the transmittance, T. Thus:

The Beer-Lambert law applies to a system if certain restrictions are im­posed. According to one source (2) the law is strictly true only for a parallel beam of monochromatic light for which the optical density is independent of the light intensity and the receiver sensitivity. It fails if there is any association or dissociation of the solute. A change in particle size also affects the optical density with larger particles usually causing a decrease in optical density. A further precaution must be taken to assure that only 180° transmitted light and no scattered or reflected light reaches the receiver (11).

A solute will absorb light relatively more strongly at high concentrations than at low concentrations and correspondingly greater path lengths. This deviation is due to van der Waal's forces between the molecules, which arise when the gas is compressed with resultant alterations in the fine structure of the electron shells. The individual molecules are thus more distorted at high concentrations than at low concentrations (4). For this reason, the Beer-Lambert law may apply in systems only up to a certain concentration level which will vary depending on the solvent and solute.

Although originally applied to liquid-solid phase measurements, the Beer-Lambert law has been tested for smoke systems and does apply under the conditions described above.

The basic procedure for making a transmission measurement is a simple one. Since the Beer-Lambert law is concerned with the ratio I /I, an absolute o measurement of light intensity is not needed, and an optical system which will give a relative measurement of I to I may be used. Data are first collected o on smoke of known concentration using a constant, known smoke chamber length. From these data, the extinction coefficient, k, is computed. If care is taken to calibrate the equipment with a smoke of the same particle size and refractive index as an unknown smoke, then the optical density of the unknown smoke can be used to calculate an accurate value of its concentration by using the experimentally determined extinction coefficient and the same chamber length (13).

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Measuring the optical density also allows particle size to be assessed if the density of the particles is known. In mathematical form:

where, n = number of particles per cubic centimeter s = projected area of each particle 1 = length of the smoke chamber.

But optical density is:

or, 2.303D = nsl

If the particles have radius r, and concentration c, in grams per cubic centi­meter then,

where p = density of the particles. Since s = π r2, the expression for optical density reduces to:

This expression can be used to find r by experimentally determining the optical density, calculating the concentration from the Beer-Lambert law, and knowing the density (12).

Theory of Light Scattering

When light strikes small particles of a suspension of smoke, the oscillating electric field of the light induces oscillating electric moments in the particles. If the frequency of the induced oscillations is much different from the natural frequency of the electrons, the smoke particle will act as a secondary source of radiation of the same wavelength, this being scattered light. A small amount of the incident light is also absorbed and the molecules of the smoke particle are raised to higher energy states. The particles re-emit the energy at certain specific wave lengths such as the Ramen spectra. This amount of radiation is usually very much smaller, however, and may be neglected. If the frequency of

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the induced oscillations is close to the natural frequency of the electrons in the particles, absorption and occasionally fluorescence occur, and the theory must be modified (15). The theory of light scattering depends upon the size of the particles and the wavelength of the incident light.

There are two ways to approach the calculation of light scattering in a smoke system. The first involves the direct calculation of the radiation of each scattering particle and summing all the contributions of the particles. The second involves treating the scattering as the result of statistical fluctuations in the density or concentration, causing fluctuations in the dielectric constant. For many light-scattering problems it was found by those who developed the scattering theories that both approaches were necessary. The interference treatment was developed by Lord Rayleigh for isotropic, spherical particles whose maximum dimensions are less than one-twentieth the wavelength of the light used. The Rayleigh theory was adopted by Debye (3), who was the first to show that it could be applied to dilute solutions of high polymers which do not strongly interact, The fluctuation theory, derived by Einstein, Schmoluchowski, Gans, and others, has been found much more useful for liquids, concentrated solutions, and strongly interacting systems in which the direct calculation of interference becomes too difficult.

Rayleigh’s theory points out that the amount of light scattered is directly proportional to the second power of the volume of the particle and is inversely proportional to the fourth power of the wavelength of the light (10, Part II, Vol. 5). The intensity of the scattered light is greatest in the direction parallel to that of the incident beam, both forward and backward, and weakest in the direction perpendicular to the incident beam (11). When a particle exceeds the size limit placed upon it by Rayleigh’s theory, however, the forward scattering greatly exceeds the backward scattering, Initially, the scattering increases with particle size, but it reaches a maximum and decreases again at still greater particle sizes. With even larger particles many maxima and minima appear (11).

When the range of particle size exceeds the Rayleigh limits and falls in the region of 0.1 to 0.8 times the wavelength of light, destructive interference of light scattered from different parts of the same particle causes deviation from the Rayleigh light-scattering theory. For particles larger than 0.8 times the wavelength of light, the theory of scattering is very complex and has been developed sufficiently to allow calculation of concentration and particle sizes for isotropic spheres only (9, Vol. 14, pp. 373-380).

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The limitations in the applicability of the Rayleigh theory are rather severe. The particles themselves must be transparent, optically isotropic spheres less than one-twentieth the wavelength of the incident light in diameter, and must exist in a highly dilute medium, where there is no interference between particles due to light obscuration or reflection In practice, for visible light, the size limits for such particles vary from about 0.03 micron in radius down to molecu­lar dimensions. The theory has a rather restricted value for the study of particulate systems in general, For smoke, in which the particles are irregular and larger than the Rayleigh limit, the theory cannot be applied. However, it provides the foundation for more general theories.

A large-particle theory which is more applicable to smoke systems was developed by Mie and is general enough to cover particles ranging in size from the Rayleigh region up to the region where classical geometric optics take over. Since Mie developed his theory, equations have also been derived by others which apply to randomly coiling polymers, rods, and thin disks.

The Mie theory defines the scattered field of an optically isotropic sphere of known refractive index as a spherical wave consisting of two groups of partial waves. The Mie equation is algebraically stated as follows:

The values of i and i are defined in terms of the coefficients of the electric1 2 and magnetic waves, a n and b n , respectively.

Total scattering by one particle for unit intensity is given by the equation:

Since 1941, tables of scattering functions have been published to cover particles of several refractive indices and a limited range of radii (9). As the equations indicate, calculations are laborious, and when particles are of a size greater than a few wavelengths in radius, the series expressions involved in the Mie theory converge slowly, and the scattering equations are very cumbersome. As a result, simpler methods have been sought to calculate the scattering. An approximation of the Mie equation is expressed by:

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where, I = intensity of scattered light n = particle number concentration r = radius of particle

The exponent p is a number which was found to be six for Rayleigh scattering and varies down to two for very large particles. The exact value of p has been experimentally determined for particles of a few different refractive indices and wavelengths, but not enough data are available to apply this equation to every system (9).

In a dilute system of particles, the intensity of the light scattered by a thin layer of n similar scattering particles is simply n times the intensity of that scattered by a single particle, In more concentrated systems, however, where each particle receives radiation reflected from other nearby particles, multiple scattering occurs and the theories developed do not apply. The problem of calculating the transmission of radiation through such a system is of great mathematical complexity, and exact solutions exist only for highly idealized conditions (9); limited tables of calculations based on the Mie theory for absorbing particles are available, but again they only deal with particles of several refractive indices.

No satisfactory mathematical analysis of light scattering has been made for polydisperse, heterogeneous aerosols, such as smoke. The main problem is one of size distribution which excludes any simple application of the scattering functions for a homogeneous dispersion. Although a quantitative measurement of scattering cannot be made on such systems, several qualitative features can be noted. The absence of distinctive color in the scattered light indicates hetero­geneity, An investigation of the amount of polarization at different angles may give some indication of the relative size of the particles, Determination of the ratio of light scattered in a forward direction to that scattered in a backward direction will also give an idea of the size range of the particles (9).

Smoke particles generally have a radius on the order of the wavelength of light, In order to apply the theory of Mie to find the relationship between scat­tering and size, it must be assumed that the particles are homogeneous spheres of known refractive index. Smoke usually consists of a conglomeration of small particles, is rarely homogeneous, its refractive index is difficult to measure or estimate, and the chances of multiple scattering are very great, The only way possible, then, of finding the law of scattering for such particles is by direct experimentation (20).

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It should be noted that for monodisperse systems, indirect optical methods are available for assessing particle size and concentration (9). These methods do not apply to heterogeneous system, however. For the sake of completeness these methods are listed here: measurement of transmission at different wave­lengths, measurements based on the intensity of scattered light, spectral colors as an index of particle size, particle size from coronae, and particle size from polarization measurements. All of these methods are rather involved and will not be discussed here.

Methods of Optically Measuring Smoke Density

A variety of relatively simple methods are available for measuring smoke density. One such method is based on a visual comparison between the smoke produced and a set of Ringelmann charts. These charts consist of sets of numbered sheets of white paper covered by a grid of black lines of different thicknesses for each sheet. At a distance, the lines merge with the white back­ground to produce a shade of gray which is compared to the smoke as seen in sunlight. The charts are usually numbered 0 through 5, and the smoke density is characterized by these Ringelmann numbers (6). A variation of this method is the smoke meter in which the open fraction of a spinning sector wheel is varied until the color of the sky, which is seen through it, matches the smoke (6). These systems are convenient and economical, but the inadequacies out­weigh the advantages. These methods are inadequate because they are completely subjective and depend on the sunlight and other atmospheric conditions; they are limited to daytime use, and depend on the thickness of the smoke beam, its temperature, and velocity (16).

Particulate sampling is another comon method of measuring smoke con­centration. The smoke is collected by suitable means, is weighed, and the concentration is expressed as weight per unit volume. The methods of collection include filter paper, filtering mats and packed beds, electrostatic cyclone and thermal precipitators, scrubbers, impingers and impactors, and air filters. In another technique, smoke is drawn through a filter paper for a given length of time, and the resulting blackness of the deposit is compared to a standard color chart (16).

The methods just described all have their limitations but the greatest potential for accurate measurements of smoke density is a practical application of the light-transmittance and -scattering theories, Several instruments or arrange­mente have been developed on the basis of these theories and the question of

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whether the Beer-Lambert law can be applied to smoke system has been the subject of many of these investigations. In one of the earliest studies that related the intensity of transmitted light to smoke concentration Tolman worked with the Tyndall beam (18).

The Tyndall beam is the luminous path formed by the scattering of a beam of light that passes through a medium containing small suspended particles. In Tolman's work, the light-intensity measurements were made at right angles to the Tyndal1 beam. Smoke was produced by carefully leading together dry ammonia and hydrochloric acid gases at known rates to form ammonium chloride smoke. After generation, the smoke was led through the examining chamber and the concentration varied by means of air dilution. The results, when plotted, indicated a linear relationship between concentration from 0.0 to 1.2 milligram per liter of ammonium chloride smoke and light intensity readings from 0 to 90 foot-candles. The conclusion was drawn that for low concentrations a strict proportionality exists between concentration and strength of the Tyndall beam.

A study directly relating light transmission and smoke concentration was made on wood smoke by Foster (5) who used an unfiltered light from a tungsten lamp. After generation, the smoke was drawn through a cell where the trans­mission measurement was made. The smoke was then electrically precipitated to determine its mass concentration. A plot of optical density against mass concentration indicated a linear relationship between the two. Foster gave further grounds to this experimental observation by theoretical calculations.

In a study by Stoecker (16), light transmission was measured against concen­tration. Again, a correlation was found between photoelectric cell readings and the weight concentration of the smoke. Several factors were found which must be taken into account when making such determinations. These are: (a) the temperature of the gases where the photocell is installed; (b) the thickness of the smoke column (a standard thickness must be used when comparing results); and (c) the percent of ash in the solid particles. The presence of ash causes a reduction in the amount of light absorbed.

In another study (8), tests from a hand-fired Lancashire boiler showed that the opacity of smoke, expressed in term of either its optical density or Ringelmann number, can be correlated with the concentration of suspended matter in flue gases.

A similar confirmation on smoke from a chimney flue is reported by Green (6), who found in his reviews of experimental work that optical density is related

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linearly to concentration. Since the completion of this work new instruments such as a high-sensitivity-recording density meter and an instrument for optical measurement of the coarser particles emitted by chimneys have been developed (9, p. 404).

At the present time, many optical measurements of smoke are being made. They vary in nature from measurement of air-pollution to measurements of effluent from smokestacks. Several commercial instruments measure smoke density in various ways. A few of these instruments are designed specifically for smoke systems while others are for air sampling or measurement of particu­late matter in general. Many of them work on a gravimetric principle in which the particulate matter is trapped by filtering or other means, but some depend on optical methods of analysis.

The optical density of smoke in chimneys is measured in three different ways. In the first, the measurement is made on the smoke as it passes up the chimney by directing a beam of light across the chimney toward a photocell. As there is not always adequate mixing of the products of combustion and the excess air, it is necessary to employ a mixer below the smoke-measuring apparatus,

In the second method a representative sample of the flue gases is drawn through an optical tube containing a photocell at one end and a lamp which can be moved along the tube manually or automatically at the other end. The position of the lamp is adjusted to give a predetermined cell output as the sample of suspended material flows through the tube. The position then gives a measure of the optical density of the smoke.

The third method allows the smoke emerging from the chimney to pass out into the atmosphere through an inclined tube, the lower end of which is sealed by a glass plate. The smoke in the tube is then matched visually against a set of calibrated neutral optical screens.

All of these system must be calibrated by determining the relationship between the optical density and the concentration of the smoke. This is done by withdrawing samples of smoke particles and weighing them (20, Vol. X, p. 775).

A method of measuring smoke density using simple light transmission measurements has been developed by the Rohm and Haas Company (1). In this method, a test apparatus is used which consists of a smoke chamber with a light source located on one side. The light beam traverses the 12-inch path through the chamber and strikes a photoelectric cell located on the opposite

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wall. The specimen to be tested is ignited and burned inside the closed container, and readings of light transmission are taken at 15-second interval. These data are plotted against time, and the smoke production rate (slope of the curve) and the total smoke produced (area under the curve) can be determined. The maximum smoke density can also be read from the curve.

A similar method to the one above has been used at the Forest Products Laboratory to measure the smoke produced by fire-retardant-treated wood. In this case, the test chamber measured 2 by 2 by 4 feet with an optical system like that used by Rohm and Haas. The specimen was burned under the container and optical readings were taken every 1/2 minute. The transmittance readings were plotted against time and the area under the curve was subtracted from the total area of the graph to obtain the loss in transmittance. The transmittance loss of the treated wood was divided by the transmittance loss of the untreated wood to obtain a relative smoke density between the treated and untreated specimens.

A method of smoke measurement by forward light scattering has been found to be effective in marine fire detection (7). In the instrument used, a photo­multiplier tube, which detects the scattered light, is alined at an angle of 30° from a line passing through the light source and the smoke cell. The instrument has very high sensitivity and, since a long smoke path is not needed to obtain a strong smoke signal, it is conveniently compact and easy to handle. A further advantage is that under no-smoke conditions the photoelectric cell is not under constant illumination, which might cause fatigue with consequent wandering of the output reading. This apparatus has been used successfully on merchant and passenger vessels in conformance with strict Coast Guard regulations.

Methods of determining the particle size of smoke are also quite common. The light microscope has long been the standard for such work, but it is limited in the size of the particles which it can distinguish. A more accurate instrument for this purpose is the electron microscope. Other methods include centrifugal. separation in which particles of different sizes are thrown out onto different screens, thermal precipitation, and gravity settling (14, pp. 97-101).

The methods discussed above give an idea of how optical measurements of smoke have been carried out. They also may facilitate the design of new and better instruments to meet the inadequacies or eliminate the drawbacks of some of the instruments now being used.

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Experimental Work

The majority of the experimental work done in this study was designed to determine how closely the Beer-Lambert law applies to smoke systems. Several parameters that affect the law were evaluated, but light-scattering determinations were not attempted; particle size was evaluated on a limited scale. The applicabil­ity of the Beer-Lambert law was studied by two methods. First, the relationship between smoke chamber length and optical density was investigated. This involved setting up suitable optical. and measuring systems, designing a smoke chamber, and selecting a suitable smoke. In the second part, the relationship between smoke concentration and optical density was studied. This involved finding a good method of generating smoke, developing a technique of collecting and quantitatively measuring the concentration of the smoke, and selecting a way to express the smoke concentration.

Optical Density as a Function of Cell Length

Apparatus.--The apparatus used in this part of the experiment consisted of a large chamber containing the smoke with a light source on one end and a photocell intercepting the light beam on the other end. The photocell position could be varied to change the cell length, The light source consisted of a tungsten lamp with a variable diaphragm. Placed in front of the light was a water-cooled green filter (wavelength--5,550 angstroms) to obtain monochromatic light. The light receptor was an uncoated silicon photovoltaic cell (Hoffman B-2,1 inch in diameter) with a spectral response from about 350 to 1,150 millimicrons. The photocell was connected to a variable resistor adjusted so that the voltage from the photocell was well below the region in which the photocell output ceased to be directly proportional to the intensity of the illuminating light. The photocell and resistor were connected to a precision d.c. voltmeter (sensitivity--1 milli­volt) made by Calibrations Standards Corporation. The smoke chamber was a fiberboard cylinder 10 inches in diameter and 3 feet long, which was painted a dull black inside to reduce light reflection and scattering. The light source was placed at a port on one end of the cylindes, and slits were provided at 6-, 12-, 18-, 24-, and 30-inch distances along the tube from the light source. The photo­cell was mounted on a small piece of plexiglass and could be inserted in the slits. Flaps to cover the slits were provided to keep the cell airtight. Ammonium chloride smoke was used because it was easy to generate and convenient to work with. The smoke was generated by placing beakers of concentrated hydrochloric acid and ammonium hydroxide inside the chamber and allowing the vapors to react.

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Method.--The voltmeter was adjusted by means of the light diaphragm to give a known, maximum possible reading when the photocell was placed in a position 6 inches from the light source. The beakers containing hydrochloric acid and ammonium hydroxide were placed inside the chamber, which was then closed, After the chamber had filled with smoke, and the smoke had had time to become homogeneously dispersed, the photocell was placed in each of the five positions and the millivolt reading recorded. After each series of such readings the chamber was cleared of smoke,

Treatment of Data--The results of each trial were plotted on semi-log paper as optical density versus distance from the source in inches (fig. 1). The milli­volt readings were plotted directly to represent optical density, since they are actually a relative ratio of the transmission I/Io’ based on the initial light

intensity of 100 millivolts which was set before the smoke was generated. In some cases, however, the initial light intensity was set at readings greater than 100 millivolts.

Results and Discussion.--In all cases, the results indicated a linear relation­ship between optical density, log10(Io/I), and chamber length. Deviations causing

slight curvature in the graphs are due to errors in the method (fig. 1). The most common errors in the method of measurement are attributed to scattered and reflected light reaching the receiver, smoke settling and adhering to the aides of the container thus changing the smoke concentration, the light source and receiver not alined exactly the same in each reading, and slight fluctuations in the photocell output because of temperature changes and fatigue,

The results of this experiment show that a definite linear relationship exists between optical density of smoke and the length of the chamber. However, no quantitative determinations were made on the amount of smoke present in the chamber, and it might prove worthwhile to determine whether this relationship holds true for all concentrations of smoke.

Optical Density as a Function of Concentration

Apparatus.--The apparatus used in this part of the experiment is shown in figure 2. The light source was the same as was used in the previous experiment and was filtered by the 5,550 angstroms filter as before. An unfiltered white

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light was also used in several evaluations because of the contention (2) that the Beer-Lambert law would apply to smoke systems only under conditions of monochromatic light; in another study unfiltered light from a tungsten lamp was used with good results (5).

The light receptor was the same photoelectric cell used in the previous experiment. It was connected in parallel to a variable resistor, which in turn was connected to a precision d.c. voltmeter. The smoke chamber was an air­tight cylindrical tube with an inside diameter of 1-1/4 inches and a length of 8 inches. Smoke entered and passed out of the chamber through glass tubes. The cylinder was sealed on one end by the photocell and on the other by a clear plastic window. The smoke was drawn through the cylinder by a vacuum pump and was deposited on a filter. The filter consisted of a mat of finely divided asbestos held together by a dilute solution of collodion and was placed in a Gooch filtering crucible.

The smoke was generated by drawing ammonia fumes into the flask containing concentrated hydrochloric acid. The two gases reacted to form ammonium chloride smoke which was then drawn into a large flask containing concentrated sulfuric acid. The sulfuric acid dissolved my excess ammonia vapor which may have been present because this would interfere with the subsequent weight determination of the smoke. The air-flow rate of the whole system was controlled by a stopcock and was measured by a rotameter calibrated in centimeters. The rotameter reading was converted to cubic centimeters of air per minute by an accompanying calibration graph.

One of the critical problems encountered was the selection of a smoke which could be conveniently generated and easily collected for weight determination. Smokes of zinc chloride, potassium chromate, arsenic trioxide, and organic smokes of oleic acid, tri-p-cresyl phosphate, and triphenyl phosphate were generated by heating, but none showed any advantage over ammonium chloride and, in fact, many were more difficult to work with because they required heating. Burning magnesium ribbon to form magnesium oxide smoke showed promise because of the ease of measuring smoke concentration by simply weighing the ribbon before and after ignition (assuming, of course, that complete combustion takes place). However, no suitable method could be found to burn the ribbon in open air and yet collect the smoke. The magnesium oxide immediately condensed on any cool surface also making it difficult to work with,

Ammonium chloride smoke was therefore chosen, and a method of collecting it was sought. Attempts to dissolve the smoke in water by bubbling it through a water column proved unsuccessful even when the bubbles were finely divided by

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Berl saddles or fine sand. Neither could the smoke be dissolved in concentrated or dilute acids and bases, ammonia, or silver solution. after trying filters of glass wool, cotton, and several other materials, the filter of asbestos and collodion was tried and found successful. The filter was prepared as a 1/8- to 1/4-inch mat and was placed in a Gooch filtering crucible,

Method and Treatment of Data.--With the smoke chamber clear of smoke, the voltmeter was adjusted to read 100 millivolts. The vacuum pump and stop­watch were then started and the stopcock adjusted to give a low air flow. As ammonium chloride built up on the filter, the air flow would naturally decrease, and the stopcock could be opened to compensate for the decreased flow, thus keeping the rotameter reading essentially constant. Keeping the air flow constant, voltmeter readings were taken every half minute. At the end of 10 minutes, the vacuum pump was stopped, the chamber cleared of smoke, and the voltmeter checked to see if the empty chamber reading was again 100 millivolts. The rotameter reading in centimeters was converted with the graph to the corre­sponding air flow in cubic centimeters per minute. Air flow multiplied by the number of minutes gave the volume of air passing through the chamber. The average of the voltmeter readings was used to compute the optical density of the smoke.

The weight of ammonium chloride collected was calculated by two different methods. The weight was first determined by weighing the filtering crucible, after it had come to constant weight, in a dessicator before and after each determination. However, since the amount of smoke collected was often only a few milligrams, and the sensitivity of the balance was only a tenth of a milli­gram, this method was inaccurate and the results were unsatisfactory.

A colorimetric method using Nessler’s reagent was much more effective in calculating the weight of smoke collected. This reagent is prepared by dissolving 50 grams of potassium iodide in 50 milliliters of cold water and adding a saturated solution of mercuric chloride until a faint precipitate persists. To this is added 400 milliliters of a 9 normal solution of potassium or sodium hydroxide, and the resulting solution is diluted to one liter. In the presence of

-7ammonia or ammonium salts in quantities as low as 10 grams, the reagent forms a colored complex which can be analyzed using a standard solution of ammonium chloride and a colorimeter, Because this method was used, it was important that the smoke contain no excess ammonia, hence the sulfuric acid was used to remove the ammonia.

For the colorimetric weight determinations the ammonium chloride was quantitatively collected from the filter by washing it with water and diluting the washings to 250 milliliters in a volumetric flask. Using a standard solution of

FPL-0137 -18-

- -Tab le I . Op t i ca l d e n s i t y as a f u n c t i o n o f smoke c o n c e n t r a t i o n

Figure 3.--OpticaI density, log (Io/I), as a function of smoke concentration (ammonium chloride particles) in miIligrams for two types of light.

-19-

ammonium chloride, it was then analyzed with a Duboscq colorimeter, and the amount of ammonium chloride was reported to the hundredth of a milligram Dividing the weight of ammonium chloride collected by the volume of air passing through the chamber gave the concentration of smoke in grams per liter. Data for the two types of light used in this experiment are shown in table 1 and figure 3.

Results and Discussion.--Meaningful results could not be obtained when optical density was plotted against smoke concentration in grams per liter. At times the data seemed to show alinear relationship, but they were not reproduc­ible indicating that the apparatus and method were not as yet reliable. Although the Nessler determination of the smoke collected is probably correct, one of the sources of error may be that some of the smoke passed undetected through the filter and was lost. In some cases, the amount of smoke flowing through the chamber was not uniform, and a wide range of voltmeter readings resulted; an average of these readings then gives a poor representation of the optical density. Probably the largest source of error was collection of smoke on the walls of the chamber and especially on the walls of the glass and rubber tubing leading from the chamber to the filter. In all cases, the voltmeter returned to the 100-millivolt reading after the smoke chamber was cleared; however, the photocell may have been subject to wandering because of light fatigue during the course of the run. These sources of error were probably largely responsible for the variability in the results obtained.

Although a correlation could not be found between optical density and smoke concentration in grams per liter, a definite linear relationship was evident between optical density and grams of smoke collected when the air-flow rate was constant (but not the same in all instances). This result is shown in figure 3. These last results are unusual and no ready explanation is offered as to why the optical density is related to the weight of smoke rather than the volume concentration. This weight relationship was used to evaluate several other parameters, and gave a common working basis from which to make comparisons.

The average radius of the smoke particles was computed using these data and is indicated in table 1. The computational formula, 2.303 D = (3c1)/(4rp), which was discussed earlier, was used to obtain these theoretical values for the radii. The chamber length, 1 was 20.32 centimeters, the density 2 was 1.53,4

and the values of optical density, D, and concentration, c, were taken from the

4 Density value for ammonium chloride particles is from the Handbook of Chemistry and Physics, Chemical Rubber Publishing Co.

FPL-0137 -20-

experimental data. The average radius obtained, about 0.30 micron, is in com­plete accord with the range generally reported for ammonium chloride smoke, 0.05 to 1.0 micron.

Determinations of optical density as a function of smoke concentration with the white unfiltered light are also shown in figure 3. They seem to indicate that the Beer-Lambert law applies up to a certain point, but it must be pointed out that reproducible results were not obtained, and the results may not be valid. Further work must yet be done to obtain reliable results.

Effect of Some Characteristics of Smoke on the Beer-Lambert Law

One of the major problems involved in the experimental work was decrease of the smoke concentration on standing due to settling and coagulation. This effect has been studied (20, pp. 43-45) and an expression has been developed which relates the decrease in concentration to time. This expression is:

where, n = number of particles per cubic centimeter at time t, n = number of particles per cubic centimeter when the smoke is first o formed K = coagulation constant.

This can also be expressed as α = α + Kt, there α and α are particulateo o volumes, For different smokes, K has different values. For the same smoke produced on different occasions, the value of K should be identical.

Tolman'a study (17) on the disappearance of smoke in a confined space has led to several important conulusions: (a) the rate of disappearance is markedly increased by stirring and agitation; (b) the higher the concentration of smoke, the greater is its rate of diaappearance; (c) the rate of disappearance is greater for small particles than for large ones, probably because the fine particles with their greater velocity of diffusion come in contact with each other and coalesce more frequently; and (d) it is impossible to raise the optical density of a smoke beyond a certain point by the introduction of further smoke material because increased concentration and increased subdivision both lead to a greater rate of disappearance.

FPL-0137 -21-

In addition to them considerations the decrease of smoke with time has been found to fall into three periods (20, p. 9). These periods are (a) an unstable initial period in which the decrease in the number of particles with time is very rapid; (b) a stable period reached after some hours in which the change in number of particles with time is very slow (this may last up to 24 hours or longer); and (c) an intermediate period in which the rate of disappearance is the resultant of the factors operative in (a) and (b). In the unstable initial period, the rapid decrease in number is due almost entirely to coagulation.

Using ammonium chloride smoke in a closed container, the effect of decrease of smoke concentration with time was studied. The results are shown in figure 4 and agree closely with the theory. The decrease in concentration with time is very rapid at first and then falls off. This rapid dispersion phenomenon is there­fore one of the major factors which must be taken into account when studying closed smoke systems, and it was certainly one of the major sources of error in the first part of this experimental work.

Although the present experimental work was limited, several other para­meters might be tested to determine whether they have a significant influence on the validity of the Beer-Lambert law for smokes. One of the factors to be considered is the kind of smoke used. A colored smoke is likely to behave differently from the white one that was used in this experiment. A result of using a different smoke would be a variation in the particle size, and this variation may have a profound effect on the Beer-Lambert law. The law has been said to apply to smoke system if the concentration of the smoke is kept below the level where particle interaction (and obscuration) occur. A deter­mination of the limits of concentration for several smokes would prove helpful. Two structural variables, the intensity of the incident light and the length of the smoke chamber, would be worthwhile investigating. Therefore, much more work remains to be done in this field before a clear-cut picture of the optical properties of smoke are known.

Conclusions and Recommendations

A study of the literature has indicated that there are several ways to measure smoke density by transmission, Ringelmann numbers, optical density, visual comparisons with colored standards, and specially calibrated scales or computing formulas (which are used only in applications for which they have been devised). Of these methods, an optical measurement based on transmission, optical density, or light scattering seems to be the most efficient in terms of accuracy and convenience of measurement. An optical method is not dependent on sub­jective methods and is a common measurement which is universally understood.

FPL-0137 -22-

Figure 4.--Light transmission as a function of time for a chamber charged with ammonium chIoride particIes.

-23-

A major drawback to an optical method is that it is very sensitive and requires a carefully designed optical system. In addition, an optical measurement gives no quantitative indication of the smoke and must therefore be calibrated in each separate application. The calibration must involve a convenient way to specify concentration. For smokes, the two most common concentration specifi­cations are weight per unit volume and number of particles per unit volume. Weight is easier to measure and probably the better to use. The number-of­particles specification is used in many of the equations applying to optical measurements, but these equations rarely apply to all smoke systems in general. There is no great loss in not using this concentration specification. A major problem is translating the optical measurement or concentration specification into a meaningful expression of the smoke hazard, and this too must be done in each separate application for each smoke.

From a review of the methods and apparatus used to measure smoke density, the most practical apparatus seems to be one which measures smoke density by forward light scattering. The major advantage of such an apparatus is its sensitivity for detecting smoke over instruments which detect smoke by light attenuation. In such light-transmitting instruments, a large amount of smoke or a long chamber length is necessary to bring about a noticeable decrease in the light transmission. A light-scattering instrument, therefore, has the advantage of compactness and, in addition, is protected from fatigue of the photocell by a nonlinear alinement of the optical system Commercial instruments for light-scattering measurements are available and would be worthwhile investigating to see if they can be used or adapted to make smoke density measurements.

Literature Cited

(1) Anonymous. 1964. A method of measuring smoke density. Natl. Fire Protect. Ass.

Quarterly 57:276-287.

(2) Daniels, Farrington, and Alberty, Robert A. 1961. Physical chemistry. Ed. 2, John Wiley and Sons, N.Y,

(3) Debye, P. 1944. Light scattering in solutions, J. App. Phys. 15:338.

(4) Eggert, John, and Gregg, S.J. 1933. Physical chemistry. Van Nostrand Co., Inc., N.Y.

FPL-0137 -24-

(5) Foster, W.W. 1959. Attenuation of light by wood smoke. Brit. J. Appl. Phys. 10:416-420.

(6) Green, H.L., and Lane, W.R 1957. Particulate clouds: dusts, smokes, and mists, Van Nostrand Co.,

Inc., London.

(7) Haessler, Walter M. 1965. Smoke detection by forward light-scattering. Fire Tech. 1:43-51.

(8) Hurley, T.F., and Bailey, D.L.R 1958. The correlation of optical density with the concentration and composi­

tion of the smoke emitted from a Lancmhire boiler. J. Inst. Fuel 31:534-540.

(9) Kirk, Raymond E., and Othmer, Donald F. 1955. Encyclopedia of chemical technology, Interscience Encyclopedia, Inc.,

N.Y.

(10) Kolthoff, LM., and Elving, Philip J. 1961. Treatise on analytical chemistry. Interscience Publishers, Inc., N.Y.

(11) Kruyt, H.R 1952. Colloid science. Vol, I, Elsevier Publishing Co., Amsterdam.

(12) Lothian, G.F., and Chappel, F.P. 1951. The transmission of light through suspensions, J. Appl. Chem.

1:475.

(13) Moore, Walter J. 1962. Physical chemistry. Ed. 3, Prentice-Hall, Inc., Englewood Cliffs,

N.J.

(14) Sinclair, D. 1950. Optical properties of aerosols. Handbook on aerosols, U.S. Atomic

Energy Commimion, Washington D.C.

(15) Stacey, K.A. 1956. Light scattering in physical chemistry. Butterworth Publications Ltd.,

London.

FPL-0137 -25-

(16) Stoecker, Wilbert F. 1950. Smoke density measurement. Mech. Eng. 72:793-798.

(17) Tolman, R.C. 1919. The disappearance of smoke in a confined space. J. Amer. Chem.

Soc. 41:304-312.

(18) . 1919. Relation between the intensity of Tyndall beam and concentration of

suspensions and smokes. J. Amer. Chem. Soc. 4l:300-303.

(19) Whiteley, M.A. 1962. Thorp's dictionary of applied chemistry. Ed. 4, Longmans, Green,

and Co., London.

(20) Whytlaw-Gray, R., and Patterson, H.S. 1932. Smoke: A study of aerial disperse systems. Edward Arnold and Co.,

London.

FPL-0137 -26-

Additional References

General references on smoke:

Anonymous. 1950. The formation and stability of aerial disperse systems. Bull. Brit.

Coal Util. Res. Ass. 14:201-211.

. 1960. The measurement of smoke. Heating, Piping, Air Conditioning 22(10):

107-115.

American Society for Testing and Materials 1963. Tentative method of test for smoke density in the flue gases from

distillate fuels. ASTM Designation D2156-63T.

Axford, D.W.E., Sawyer, K.F., and Sugden, T.M. 1948. The physical investigation of certain hygroscopic aerosols. Proc.

Roy. Soc. A195:13-33, London.

Bumgardner 1938. Smoke density measurements. Mech. Eng. 60:610-612.

Coolidge, J.E., and Schulz, G.J. 1951. Photoelectric measurement of dust. Instruments 24:534, 544, 578-580.

Friess 1937. Optical properties of smoke particles. Gasmaske 9:137-140.

Gibbs, William 1924. Clouds and smoke. J. and A. Churchill, London.

Kibler 1937. Principles of smoke production. Chem. Warf. Bull., 23:71-75.

Langatroth, G.O., and Gillespie, T. 1947. Coagulation and surface losses in disperse systems in still and turbulent

air. Can. J. Res. 25:455.

Shaw, Hurley, and Fox 1952. Smoke concentrations using optical density and concentration. Heat.

Vent. Eng. 25:494.

FPL-0137 -27-

References on light scattering:

Anonymous. 1962. Light scattering of coated aerosols, J. Colloid Sci., 17:26-38.

Billmeyer, F. W., Jr. 1962. Textbook of polymer science, (Interscience) John Wiley and Sons, N.Y.

Flory, Paul J. 1963. Principles of polymer chemistry, Cornell University Press, Ithaca,

N.Y.

Freundlich, H. 1926. Colloid and capillary chemistry. (tr. H.S. Hadfield) Methuen, London.

Geiduschek, E.P., and Holtzer, A. 1958. Adv. Biol. Med. Phys. 6:431.

Osier, G. 1948. Applications of light scattering to chemistry. Chem. Rev. 43:319.

. 1960. Eight scattering, in A. Weissberger ed., Physical methods of organic

chemistry (Vol. I of Technique of Organic Chemistry), Ed. 3, Part 3, pp. 2107-2145, Interscience, N.Y.

Peaker, F.W. 1959. Light-scattering techniques, in P.W. Allen ed., Techniques of polymer

characterization pp. 131-170. Academic Press, N.Y.

Stratton, J.A. 1941. Electromagnetic theory. McGraw-Hill Book Co., N.Y.

Tanford, C. 1961. Physical chemistry of macromolecules. John Wiley and Sons, N.Y.

Van de Hulst, H.C. 1967. Light scattering by smoke particles. John Wiley and Sons, N.Y.

FPL-0137 -28-

References that describe light-scattering instruments:

Anonymous. 1960. E88 Turbidity Instruments, Photomation, Inc., 96 S. Washington Ave.,

Bergenfield, N.J.

. 1960. Sinclair-Phoenix forward-scattering aerosol, dust, and smoke photo­

meter. Phoenix Precision Instrument CO., 3803 North 6th Street, Philadelphia, Pa.

1960. Smoke-dust turbidity, Bailey Meter Co., 1050 Ivanhoe Road, Cleveland, Ohio.

American Society for Testing and Materials. 1965. Atmospheric sampling and analysis. 1965 Book of ASTM Standards,

Part 23, ASTM, Philadelphia, Pa.

Bishop, J.F., and White, R.S. 1954. Ind. Eng. Chem 46:1432.

Brice, Halwer, and Speiser 1950. J. Opt. Soc. Amer. 40:768.

Collins, and Steele 1961. Instruments 38:186.

Crosse, Lucas, and Snowsill 1961. Int. J. Air. Wat. Pol. 4:212.

Debye, P.P. 1947. J. Phys. Colloid Chem. 51:18.

. 1946. J. Appl. Phys. 17:392.

Doty, P.M. 1946. J. Amer. Chem. Soc. 68:159.

Wagner, and Singer 1947. J. Phys. Colloid Chem 51:32.

FPL-0137 -29-

Hadow, Sheffer, and Hyde 1949. Can. J. Res. B27:791.

Hermans, and Levinson 1951. Some geometrical factors in light scattering apparatus. J. Opt. Soc.

Amer. 41:460.

Kay, K. 1957. Anal. Chem 29:593.

. 1959. Anal. Chem. 31:633.

Kremen, and Shapiro 1954. The design of an optical system for the absolute measurement of

turbidity, J. Opt. Soc. Amer. 44:500.

Putzeys, P., and Brosteaux, J. 1935. Trans. Faraday Soc. 31:1314.

Sinclair, D. 1963. Air Repair 3:51.

Speiser, R., and Brice, B.A. 1946. J. Opt. Soc. Amer. 36:364.

Zimm, B.H. 1948. J. Chem. Phys. 16:1099.

FPL-0137 -30- 1.-30

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FOREST PRODUCTS LABORATORY

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