INTRODUCTION TO DYNAMIC LIGHT SCATTERING
OVERVIEW OF DLS
HYDRODYNAMIC DIAMETER
DLS PRINCIPLE
CORRELATION FUNCTION
EXPERIMENTS PERFORMED USING LS SPECTROMETER
INTRODUCTION TO LS SPECTROMETER
STEPS FOR SUCCESSFUL SOLUTION PREPARATION
STEPS FOR USING THE LS SPECTROMETER
DATA ATTAINED FROM LS SPECTROMETER
INRODUCTION TO FORWARD-ANGLE-SCATTERING-
OVERVIEW OF FAST TECHNIQUE
The FAST technique is a method for determining particle parameters while suspended in media using light scattering data. The DLS method is not suitable for obtaining particle size measurements for particles diffusing in a high velocity gas stream. The FAST technique has been successful in determining average particle sizes of monodisperse and polydisperse solutions (Nefedov, 1998).
The experimenters in the Nefdov paper were able to measure the size of polystyrene spheres distilled in water using the FAST technique. The purpose of this experiment is to use the FAST technique to measure alumina particle size distribution while subjecting the particles to turbulent airflow in a high-velocity stream.
EXPERIMENTAL SETUP
BRIEF DISCUSSION ON LIGHT SCATTERING
Given that the laser light source used in this experiment has a wavelength of 633 nm, the alumina particle sizes of 0.3, 1, and 3 microns certainly fall within the region where Mie scattering occurs. However, due to its size and the wavelength of laser light, the 0.05 micron alumina particle size appears to be on the threshold of the Mie scattering regime. Because of this, 0.05 micron alumina particles are likely to exhibit characteristics of both Mie and Rayleigh light scattering.
THEORETICAL BACKGROUND
Now define the geometric path length for the sample volume of particles to be 𝑙, and the distance between the sample volume of particles and the aperture diaphragm to be 𝐿. According to Nefedov, if we consider that some of this scattered light enters at angles 𝜃 ≤ 𝜃‡ 𝑃𝐷r, where 𝜃‡ = polar angle of the solid angle subtended by the 𝑃𝐷r, then the cross-section measured by the photodetector can be theoretical integral❜d . 8) where 𝑝Œ = the single-particle scattering phase function, and 𝜃 = scattering angle of light. Considering the scenario when the number density (𝑁x) of particles is unknown, the scattered light intensity measurement recorded will yield a relative value of the integral cross section measured by the photodetector 𝜎∗(𝜃‡) (Nefedov, 1998) .
Changing the angle for which the scattered light is measured by 𝑃𝐷r can be achieved by collecting the scattered light through eight different aperture sizes. According to Nefedov, by measuring the intensity of light at different points in the experimental setup, the experimental angle. The angular distribution function 𝑞(𝜃‡) is important because the extinction cross section 𝜎|}~ and the integral cross section 𝜎∗(𝜃‡) are related to it by the formula.
A complete solution to 𝑞ŠkƒŠ(𝜃‡) also requires a formula to describe the particle size distribution function, 𝑓(𝑟). This function can be modeled by many different formulas, but the most appropriate mathematical model would be a Gaussian shape. Once experimental measurements are made, it is therefore possible to generate measured angular distribution functions and plot them for each particle size.
Once the theoretical alumina extinction cross section and the single particle scattering phase function are calculated from Mie theory, the theoretical angular distribution function can be calculated and plotted. These two functions will be compared with each other and if they are the same, the alumina particle size will be confirmed, marked with the manufacturer.
INTRODUCTION TO MIE THEORY
The Mie coefficients 𝑐Q, 𝑑Q are needed when the internal electric field of the particle is of interest, for example, if the particle significantly absorbs light radiation. Therefore, if the particle strongly absorbs light radiation, it is necessary to know the imaginary part of the refractive index in order to obtain the exact parameters calculated according to Mie. This claim is supported by detailed studies conducted to determine the spectral absorption coefficient for aluminum oxide in the near-infrared spectrum of light (Aleksey.
Figure 6 below shows a graph of the spectral absorption coefficient of aluminum oxide depending on temperature and light wavelength. The laser light used in this experiment is 633 nm (0.63𝜇𝑚) and the experiments will be performed at room temperature. By using equation 13 to calculate the absorption index using the spectral absorption coefficient, one will find out.
Therefore, the imaginary part of the complex refractive index of alumina is assumed to be 0, making the absorption of light energy by alumina negligible. Once the scattering efficiency is calculated, the extinction cross section can be solved for use. This function of the scattering phase is important because when incident light at a particular wavelength hits a particle of a particular size, the light scatters at a precise angle corresponding to the particular size of the particle.
The scattering amplitude functions, 𝑆• and 𝑆K, are critical to solving the phase function because they describe the far-field distribution of light and are defined as. If the incident light is unpolarized (Hovenier, 2004) and the assumption of a homogeneous sphere is made for the particles, the formula for the phase function can be simplified (McLinden, 1999).
OBTAINING SCATTERING PARTICLE PARAMETERS FROM
MatScat calculated values of the theoretical extinction cross section (𝜎|}~) for each alumina particle size used in the experiment are shown in Table 2 below. The setup used for the FAST engineering experiments performed at NCPA was based on the experimental setup used by Nefdov, which is outlined in Chapter 3.2. The pulse generator associated with the oscilloscope would send a signal to the computer to take light intensity measurements at a frequency proportional to the disk's angular frequency.
For the purpose of verifying that the FAST setup was working properly, experimental tests using the FAST technique were performed on aluminum particles suspended in ethanol solution in room 1052 of the NCPA. Plots of the angular distribution function for each event number and particle size are shown below in Table 4. The reason for this was a combination of the tested solutions being too concentrated (resulting in multiple scattering), along with defects in the device holding the tested solution.
The vortex generator was designed using FUSION 360 software and built using 3D printing at CME's Makers Space at the University of Mississippi. Photographs of the vortex generator (assembled and disassembled) along with the PVC piping configuration are shown in Figures 16-18 below. Plots of the mean angular distribution function for each particle size are shown below in Table 5.
Experiments performed using the FAST technique were ultimately unsuccessful in validating alumina particle size under both environmental conditions. The swirled bed of particles is mixed with air to inject the particles into the flame body, creating a dispersed aerosol.
EXPERIMENTS PERFORMED USING FAST TECHNIQUE
EXPERIMENTAL SETUP USING FAST TECHNIQUE
In order for the photodiodes to perform light intensity measurements simultaneously and in coordination with the rotating disk, the oscilloscope was connected to a pulse generator. For example, if the disk rotates at 120 revolutions per minute, the pulse frequency will be 0.0625 seconds. At 120 revolutions per minute, the disk rotates at 2 revolutions per second, and since there are 8 apertures on the disk, it will be necessary to measure the light intensity at 0.0625 second intervals.
The computer program used to run the experimental setup and analyze the light intensity after each measurement was written in LabView by Dr.
FAST TECHNIQUE FOR ALUMINA IN SOLUTION
MEASUREMENTS OF THE FAST TECHNIQUE FOR ALUMINA IN
For each particle size, 4 different solution concentrations were prepared and tested, shown in Table 3 below. The experiments carried out using the FAST technique for 0.05 micron and 0.3 micron alumina particles suspended in ethanol solution helped to reassure the. To properly introduce a dispersed cloud of alumina into the mobile FAST optical setup measurement space, the alumina powder was fed through a constructed PVC pipe system.
Measurements using the FAST mobile setup were conducted in the aircraft anechoic laboratory chamber located at NCPA shown in Figure 19-20 below. After the light intensities at each photodiode were recorded, the LabView program generated values for the experimental angular distribution function. However, the FAST technique should not be seen as a flawed method for obtaining particle size.
Since calculation of the phase function for the theoretical angular distribution function requires the assumption of unpolarized light, it is important to implement a laser depolarizer in the experimental setup. Additionally, removing the rotating disc and using a motorized iris shutter instead would eliminate previous problems with warping and misalignment due to high rpm readings. Using an iris shutter would also provide a more even angular distribution function, as forward scattered light could be collected through a wider range of aperture diameters.
Therefore, implementing a lower wavelength laser would increase the size parameter for the alumina particle size of 0.05 microns and promote the Mie (forward) scattering of light. However, if implemented for future measurements, these discussed solutions should improve the acquisition of valid data using the FAST technique. Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave.” Journal of the Optical Society of America A, vol.
Application of forward angle scattering transmissometer for simultaneous measurements of particle size and number density in an optically dense medium.
FAST TECHNIQUE FOR ALUMINA IN TURBULENT AIR
MEASUREMENTS OF THE FAST TECHNIQUE FOR ALUMINA IN
The LS spectrometer was able to verify manufacturer-specified alumina particle sizes of 0.05 micron, 0.3 micron, 1 micron, and 3 micron while suspended in ethanol solution with a single angle measurement. Successful solution preparation required a very low particle mass (<0.01 g) of alumina to limit multiple scattering effects. Additionally, adding more sensitive photodetectors to the setup would allow better detection of scattered light from experimental measurements.
For solution measurements, building a solution holder using an adhesive alternative, such as 3M clear adhesive, should alleviate the negative effects that the epoxy had on the transparency. For airflow measurements, Nefedov provides a technique for introducing a steady particle mass concentration into a sample space using a laminar-diffusion-flame design (Nefedov, 1997). For this design, a flat flame burner is composed of multiple flames in a closely spaced array.
Due to time constraints, solutions to the above problems could not be applied in the experimental setup. Approximate analytical scattering phase function depending on microphysical characteristics of dust particles. Applied optics, vol. Analysis of particle sizes, concentration and refractive index when measuring light transmission in the forward scatter angle range.
CONCLUSION
