Nowadays, the pharmaceutical sector mitigates the separation of granular feedstocks by using one of the two formulation routes. Dry blending happens to be the first methodology and, to date, it is regarded as the simpler route.
Dry blending involves mixing separate ingredients to create dry blends, which are then packed into capsules and tablets. Wet granulation is the second methodology, in which raw ingredients are mixed with liquid and then granulated to form particles of large size.
Next, these particles are dried to eliminate the binding liquid, then sized to ensure a quality product, and finally packed in capsules and tablets. In wet granulation phase, a recycle step is usually involved that makes the process as well as batch inventory management rather complicated. Wet granulation can also cause undesirable reactions that impact the quality of drugs.
The dry blend is simplest but it is more prone to segregation, and while wet granulation is less sensitive to segregation, it is more complex and expensive. Obviously, pharmaceutical firms will select the simpler process, if feasible. Hence, there is a need for a tool that can help establish the possible segregation issues associated with dry blends.
This article describes a methodology that addresses the particular requirement in regular dry blend processes, and it is believed that both the methodology and tool can also be applied to promising segregation measurement in wet granulation processes. Furthermore, the method and tool elucidated in this article can be used in the paint, cosmetic, food, chemical, ceramic, and powdered metals sectors.
Being a mechanistic phenomenon, segregation is very useful to figure out the extent of segregation, to determine the pattern, and, if likely, to deduce the cause. In addition, segregation is known to be a multi-component phenomenon, in which a single component could have one or more causes of segregation. For this reason, a brief analysis of certain causes of segregation may be informative. A brief list of some of the standard segregation mechanisms is given in the following sections.
During handling, fine particles can sift through a matrix of coarse particles. For such a mechanism, the void space existing between adjacent particles should be sufficiently large to allow the fine particle to pass through. This generally needs a particle size difference of approximately 3:1 . Moreover, an inter-particle motion is needed, so that empty void spaces can be exposed to fine particles . The fine particles should be able to flow quite freely so that arching between neighboring particles can be prevented, while the void spaces also have to be adequately empty to accept fine particles . Through this kind of segregation, a radial pattern is normally produced as material creates a pile in process equipment . After collecting close to the pile charge point, the fine particles reduce in concentration toward the pile edge.
The Angle of Repose Differences
Different materials can have different angles of repose. For example, when two materials flow down a pile, they actually produce overlapping piles in which the material with the flattest repose angle collects close to the edge of the pile, while the material with the steepest repose angle collects close to the pile top . There is usually a distribution of these two materials along the surface of the pile. Significant segregation can be caused by repose angle differences of around 2° .
To promote this kind of segregation, a material with varied particle sizes can have an adequate difference in repose angles. Yet, the difference in particle size is not a prerequisite angle of repose segregation, and the same-sized materials can segregate through this mechanism. Moreover, to cause this kind of segregation, the users’ process should also create piles at the time of handling or processing.
Very small and fine particles that can be carried by air currents in the handling system may be present in the mixture . Such particles drop out of the air stream when velocities of gas reduce below the entrainment velocity. As a result, the fine and coarse particles are segregated in handling systems. Usually, fine particles accumulate close to the container walls.
For this kind of segregation, a source of air currents is required in process equipment; this source of air can originate when a compressible material falls freely. When the material level is impacted by the falling stream, the entrained air is forced out of the interstitial pores, carrying the fine particles in the ensuing dust cloud. Usually, this segregation results in a radial pattern at the time of pile formation; however, the fine particles remain at the base of the pile and not at the top .
If the mixture is adequately fine, the material can fluidize due to the air trapped in the interstitial voids. When a huge particle drops into this fluidized layer, momentum makes the large particles to enter this layer of fluid, leading to a top-to-bottom separation of coarse and fine particles . Such a mechanism needs a source of air and the potential of the bulk material to remain in the entrained air for a moderate period of time.
Any type of materials can segregate because of any kind of variation in particle scale properties — if the handling system can promote a stimulus that improves that specific kind of particle separation. For example, differences in surface friction can result in the angle of repose segregation, but this will happen only when the piles are formed in process equipment. The material flow rate and the fall height alter the amount of entrained gas in the material, robustly impacting air entrainment.
However, this will be significant only in a process subject to huge free fall distances. This indicates that any feasible segregation tester should have the potential to change feed as well as pile formation conditions in order to correlate with reality. A random amount of gas injected by certain segregation testers is usually relatively higher than would be present in any real gravity feed process, and subsequently determine a segregation potential of fine particles versus coarse particles depending on this stimulus .
A segregation method like this lacks the potential to predict reality. For a segregation technique to be useful, it should be able to approximate the kind of stimulus in regular handling processes and offer some ways of regulating this stimulus to enable matching process operations (that is, the test method should expose the material to the same or analogous behavior found in filling containers in traditional systems). Subsequently, this becomes the first judgment criteria for a feasible segregation methodology.
A segregation technique that can determine more than just a pair of components is another requirement. Multiple components are present in real mixtures. Present-day segregation analysis techniques concentrate on the measurement of only two components — usually coarse and fine particles [8–10]. The methodology and tool presented and assessed in this article will consider concurrent segregation potential measurement of a mixture containing around six components.
Such a limit is rather random and can be extended to a large number of components, but data from mixtures of around six components have been assessed currently. All the available data will not be described here because the aim of this article is to introduce and verify the robustness of the technique, and therefore, the potential for the technique to be usually applied to more than a couple of components is considered as a significant criterion for a powerful segregation analysis technique.
For a measurement system to be successful, the method should be able to generate steady and consistent results and should remain so within a reasonable error range. The overall calculations in segregation pattern as well as in segregation intensity for every component should be reasonably strong. Therefore, consistency and robustness are the third criteria for a feasible segregation methodology. Finally, in order to ensure a reasonable correlation, the novel methodology must be compared to at least one former methodology wherever possible.
The new methodology does not necessarily have to match precisely with earlier techniques because the results provided by each technique can be somewhat different. For instance, a wide range of particle size measurement methods is available, which apparently determines the same thing, but none of these techniques can accurately determine the same particle size distribution. Segregation potential measurements provide the same outcome, more or less; although the segregation potential measurement from one method to another will not essentially fall on top of one another, they have to be reasonably close. Hence, the final criterion requires the test methodology to correspond with other measurements and at least determine the same trends.
Method and Materials
The latest methodology involves filling a container with a representative product sample such that segregation similar to the one found in a standard handling process is induced, followed by determining the segregation pattern through an optical method and calculating the segregation intensity and segregation magnitude from the quantified segregation pattern (see Figure 1).
Figure 1. Schematic of segregation tester. Dump material into a box and observe the change in color intensity along the pile as measured just below the top surface of the pile (rectangle section). These changes in color intensity are an indication of differences in either chemical composition or in particle size and can be used to estimate the segregation of key components in the system.
All these criteria will be analyzed for this latest methodology, and quantitative judgments will be made wherever possible to assess how well the latest test method meets the criteria.
The segregation pattern of multi-component mixtures was measured using the following basic procedure. Here, only the general steps are described; the details of every step are given below, including the details of the required calculations.
- The mixed material should be fed into the segregation slice model bin at a preset fall height (as detailed above) and at a controlled flow rate.
- The bottom of the pile and the top position of the pile should be recorded (see Figure 3).
- The active measurement zone should be established by measuring the mixture parallel to the pile and at 6 mm depth from the top surface (see Figure 3).
- The overall average concentration of the main components in the mixture should be recorded.
- The average spectrum of each pure component in the mixture should be determined.
- A viewport must be selected for segregation measurements of mixture placed in a segregation slice model bin.
- The number of viewport areas should be selected to examine along the pile and the number of spectral measurement points should be subsequently selected to achieve per viewport.
- The average spectrum of the mixture material should be measured in a viewport for all the viewport areas preferred along the pile.
- The spectra of the main components, the total average concentrations of the mixture, and the spectra of the mixture acquired along the pile to calculate the local concentrations of main components along the pile should be used.
- The concentration profiles should be used to calculate the segregation intensity numbers for every main component.
Although the procedure described above is general in nature, the details of every step will enable the user to achieve consistent data. Explanations will be given for choosing each procedural step so that readers will learn about the type of procedural details required for a successful data collection.
Control of the filling process to imitate or relate to behavior in a standard procedure is the first detail to be taken into account. Two process situations should be considered when applying segregation test data to estimate process behavior. The first general case is the creation of the static segregation pattern when a process container is being filled by a material. Likewise, the segregation arising in a dynamic operating condition is the second general case. For instance, does the test data forecast segregation that might exist in a rotary shell blender as piles are formed repeatedly? Similarly, does the segregation test data relate to the separation of particles that may occur in a fluid bed?
The static condition will be considered here, in which a material falls freely into a container at a specified rate. Consider what occurs in this situation from a physics viewpoint. A set of particles falling into a container are inclined to spread as they accelerate. These particles may travel as individual particles or may travel as a stream. In both cases, as the material falls, it entrains air in the surrounding area. In case the material travels as a stream, it will impact the pile at a velocity close to that provided in Equation 1.
This initial free-fall velocity is dependent on the fall’s distance (h). Yet, if the flow rate of the solid is small, then the spreads of the free fall stream as well as the velocity of impact will be dependent on the terminal velocity depending on air drag (Equation 2). In such a situation, the initial velocity of impact will be a function of the effective particle size (Dp), the viscosity of the air (μair), the density of the air (ρair), and the density of solid particles (ρs). The real impact velocity will be somewhere in between. As per Equation 1, velocity increases until reaching the terminal velocity in Equation 2.
The impacting material has also associated kinetic energy. When the surface is impacted by a material, it can compact and deform plastically. If there is excessive compaction, then the strain energy needed to achieve this compression will impact the kinetic energy of the free fall and decrease the velocity. It is assumed that the loss of strain energy as a result of compaction with standard materials will be negligible.
Therefore, this article addresses only the drag forces that slow down the free fall velocities of particles. It is assumed that upon hitting the pile, the particles glide down the pile at the velocity that is compatible with friction angles of material sliding on the material. Equation 3 shows the velocity (Vpile) traveling down a pile of length (L).
This velocity is dependent on the effective friction of material flowing down the pile (φ) and the pile slope angle (θr). The velocity down the pile will slow and ultimately stops if the friction angle is higher than the pile slope angle. As a matter of fact, Equation 4 can be used to calculate the stopping distance.
With regards to non-terminal velocity flow, the distance traveled down the pile is provided by Equation 5, demonstrating a linear association between drop height and the distance traveled down a pile.
This indicates a linear scale association between fall height and the distance traveled down a pile for the process and small-scale segregation test hopper dedicated for non-terminal velocity flow in a process.
For terminal velocity behavior, Equation 6 can be used to calculate the scale relationship between process geometry and the lab-scale experiment.
In both cases, a scale relationship exists between the small-scale segregation test hopper and the process. The above-described simple analysis indicates that two key variables, such as solids flow rate and free fall height, are imperative in scaling between full- and lab-scale conditions. With regards to terminal flow conditions, certain information concerning particle size will also be needed.
Therefore, as a minimum set of scale parameters, the segregation tester should be able to alter the flow rate as well as the drop height. This can be accomplished by outfitting the tester with a vibratory feed system connected to an extendable platform. This extendable platform can be used to raise and lower the feeder’s position. The vibration control can alter the flow rate into the segregation test hopper.
The next detail involves the analysis of properly feeding material into the instrument. A material is guided into the slice model through a feed tube to form the pile (see Figure 2). The vibratory feeder tube/pan lies flat on the bottom and is just as broad as the slice model; it directs the flow into the segregation measurement chamber. This is an important component of the feed design.
Figure 2. Segregation tester flow control
When the material comes out from the vibratory feeder, it does so in a solids particle curtain, or sheet, that spreads the particles over the feeder tube and provides a consistent flow to the whole width of the segregation slice box. This causes the pile to build up without any radial pile impacts. The hopper feeder tube is positioned in such a way that the top of the pile created in the segregation test cell is located at one wall of the segregation test cell (see Figure 3).
Figure 3. Segregation test hopper
The pile surface is a plane forming on one side of the slice model or segregation test cell. When the cell is filled in this manner, the same pattern is produced at the front surface of the slice model bin just like the one produced on the back surface of the slice model bin. Earlier, researchers  found that when it comes to wall effects in slice model bins containing granular material and powders, the models need to be 25 mm or broader in order to eliminate wall-induced banding.
Banding can also take place naturally with somewhat cohesive materials as they create a pile. After building up the pile, cohesive materials occasionally cascade down the pile, sifting at the time of the cascade event and creating layers of coarse and fine particles . This phenomenon is natural and represents a part of actual systems. The same banding behavior occurs when the material is fed into the slice model in which the walls are close together. Here, the tester should not measure tester-induced events, but only real segregation events. Hence, the width of the segregation test cell was restricted to a minimum of 25 mm so that the occurrence of banding in the segregation test bin is considerably reduced.
The segregation bin measurement zone is placed parallel to the pile surface at around 6 mm depth beneath the pile’s top surface. This pile is viewed via an optical glass plate located at the rear of the test cell with a typical fiber optic reflectance probe angled at 45° to diminish the glass surfaces’ spectral reflectance. The whole zone parallel to the pile surface is assumed to be representative of the average material located in the tester.
Trial and error revealed that in the case of materials that segregate badly, there may be more segregation at the end of emptying the feed hopper. This impact was observed in the last 11% of the emptying cycle for material present in the feed bin. In order to ensure a representative sample in the segregation test cell, the feed hopper should be filled in tiny piles so that segregation in this bin is kept to a minimum. Once the level in the feed bin is 30% empty (or to the fill line indicated on the test cell), flow into the tester segregation test cell must be ceased. Consequently, conditions that would promote segregation as a result of feed bin operation were avoided.
In order to confirm the segregation consistency from back to front, a slice model made of glass end walls was filled with a poorly segregating material and an image of the front and back material surfaces was captured to establish the close correlation of these images using typical grayscale image correlation algorithms [13, 14]. The average gray scale was calculated as a function of dimensionless radius from the pile’s top and these data were used to calculate a regression coefficient.
For this analysis, the calculated regression coefficient is r = 0.971 (r2 = 0.942), suggesting that 94.3% of the deviation is the result of a linear relationship between these curves and that 5.7% of deviation between these curves is because of arbitrary uncontrolled events. It is believed that regression coefficient of 0.971 is a robust positive coefficient, indicating that Figure 4 depicts rational agreement between the back and front segregation profiles and demonstrates that the controlled feed approach along with the observation of the side of the pile can relate to segregation in true systems since the pattern determined on both sides of the segregation test cell is effectively the same. Despite this, it is essential to prove that observations determined at the side agree well with volume-based concentrations determined across the segregation test cell.
Figure 4. Correlation between front and back segregation pattern
Further evidence is presented below when segregation profiles determined with the latest test method are compared to alternate manual segregation test measurements that incorporate the concentrations on the basis of the volume in the test cell. Moreover, regulating flow behavior into a slice model, together with the potential to regulate the drop height and the feed rate, indicates that it is possible to adjust the segregation tester to approximate the process fill behavior.
The data obtained from this segregation tester should be applicable in dynamic segregation in which segregation in blenders forming inter-particle shear or piles occurs. Conversely, this test technique may not be applicable to conditions where most of the material is fluidized and segregation is induced by the fluidization act. To accomplish this task, the present filling methodology should be modified.
The subsequent detail in the methodology is to determine the mixture’s reflectance spectra along the pure components and the pile, and apply this information to calculate the concentration profile of major components down the pile. Yet, it would be useful if there is a discussion on the concept behind these measurements and calculations.
Multi-Component Segregation Theory and Measurement
In order to be useful, the measurement method should be able to measure segregation patterns for more than a couple of ingredients. A lot of theories and examples are given in the literature, in which the segregation of bimodal mixtures has been emphasized. Such measurements as well as the theories derived from these measurements have been oversimplified. In case the target component does not accumulate in a single location, then another component makes up for this difference by increasing its concentration. If three or more components are introduced to the mix (multi-component), the situation turns out to be much more complicated.
Although two components can possibly separate in relation to one another, the inclusion of extra components considerably expands the potential interactions. This possibility should be allowed by theories elucidating this complicated situation. In a similar way, the segregation pattern of three or more components should be easily determined by the measurement method. If the topic of segregation modeling is to progress further, then the measurement of multi-component segregating systems is at the core of the discovery process.
The author contends that at times the modeling leads the measurement, and while at other times it is vice versa, that is, the measurement leads the mathematical modeling and also points the direction for it. Conversely, both are needed to make major steps forward in inferring a scientific topic. However, not much is being done in the field of multi-component segregation theory. This is mainly because of the lack of an instrument that can easily determine the segregation potential of multi-component systems. A standard approach for determining the segregation potential of multi-component systems is presented in the following analysis.
A number of simplifications and assumptions have been made to further simplify the measurement and calculations. Evaluation and application of reflectance spectra are at the core of these measurements. In the instances described in this article to verify the method, reflectance spectra are used in both the visible and near-infrared (NIR) wavelengths.
It might be useful for the reader to have a fundamental discussion of reflectance spectral measurements. When diffuse light of a specified wavelength illuminates on a sample of particles — all at a recognized distance from the probe — the intensity of the light which is reflected back relies on three major interactions. Firstly, the light can be dispersed by the particles depending on simple light scattering. In such a case, the finest particles are responsible for causing the brightest intensity. Secondly, if colored chemicals or pigment, preferentially absorbing a specified wavelength of light, are present in particles, then the light being reflected back is only that which was not absorbed by specific chemicals or pigment.
A surface appears red because except for the red light, all light striking the surface is absorbed. Then, the intensity of a reflectance spectrum is a function of the pigment and chemical composition in the measurement zone. Finally, in certain situations, the absorbed light stimulates bond in a specific chemical, and as a result, the photonic energy is absorbed and changed into photonic energy of a varied wavelength. This happens to be the rudimentary principle involved in fluorescence. The analysis described here considers that fluorescence does not have a significant impact on the analyzed systems. Therefore, the intensity of a reflectance spectrum becomes a function of the particle size and the chemical or pigments in the observation zone.
Furthermore, a reflectance spectrum relies on the distance to the target. When non-laser light is emitted from the source, it tends to expand at some angle. The intensity of the light that reaches the target obeys an r2 law and relies on the distance from the source. Upon striking the target, the light is often reflected back in a diffuse fashion. Hence, the reflectance probe does not capture all the reflected light, even if none of the light is absorbed chemically. One can consider the example of a powder material surface positioned against an optical glass plate.
The distance to target relies on the particle surface position in relation to the surface of the plate. While the reflectance probe can be at a specified distance from the optical plate, the particle on the other side of the plate will be the target. When the light illuminates directly on the particle against the plate, the intensity of light will become a maximum value. When the light strikes a particle between the spaces of the particle pressed against the plate, the intensity of the reflectance spectrum will become lower. When a reflectance spectrum of a powder is being measured, there will be differences in spectral intensity owing to the effects of particle size distribution. The powder’s average reflectance spectrum cannot be adequately determined by a single reflectance measurement. Hence, multiple spectra should be averaged to get a representative spectrum value.
The general assumption is that all data obtained by spectral measurements are meant for a material having a known average concentration of major components; this is an essential part of the measurement process applying this method. In other words, when all the spectral data are collected and averaged together, they represent the spectrum of a reliable mixture made of the given concentrations of the major components. Average concentrations (Step 4) like these are required to compute the concentrations in the mixture. With the help of these average concentrations, the spectral data can be calibrated to change the quantified spectra to concentrations. An important detail is to properly identify the anticipated concentration of any specified component in the mixture. In Step 5, pure components in a loosely packed condition are transferred to the component trays (see Figure 5). During this process, the component trays are filled carefully by scooping the material into the tray utilizing side-to-side motion so that a single pile in the middle of the tray does not occur.
Figure 5. Filling the component trays
The aim of this filling procedure is to present a representative sample to the optical glass in terms of the size of particles. Therefore, the trays were filled with least segregation. As described above, the average spectrum of any pure component cannot be sufficiently characterized by a single measurement alone. With the probe measurement area being approximately 2.0 mm, 10 measurements are taken at offsets of 1.2 mm to ensure certain overlap of spectral measurement. Then, all the 10 spectra are averaged, and the spectral fingerprint of every pure component in the system is represented by these averaged spectra. Measurements are avoided close to the top of the component tray or the edge of the component tray. The probe measurement position for the material in the component trays should be at the same exact distance as the measurement position for the mixture. To accomplish this, the distance between the optical glass and the probe is calibrated. To do the final calibration, a homogeneous reflective surface is placed on the glass in every measurement area (pure component trays and segregation bin areas) and the intensity of the signal is tuned to be uniform at every measurement location.
In Step 6, the tiniest representative size describing the segregation event(s) with the target material has to be identified. Segregation measurement represents a scale problem. The size of the selected viewport must be sufficiently large to contain a representative number of particles but, at the same time, it should be sufficiently small so that variations in local compositions are not lost in the averaging scheme (see Figure 6).
Figure 6. Typical measurement zone along the pile top surface
Generally, if clear pattern or banding is not visualized, then the error between the consistent viewports can be limited to less than 1% by choosing the viewport to be at least 10 times the average size of particles. If there is banding, then the viewport should be sufficiently large to cover a couple of banding periods. If there is no distinct method to assign the viewport, then a number of viewports must be chosen and calculations should be carried out using all the viewport sizes.
Plotting the segregation intensity factors as a function of viewport size can provide the perfect viewport size. When the viewport size is sufficiently large (see Figure 7), the quantified segregation intensity factors converge to a reliable value. In order to reach a stable segregation intensity, the sand with an average particle size of 1500 µm needs a viewport size of approximately 4500 µm, as indicated in Figure 7.
Figure 7. Segregation variance as a function of viewport for sand mixture Dp = 1500 µm
This does not necessarily mean that the viewport has to be precisely three-fold the average particle size, because particle shape, size, banding, as well as segregation pattern formation actually indicate that the viewport may have to be modified. In Steps 7 and 8, the acquisition of a spectrum for the mixture at each target location has to be realized. The probe measurement zone has a diameter of approximately 2.0 mm. Preferably, adjacent measurements should overlap or touch, implying that a 12 mm viewport should have around 36 measurements (six on each side) in order to ensure an excellent coverage; 25 measurements (five on each side) will be sufficient if the viewport is 10 mm.
An optimization problem is choosing the number of measurements in every viewport. While some acquisition time is required by larger measurement increments, it will provide a much better outcome. For greater than 14 mm viewport, over 49 measurements have to be averaged to preserve the optimal coverage. It takes roughly 30 minutes to take 49 measurements at 50 locations along the pile in order to obtain data and carry out the needed calculations. The following detail involves the decision concerning the type of spectrum employed in the mixture analysis. This is the ninth step, needing a spectral-mixing law adequately general to be applied to all kinds of materials.
One alternative is to apply the entire reflectance intensity spectra — modified for the first derivative, the second derivative of that entire intensity spectra, or black balance. It is possible to scale the intensity in relation to another intensity spectrum of one of the pure components. Doing so will improve the variations between the peaks from varied components. The use of the second derivative provides one benefit —most of the spectral data, owing to particle size and other effects that can possibly impact the spectral intensity, are removed by the second derivative of the visible or NIR spectra.
The outcome is a signal containing most of the color or chemical difference data with small effects of particle size. Even in a case like this, some effect of particle size and other influences still exist. Therefore, a spectral-mixing methodology that includes the impact of particle orientation, particle size, and the filling of gaps between the coarse particles was used. Spherical particles having the same size will not create an optical variation between the pure particles placed in the component trays and particles in the mixture. In this extraordinary case, the spectral intensity of the mixture FSmixj(λ) would be a modest linear combination of the spectral intensity of pure components (FSi(λ)) depending on the local fraction (xfi,j) of every component.
Yet, the voids between coarse particles are filled by tinier particles, producing a shadow effect for the coarse particles. Within the voids, these fine particles take up a significantly greater percent of the area than the volume fraction would indicate. This shows that the mixture spectra will not be accounted for by a linear combination of pure spectra. The mixture spectra will tend to bias toward the fine materials. In a similar manner, if a component is a flake, then particle orientation in relation to the glass will determine the amount of area viewed by the spectral probe.
Other shape and size effects are also there that can bias the spectral area viewed by the probe for any single component. Therefore, to account for the probe measurement area effects, a weighting factor is added to the additive spectra law rather than producing a sturdy model to account for all the possible probe view effects. A special weighting factor exists for every component.
In fact, this weighting factor is a tensor or matrix because a weighting factor exists for every component and perhaps for every particle size. For the purpose of this analysis, the weighting factors are assumed to rely only on the components. Based on this simplifying assumption, it would be possible to model the spectral additive equation by introducing a weighting factor for component i (Wi) to the linear combination of spectra (see Equation 7).
The computed spectrum for the jth position on the pile is represented in Equation 7. One of these equations will be there for each position determined on the pile. An error function (see Equation 8) refers to the sum of the square variation between the computed spectra (FSmixi(λ)) and the measured spectra (Fmixi(λ)) for all the spectra determined along the pile.
The aim is to reduce the error function represented in Equation 8, but there are a number of other limitations that need to be satisfied for the optimal solution to be valid. The fractional concentrations of the components — at each point on the pile — should sum to 1.0 (see Equation 9). Similarly, all fractional concentration values should be in the range of 0.0 to 1.0 (see Equations 10 and 11).
At last, the average of all fractional concentrations for every component in the system should correlate with the total overall mixture concentration (xftoti) in Equation (12).
The target optimization function is provided in Equation 8. Equations 9 to 12 offer the equations and limitations that have to be solved to create the local concentrations of main components along the pile. All these equations should be solved together. Other investigators used spectral mixing methods that fall into one of two categories. Certain techniques [15–17] determine the spectrum of the pure compound, subsequently storing these data in a database of spectral fingerprints.
These database spectra are compared to new spectra by using cross-correlation methods, and the percent of correlation or match between the database spectra and the new spectra indicates the possibility that the new spectra are identical to the database spectra. In case a number of mixtures of spectra are present in the database, then this technique can be used for approximating the concentration of the new mixture through statistical correlation with analogous mixtures.
Other spectral mixing techniques [18–20] are capable of viewing the spectra of a prescribed mixture and focusing on the spectral variation with change in a single component. Next, the spectra of samples comprising of numerous known concentrations of the main component of interest are recorded eventually. A specific wavelength or band of wavelengths exhibiting plenty of intensity difference with the target component is often used for producing a least squares curve elucidating the association between the spectral intensity and concentration.
After defining this relationship, the mixture spectrum is examined and the intensity in the target wavelength band is used for changing the intensity to a concentration of the main components. If multiple concentrations are required, then it would be best to use multivariate least squares analysis to calculate the other concentrations from the spectral data.
The reflectance spectral signal is essentially a function of light absorbed by the chemical species and light scattered or dispersed by the particle size of the viewed surface. Such an association was initially hypothesized through the Kubelka-Munk theory [21, 22] of reflectance of sheets or films. The overall outcome is that reflectance is a function of the ratio (K/S) of the scattering coefficient (S) and the absorption coefficient (K).
The analysis is complicated by reflectance, which is a function of the ratio of these two coefficients, and therefore, this ratio has to be de-convoluted to consider the influence of chemical composition (absorption) and particle size (scattering). Conversely, if the system of interest is mainly controlled by one coefficient or the other, a mono-modal association will exist between either reflectance and absorption, or reflectance and scattering.
Results and Discussion
After comparing the measured intensity curve with the actual quantified curve, the tester adjusts the weighting factors as well as the local fractions at all quantified locations along the pile to reduce the error between the two curves. Furthermore, the technique used for solving this set of equations is a non-linear least squares optimization with limitations employed in NI LabView®. This is a standard solution method combining the data and constraints in the same matrix and solving all the weight and concentration factors together .
It is also believed that the average material placed in the tester is represented by the overall collected data. This offers a means of simplifying the calculations. Generally, during a visible or NIR spectral measurement, the spectra of a number of known concentrations of components in a mixture have to be entered in the visible or NIR unit to serve as calibration spectra to “train” the instrument. Usually, the spectra of these numerous concentrations would be used for generating a regression plot between spectral intensity and concentration at some vital wavelength of light.
In this latest technique, the spectra of the pure components combined with the known overall average concentration offer a method for training the instrument. Here, one difficulty is that all the spectral data are needed to calculate the concentration data and, as a result of, an extremely large number of concurrent equations are required. The software considers all the spectra and then, applying least squares correlation methods, establishes the most optimal guess of the concentration of main components. The outcome is a measurement of the concentration of major ingredients along the pile length for all measurement points along the pile (see Figure 8).
Figure 8. Segregation variance compared with the alternate method of measuring segregation for a mixture of three bird seeds.
No other technique is presently available to determine the segregation profile of multi-component mixtures, and hence comparison data in the literature have not been provided. Despite this fact, seven mixture systems were examined to establish if the segregation pattern was akin to manual segregation patterns determined in analogous tests. To do these manual segregation tests, a slice model was filled with a mixture, taking care to tip the slice model backward and then remove the front plate to expose the material within the slice model.
Next, the top of the pile was divided into five or six sections and the concentrations of main components in every sample collected along the pile were measured manually. The same procedure was again performed for seven varied systems containing two to five components. This manual segregation technique was compared to the above-described spectral segregation technique, and the data obtained from the latest spectral segregation tester were determined at more points along the pile than can possibly be collected through the manual technique.
Therefore, the resultant data were grouped and averaged over suitable dimensionless radius values to calculate points similar to the data determined with the manual technique. Figure 8 shows one such data, demonstrating the separation of three types of bird seed. An excellent agreement was observed between the manual measured points as well as the concentration points produced from the spectral segregation technique.
Depending on the entire set of data produced from this validation technique, the standard deviation was predicted to be 2.6% thus suggesting that the latest methodology approximates other means of measuring segregation with reasonable precision. This indicates that the aforementioned spectral technique can be used to precisely estimate the segregation concentration profiles of complex mixtures.
The segregation measurement procedure should be reproducible if the measurement technique is to be of value. There should be a reasonable repeatability, even in the case of relatively easily segregating material. The segregation measurement procedure described above was used to perform a protocol to test this repeatability sensitivity. A collection of three free-flowing sands of varied color and size was combined together, the resultant mixture was introduced into the tester thrice, and the process was followed to create the concentration profiles (see Figures 9 and 10).
Figure 9. Segregation variance due to repeated tests using spectral segregation measurement.
Figure 10. Segregation variance due to repeated tests as a function of radial position using spectral segregation measurement.
Subsequently, 20 samples along the pile were examined and the deviation from the average for the three tests was determined. This experiment indicates that, depending on a three-sigma estimate, the error induced by repeated measurement is roughly 7.0% for a material that is extremely sensitive to segregation. When other data were used with a material less prone to segregation, it was found that error caused by repeated measurement for that case was only 0.5%. Therefore, the repeated measurement error for this latest method was fixed between 0.5% and 7.0%. As indicated in Figure 10, some spatial difference effects might be there in the error of the test. Yet, this might have also been caused by the nature of the segregation pattern. According to the data, this spectral segregation test technique utilizing controlled filling replicates segregation patterns with reasonable precision.
It is equally significant that the calculation technique used for computing the concentration profiles should be consistent. In order to test the reliability, the mixture of three sands was positioned in the tester and the concentration profile was determined for this same pattern three times (see Figures 11 and 12).
Figure 11. Segregation variance due to repeated calculations of a segregation pattern using spectral segregation measurement.
Figure 12. Segregation variance due to repeated calculations of a segregation pattern as a function of radial position using spectral segregation measurement.
Based on three sigma deviation, the repeated solution of these concentration profiles specifies that the measurement error in the case of the segregation-sensitive material was 0.3%.
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