Lec 05 : Size Analysis by Screening
NPTEL IIT Guwahati・2 minutes read
The lecture on Size Analysis by Screening highlights the process of arranging screens by opening size to separate crushed material, with calculations on mean diameters and specific surface area. Different particle shapes and specific calculations are detailed, providing insights into analyzing particle size distribution for various mixtures.
Insights
- Screening in Size Analysis involves arranging screens from finest to largest openings, with material mechanically agitated to pass through based on size, enabling collection and weighing of specific fractions on each screen.
- Size Analysis utilizes Tyler screen series with consistent aperture sizes and intermediate screens for closure sizing, ensuring uniformity in particle distribution for accurate calculations.
- Cumulative Analysis in non-uniform mixtures allows visualization of particle size distribution, aiding in understanding sample composition through plotting cumulative sums against maximum particle diameters.
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Recent questions
What is the process of Size Analysis by Screening?
Screening involves arranging metal pans with screens from finest to largest openings. Crushed material is placed on the top screen and agitated. Material particles pass through screens based on size, collected and weighed. Average particle size retained on each screen is calculated.
How are non-uniform mixtures analyzed?
Non-uniform mixtures are divided into fractions treated as uniform mixtures. Differential analysis divides fractions with constant density and size. Cumulative analysis adds individual increments to plot cumulative sums against particle size.
What calculations are involved in determining mean diameters?
Mean diameters like mass mean, volume mean, and Sauter mean are calculated using xi/Dpi bar and xi/Dpi bar cube values. Equations help find the number of particles in each increment for distribution.
How is sphericity calculated in particle analysis?
Sphericity is calculated using the formula 6Vp/DpSp, with values for different shapes determined. Specific surface area is calculated as 6ρp x 0.00265 x 4.8.
What is the significance of cumulative analysis in mixtures?
Cumulative analysis allows for obtaining differential analysis results through linear interpolation. It involves plotting mass fraction X i versus particle size Dp, aiding in understanding sample composition.
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Summary
00:00
Size Analysis by Screening in Mechanical Operations
- The lecture focuses on Size Analysis by Screening in the Mechanical Unit Operations course.
- Screening involves arranging metal pans with screens at the bottom in a sequence from finest to largest openings.
- Crushed material is placed on the top screen and mechanically agitated for 20-30 minutes.
- Material particles pass through screens based on size, with each screen collecting a specific amount of material.
- Screens are numbered from bottom to top for organization, with the top screen having the largest opening.
- Material collected on individual screens is weighed and converted into mass fractions.
- Average particle size retained on each screen is calculated using the arithmetic average of screen apertures.
- Tyler screen series provides standard screens based on the opening of a 200 mesh screen at 0.074 mm.
- Screens are designed with specific ratios to ensure consistent aperture sizes.
- Intermediate screens are available for closure sizing, with mesh dimensions based on the fourth root of 2.
15:30
Calculating Surface Area in Particle Mixtures
- To determine the total surface area of a uniform mixture, calculate the total number of particles and the total surface area of spherical particles with a size of 2 mm and a density of 2650 kg per meter cube, with a sample mass of 20 kg.
- The total number of particles in the uniform sample is 1,801,714, and the total surface area of the sample is 22.641 meter square.
- For short cylindrical particles with a diameter of 1 mm and a height of 1 mm, the total number of particles in the sample is 9,609,141, and the total surface area is calculated to be 45.262 meter square.
- In non-uniform mixtures, the particles have varying sizes, requiring screening and division into fractions with more uniform particle size distributions.
- Each fraction in a non-uniform mixture is treated as a uniform mixture, applying the principles of size analysis for uniform mixtures to calculate the surface area of individual fractions and then adding them together for the entire sample.
- Two approaches for reporting results in non-uniform mixtures are differential analysis (fractional analysis) and cumulative analysis.
- Differential analysis involves dividing the mixture into fractions with constant density and approximately constant size, calculating the number of particles and surface area for each fraction, and then adding the results.
- Cumulative analysis involves consecutively adding individual increments starting with the smallest particles and plotting cumulative sums against the maximum particle diameter in each increment.
- Cumulative analysis can be done for both undersized and oversized particles, calculating the cumulative fraction of material smaller or larger than a specific particle size.
- By plotting cumulative fraction against particle size, a distribution of particle sizes in non-uniform mixtures can be visualized, aiding in understanding the sample composition.
31:03
"Particle Size Analysis Using Cumulative Methods"
- Cumulative analysis involves plotting cumulative sums against the maximum particle diameter in increments.
- Size analysis from a crusher or grinder often results in linear plots on log-log or similar papers.
- Cumulative analysis allows for obtaining differential analysis results through linear interpolation.
- Cumulative undersized and oversized analysis involves plotting mass fraction X i versus particle size Dp.
- Example problem involves mesh screen openings like 10 mesh, 14 mesh, etc., with corresponding mass fractions.
- Average diameters Dp1 bars are calculated by averaging screen openings like 10 mesh and 14 mesh.
- Cumulative fraction smaller than Dpi bar is determined by adding corresponding fractions of smaller sizes.
- Cumulative fraction larger than Dpi bar is calculated by adding corresponding fractions of larger sizes.
- Specific surface area calculations involve multiplying number of particles by surface area of particles in a fraction.
- Average particle size can be determined through volume surface mean diameter or Sauter mean diameter calculations based on mass fractions or total number of particles in each increment.
46:49
Particle Size Analysis and Mean Diameters
- The sample's unit mass is divided by capital M to get xi by rho p Vp, where Vp is Dpi bar cube, the average diameter of the sample for a given increment.
- The volume of the sample is a constant multiplied by Dpi bar cube, with a as the volume shape factor.
- Mi is rho p multiplied by the volume of all particles in the mixture, which is A Dpi bar cube.
- The mass mean diameter D w bar is sigma xi Dpi bar divided by sigma xi, with sigma xi being 1.
- The volume surface mean diameter Ds bar is 1 by sigma xi by Dpi bar, and the volume mean diameter D v bar is 1 by sigma xi by Dpi bar cube whole power 1 by 3.
- Different average diameters may vary widely in a mixture containing particles of various sizes.
- The volume of all particles in the mixture is calculated using the volume mean diameter D v bar.
- The total number of particles in the mixture is calculated as mi by rho p Vp for one fraction and as the summation of mi by rho p Vp for the total mixture.
- Different volume shape factors are used for different particle shapes, with a being pi by 6 for spheres, 0.7854 for short cylinders, and 1 for cubicle particles.
- In an example, screen analysis of a sample is done to calculate specific area, total number of particles, and various mean diameters, with careful consideration of particle sizes and fractions.
01:02:30
Particle Shape Analysis and Size Distribution Calculations
- Sphericity can be calculated using the formula 6Vp/DpSp, with values for different shapes such as short cylinders, hemispheres, and cubes already determined in a previous lecture.
- The specific surface area can be found using the formula 6/(ρpσxi/φSiDpi).
- Sphericity varies between different particle shapes, with φSi coming into play in the summation.
- The calculation involves finding φSiDp as 6Vp/Sp and then combining the values to get 4.8.
- The specific surface area is calculated as 6ρp x 0.00265 x 4.8, resulting in 10867.92 mm²/g.
- A sample's product size distribution obtained through screen analysis is detailed, with mesh numbers, screen openings, and mass fractions provided.
- The task involves drawing undersized and oversized cumulative analyses, calculating the specific surface of the sample, total number of particles, and obtaining mean diameters.
- The shape factor and sphericity values required for the problem are 0.78 and 0.874, respectively, with a sample density of 2700 kg/m³.
- Cumulative undersized and oversized plots are constructed based on the mesh increments and corresponding mass fractions.
- Calculations for average mean diameter, volume mean diameter, and Sauter mean diameter involve using xi/Dpi bar and xi/Dpi bar cube values obtained from the table.
01:17:49
Particle Distribution Calculations for Powdered Materials
- To determine the particle distribution, the N, N distribution must be found by calculating the number of particles in each increment to obtain the sauter mean diameter and mass mean diameter.
- The equations provided in the problem help in finding N, with the first equation yielding N = Dp bar square / 2 + C1 for Dp bar 0 to 10 microns, and the second equation giving N = 10^5 Dp bar^-3 / -3 + C2 for Dp bar 10 to 100 microns.
- By substituting boundary conditions, C1 is found to be 0 for Dp bar = 0, and C2 is determined to be 83 when N is known as 50 from the first equation.
- The particle distribution is then calculated as N = Dp bar / 2 for 0 to 10 microns and N = 83 - 0.333 * 10^5 / Dp bar^3 for 10 to 100 microns.
- Tabulating data using the derived equations involves using N = Dp bar square / 2 for Dp bar 0 to 10 microns and the other equation for Dp bar 10 to 100 microns to obtain the total number of particles.
- The sauter mean diameter is calculated as 83.07 microns, and the number mean diameter is found to be 50.7 microns, showcasing the difference between the two mean diameters.
- The mass distribution of a powdered material represented by a straight line from 0 percent mass at 1 micron to 100 percent mass at 101 microns requires calculating the mean surface diameter using the relation Dp i bar = 100 x i + 1. The sauter mean diameter is determined to be 21.7 microns through integration.
