Sphericity and Shape Analysis Exercise 3.3

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Questions and Answers

What is the sphericity of the sample in Exercise 3.3 (i)?

  • 93.1%
  • 92.9% (correct)
  • 0.929 (correct)
  • 0.931

What is the arithmetic sphericity of the sample in Exercise 3.3 (ii)?

  • 0.931 (correct)
  • 0.929
  • 93.1% (correct)
  • 92.9%

What is the volume of the sample in Exercise 3.3 (iii)?

  • 60.22 mm3
  • 55.926662 mm3
  • 86.3%
  • 91591.43317 mm3 (correct)

What is the sphericity of a perfectly spherical particle?

<p>1 (A)</p> Signup and view all the answers

What is the value of dv in Exercise 3.3 (iii)?

<p>55.926662 mm3 (C)</p> Signup and view all the answers

What is the formula for the roundness factor 'R'?

<p>$R = \frac{A_p}{A_c}$ (A), $R = \frac{A_p}{A_c}$ (F)</p> Signup and view all the answers

Which of the following is NOT a method used to calculate sphericity?

<p>Roundness Factor (B)</p> Signup and view all the answers

What is the shape of the sample, as suggested by the sphericity calculated in Exercise 3.3 (iii)?

<p>Cylinder (C)</p> Signup and view all the answers

What does the value of the Wadell sphericity factor indicate about a particle’s shape?

<p>How close the particle is to a sphere (C)</p> Signup and view all the answers

How does shrinkage affect the diffusion coefficient of a material during drying?

<p>It decreases the diffusion coefficient. (A)</p> Signup and view all the answers

What is the significance of specifying the equivalent diameter when calculating the form factor?

<p>Different equivalent diameters result in different form factor values (C)</p> Signup and view all the answers

What does the phrase 'pressure imbalance' refer to in the text regarding shrinkage?

<p>The difference in pressure between the inside and outside of the food due to the removal of moisture. (D)</p> Signup and view all the answers

What is the implication of a particle having a roundness factor close to 1?

<p>The particle is almost perfectly spherical (E)</p> Signup and view all the answers

When calculating sphericity using the volume ratio method, what is the volume of the equivalent sphere compared to?

<p>The volume of the smallest sphere that encloses the particle (A)</p> Signup and view all the answers

What does the term 'projected area' refer to in the context of particle roundness?

<p>The shadow cast by the particle when illuminated from above (B)</p> Signup and view all the answers

What is the primary characteristic that influences the texture of products made from wheat flour?

<p>Particle size of the flour (C)</p> Signup and view all the answers

Which diameter is determined when the mass fraction is known?

<p>Mass mean diameter (B)</p> Signup and view all the answers

What is the consequence of using flour that is too fine in wafer production?

<p>Formation of light and tender products (C)</p> Signup and view all the answers

Which type of analysis is used for determining the volume surface mean diameter of wheat flour?

<p>Differential analysis only (C)</p> Signup and view all the answers

What happens if the flour used in wafer production is too coarse?

<p>Unsatisfactory and incomplete sheets are formed (C)</p> Signup and view all the answers

What does the term 'Sauter mean diameter' refer to?

<p>Volume surface mean diameter (D)</p> Signup and view all the answers

When is cumulative analysis typically used?

<p>When the number of particles is known (C)</p> Signup and view all the answers

Which method assesses the grinding performance of flour in wafer producing factories?

<p>Sieve analysis (B)</p> Signup and view all the answers

What is one of the main reasons size and shape are important in food technology?

<p>Heat and mass transfer calculations (C)</p> Signup and view all the answers

Which tool is commonly used to measure size in food physics?

<p>Vernier calliper (C)</p> Signup and view all the answers

What is evaluated to determine the quality of food materials?

<p>Particle size distribution (B)</p> Signup and view all the answers

What is 'sphericity' used to describe in food physics?

<p>The geometric shape of particles (B)</p> Signup and view all the answers

How are equivalent diameters related to measuring food particles?

<p>They help describe individual and bulk materials (C)</p> Signup and view all the answers

Which of the following shapes is NOT listed as an example in the standard chart for fruits and vegetables?

<p>Grapefruit (A)</p> Signup and view all the answers

What measurement is utilized to separate foreign materials from solids in food technology?

<p>Screening based on size and shape (A)</p> Signup and view all the answers

What is one technique for measuring size that utilizes visual analysis?

<p>Image analysis (B)</p> Signup and view all the answers

What is the purpose of shaking the stack in screen analysis?

<p>To facilitate the movement of particles through screens (A)</p> Signup and view all the answers

In the context of screen analysis, what does a 'mesh number' refer to?

<p>The size of particles that can pass through the screen (C)</p> Signup and view all the answers

What happens to particles that pass through the finest screen during screen analysis?

<p>They are collected in a separate container (C)</p> Signup and view all the answers

How are mass fractions calculated in screen analysis?

<p>By dividing the weight of particles by the total weight (A)</p> Signup and view all the answers

What does the notation '6/8' signify in particle size distribution?

<p>Particles passing through the 6-mesh and retained on the 8-mesh (A)</p> Signup and view all the answers

What type of graph is typically used in differential particle size analysis?

<p>Line graph of mass or number fraction versus particle size (A)</p> Signup and view all the answers

Which of the following statements about a Particle Size Analyzer is true?

<p>It measures the size distribution of particles (B)</p> Signup and view all the answers

Which organization is known for establishing standard testing sieves?

<p>American Society for Testing and Materials (ASTM) (B)</p> Signup and view all the answers

What is the volume equivalent diameter of a cube with edge length of 0.70 mm?

<p>0.87 mm (B)</p> Signup and view all the answers

What is the surface equivalent diameter of a tetrahedral shape with edge length of 0.70 mm?

<p>0.52 mm (B)</p> Signup and view all the answers

Which shape has a volume equivalent diameter of 0.68 mm when the edge length is 0.70 mm?

<p>Regular Octahedron (C)</p> Signup and view all the answers

The formula for the surface area of a cube is represented as which of the following?

<p>$A = 6a^2$ (A)</p> Signup and view all the answers

For a hypothetical sphere, what is the equation used to determine the diameter based on the area of the respective shape?

<p>$d_A = \sqrt{A/\pi}$ (A)</p> Signup and view all the answers

What is the surface equivalent diameter of an octahedral regular shape with an edge length of 0.70 mm?

<p>0.74 mm (B)</p> Signup and view all the answers

What does form factor relate to in the context of food physics?

<p>The quality control or processing line (C)</p> Signup and view all the answers

Which of the following shapes corresponds to a volume equivalent diameter of 0.43 mm?

<p>Regular Tetrahedron (B)</p> Signup and view all the answers

Flashcards

Importance of Size and Shape

Size and shape are crucial in food technology for factors like heat transfer and product quality.

Sphericity

A measure of how closely the shape of an object resembles a sphere.

Form Factor

A ratio representing the relationship between dimensions of an object to its overall size.

Roundness

A geometric property describing the degree to which a shape resembles a circle.

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Measurement Tools

Devices such as Vernier calipers and micrometers used to measure size accurately.

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Equivalent Diameters

Diameters used to represent particles based on their geometry or volume.

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Particle Size Distribution

The distribution of sizes of particles in a sample, crucial for quality control.

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Specific Surface Area

The total surface area of a material per unit mass, important for reactivity and processing.

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Screen Analysis

A method to separate particles by size using a series of screens.

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Sieve Number

A number indicating the size of openings in a sieve, determining particle size.

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Mass Fraction Calculation

The process of determining the proportion of each particle size after sieving.

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ASTM Sieve Standards

Standard specifications set by ASTM for sieve sizes and testing procedures.

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Particle Size Analyzer

A device used to measure and analyze the distribution of particle sizes.

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Particle Size Distribution (PSD)

Describes the sizes and quantities of particles within a sample.

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Differential Analysis of PSD

A method to plot the fraction of particles in size increments against their average size.

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Mesh Size Example

A specific particle size separation, e.g., 6/8 meaning passing through 6-mesh but retained on 8-mesh.

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Wadell Sphericity

A measure of particle shape ranging from 0 (needle) to 1 (spherical).

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Sphericity Value Range

The values of Wadell sphericity can range from 0 to 1, indicating different shapes.

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Roundness Factor (R)

Defined as the ratio of projected area to the area of the smallest circumscribed circle.

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Projected Area (Ap)

The largest two-dimensional area visible when observing a three-dimensional particle.

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Circumscribed Circle Area (Ac)

The area of the smallest circle that can completely encompass the particle.

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Wadell's Sphericity Factor

A specific sphericity measure using ratios for defining particle shape characteristics.

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Shape Calculation Examples

Sphericity calculations can include volume ratio, diameter ratio, and Wadell’s sphericity factor.

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Volume Equivalent Diameter (Cube)

The diameter of a sphere with the same volume as a cube with edge length 0.70 mm is 0.87 mm.

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Volume Equivalent Diameter (Tetrahedron)

The diameter of a sphere with the same volume as a tetrahedron with edge length 0.70 mm is 0.43 mm.

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Volume Equivalent Diameter (Octahedron)

The diameter of a sphere with the same volume as an octahedron with edge length 0.70 mm is 0.68 mm.

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Surface Equivalent Diameter (Cube)

The diameter of a sphere with the same surface area as a cube with edge length 0.70 mm is 0.97 mm.

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Surface Equivalent Diameter (Tetrahedron)

The diameter of a sphere with the same surface area as a tetrahedron with edge length 0.70 mm is 0.52 mm.

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Surface Equivalent Diameter (Octahedron)

The diameter of a sphere with the same surface area as an octahedron with edge length 0.70 mm is 0.74 mm.

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Mass Mean Diameter

Average diameter of particles based on their mass.

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Arithmetic Mean Diameter

Average diameter calculated from the number of particles.

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Volume Mean Diameter

Average diameter calculated based on the volume of particles.

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Sieve Analysis

A method to determine particle size distribution using screens.

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Sauter Mean Diameter

A measure that represents the average diameter based on surface area.

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Differential Analysis

A method that analyzes size distribution based on mass fraction.

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Cumulative Analysis

A method that aggregates size distributions of particles in a group.

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Grinding Performance

Effectiveness of crushing materials to achieve desired particle size.

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Volume of Solid Sample Sphericity

The ratio of the volume of a solid sample to that of a circumscribed sphere.

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Arithmetic Mean Sphericity

The average value of various diameter measurements of the sample.

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Diameter Calculation in Sphericity

Formula involving the diameter and volume to assess sphericity.

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Shrinkage in Food Processing

The decrease in volume of food due to moisture removal during processing.

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Effects of Shrinkage

Influences the diffusion coefficient and drying rate of food materials.

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Pressure Imbalance

The difference in pressure between the inside and outside of food causing shrinkage.

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Contracting Stresses

Stresses generated during drying that cause material to shrink or collapse.

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Volume Calculation for Sphericity

Mathematical expression to determine volume in relation to sphericity.

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Study Notes

Introduction to Food Physics - Geometric Properties - Size and Shape

  • Geometric properties of food materials are crucial in food technology for various applications, including heat and mass transfer calculations, screening of foreign materials, grading, and quality evaluation of fruits and vegetables.

Importance of Size and Shape

  • Food size and shape are significant for various processes and applications.
  • Size and shape influence heat and mass transfer during processes.
  • They are also important in separating foreign materials, grading products, and evaluating food quality.

Shape

  • Standard charts are used to describe food shapes.
  • Sphericity and form factor are used to quantify shape.

Techniques to Measure Size

  • Instruments used for measuring size include vernier calipers and micrometers.
  • Image analysis techniques are also utilized to measure size and shape.

Equivalent Diameters

  • Geometric equivalent diameters and physical equivalent diameters are calculated based on different properties (volume, surface area, etc.).
  • These measurements are based on individual particles or bulk materials.

Specific Surface Area

  • Specific surface area is an important property in various food processes.
  • It is calculated to analyze particle size distributions.

Particle Size Distribution

  • Particle size distributions (PSD) affect food properties.
  • The hardness of grain plays a significant factor in the PSD of flour.
  • PSD is a crucial factor in the quality of final products.
  • Techniques such as sieving (using screens) are used to measure PSD.

Shrinkage

  • Shrinkage is the decrease in volume during food processing, particularly during drying.
  • A pressure imbalance between the inside and outside of the food drives the contraction.
  • It impacts the drying rate due to its effect on the diffusion coefficient.

Sphericity: Volume Ratio

  • Sphericity is a shape factor defined as the ratio of the volume of a solid sample to the volume of the circumscribed sphere (volume ratio method).
  • The diameter of the circumscribed sphere equals the major diameter of the solid sample

Sphericity: Diameter Ratio

  • Sphericity is calculated using a dimensionless ratio of any specified equivalent diameter.
  • Dividing the specific equivalent diameter by the major diameter of the particle, resulting in a dimensionless value.
  • This approach involves specifying the equivalent diameter to be used in calculations.

Image Analysis

  • Techniques are used to analyze the images of particles.
  • Arithmetic mean diameter and geometric mean diameter are calculated.

Form Factor - Definitions

  • Form factors, depending on the sample type, can be defined by using different equivalent diameters, as listed in specific tables.
  • This approach uses diameter as a metric for defining the factors, and each factor relates to particular definitions (listed in the provided tables).
  • This approach includes determining the various equivalent diameters.
  • These factors provide details of the shape and size parameters.

Roundness

  • roundness is defined by the projection of the particle.
  • There are different roundness factors which can be used to quantify the roundness (based on an example provided in the OCR).

Exercises

  • Calculation exercises provided to demonstrate calculation of different forms of equivalent diameters and sphericity, depending on the shape and type.
  • These exercises involve calculating equivalent diameters for hypothetical shapes, as well as determining sphericity based on different methods.

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Chapter 3-Geometric Properties (Size and Shape) - PDF

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