Physical Characteristics Dr. Muanmai Apintanapong

Physical Characteristics

Dr. Muanmai Apintanapong

Physical Characteristics

Considering either bulk or individual units of material.– Shape, size, volume, specific gravity

surface area, bulk density and etc.

Size

Weight

Shape

Volume

Shape and size

Inseparable in a physical object

= (sh, s)

= Index

sh = shape

s = size Other applications

= (sh, s, o, p, f,…)

Y = b1X1+b2X2+b3X3+b4X4+b5X5

Irregular in shape

Seeds, grains, fruits and vegetables are irregular in shape

important to know what criterion should be used to decide when adequate number of measurements has been made to define the form of object.

Griffith (1964) : related volume (V) to their axial dimension (a)

V = a1b1 a2

b2 a3b3 … an

bn

log V = b1 log a1 + b2 log a2 +….+ bn log an

Criteria for describing shape and size

Size : a representative dimension In fruit and cereal: 3 main projected area

– a = length– b = width– c = thickness

Average dimension

Arithmatic mean size

Geometric mean size

Size based on volume

3

thicknesswidthlength

31)( thicknesswidthlength

313 )6(6 VDDVee

Average dimension

Size based on surface area

Size based on projected area

212 )( AssA SDDS

212 )4(4/ pppp ADDA

Measuring Grain Dimension

Grain TypeGrain TypeLength Length ((mmmm))

very longvery long >> 7.57.5longlong > 6.5 <> 6.5 < 7.57.5mediummedium >5.5 <>5.5 < 6.56.5shortshort < 5.5< 5.5

Physical Properties>>shape

The concept of shape factor– Geometric

dimensions (L,W,T) of various objects are plotted against their volumes, surface areas or projected areas

– The slope of regression line yields shape factor (α)

V

LWT

αv

SA

(LWT)2/3

αSA

Ap

(LWT)2/3

αAp

Example

Determine: v, density, equivalent diameter of sphere, average diameter, geometric mean

diameter

Axial dimension (cm) Weight

(g)

Volume

(cm3)a b c

apples 7.0 6.76 5.64 145.5 180.3

potatoes 8.2 7.2 5.3 204.0 184.0

tomatoes 6.45 5.92 4.72 127.3 126.2

Charted standards

Compare longitudinal and lateral cross section with the shapes listed on a charted standard

Roundness

Measure of sharpness of the corners of the solid

Ap = largest projected area in natural rest position

Ac = area of smallest circumscribing circle

Roundness

r = radius of curvature as defined in figure R = radius of maximum inscribed circle N = total number of corners summed in

numerator

NR

rRoundness

Roundness

r = radius of curvature of the shapest corner

R = mean radius of object

R

rRoundness

Sphericity

di = diameter of the largest inscribed circle

dc = diameter of the smallest circumscribed circle

c

i

d

dSphericity

Sphericity

de = diameter of a sphere of same volume of object

dc = diameter of the smallest circumscribed sphere (usually the longest diameter of object)

c

e

d

dSphericity

dc

Sphericity

31

spherebedcircumscriofVol

solidofVolSphericity

31

2

31

3

6

6

a

bc

a

abcSphericity

a

abc

a

abc

diametermajor

diametermeangeometricSphericity

31

31

3

6

6

a = longest intercept

b = longest intercept normal to a

c = longest intercept normal to a and b

Shape factor ()

objectofSA

volumesamehavingsphereofSAfactorShape )(

Measurement of axial dimension

Use photographics enlarger to determine a, b, c

Use shadowgraph

Resemblance to geometric bodies

Shape can be approximated by one of the following standard geometric shapes:– Prolate spheroid– Oblate spheroid– Right circular cone or cylinder

Resemblance to geometric bodies

Prolate spheroid

– Volume

– Surface area

a, b = major & minor semi-axes of ellipse of rotation

e = eccentricity

V = volume

S = surface area

V =

S =

21

2

1

a

be

A prolate spheroid is a spheroid in which the polar diameter is

longer than the equatorial diameter.

Resemblance to geometric bodies

Oblate spheroid

– Volume

– Surface area

a, b = major & minor semi-axes of ellipse of rotation

e = eccentricity

V = volume

S = surface area

V =

S =

21

2

1

a

be

An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the

diameter of the equatorial circle whose plane bisects it.

Resemblance to geometric bodies

Frustum of right cone

– Volume

– Surface area

r1 & r2 = radii of base & top

h = altitude

V =

S =

A cone that has its apex aligned directly above the center of its base.

Right Circular Cylinder

A right cylinder with bases that are circles.

Resemblance to geometric bodies

Estimation of V and S in this manner should be corrected.

Correction factor is determined by finding actual volume and surface area

experimentally and establish correction factor for the typical shape of each variety

of product.

Average projected area

Camera set up for recording the criterion area (above left) of fruits and vegetables for several orientations.

Average projected area

Based on Theory of Convex body (Bannesen and Fenchel, 1948)– Sphere:

– Nonsphere:

36

16

,6

32

23

3

2

23

D

D

S

V

DSDV

361

3

2

S

V

Polya & Szega (1951)

Assume averaged projected area of convex body = ¼ of surface area

32

3

2

3

2

21.1

36

1

4

4,36

1

:

VA

A

V

ASS

V

sphereFor

p

p

p

21.1:

21.116

9 31

KnonsphereFor

K

Volume and Density

Platform balance method: for large objects such as fruits and vegetables

waterdisplacedofwt

waterofgrspairinwtgravityspecific

waterofdensitywt

waterdisplacedofwtV

.

...

.

.

Example

Assuming a specific gravity of 1.0 and a weight density of 62.4 lb/ft3 for water, using a platform scale method, the volume and specific gravity of an apple was determined as follows:– Weight of apple in air = 0.292 lb– Weight of container+water = 2.24 lb– Weight of container+water+apple submerged =

2.61 lb– Weight of displaced water = 2.61-2.24 = 0.37

lb

Specific gravity balance

For smaller objects such as small fruits, peas and beans, kernels of corn, etc.

Specific gravity balance

If solid is heavier than water:

If solid is lighter than water (attach another solid as sinker)

Wa = wt. in air Ww = wt. in water

waterofSGwaterinwtairinwt

airinwtgravityspecific

waterofdensitywt

waterinwtairinwtV

.

.

.

.

waterofSG

WWbothWW

objectWgravityspecific

wawa

a

kersin

Specific gravity gradient tube

Fast and accurate Ex: toluene & CCl4

(sp. gr. 0.87-1.59) Measure the height

after object reaches equilibrium and calculated and compared with calibration curve.

Air comparison pycnometer

The density of a solid in any form can be measured at room temperature with the gas comparison pycnometer. The volume of a substance is measured in air or in an inert gas in a cylinder of variable calibrated volume. For the calculation of density one mass measurement is taken after concluding the volum

e measurement.

Air comparison pycnometer

Pycnometer method

Specific gravity bottle and toluene Toluene (C6H5CH3) has the advantages of:

– Little tendency to soak into the kernel– Low surface tension, enabling it to flow smoothly

over kernel– Little solvent action on constituents of kernel

especially fats and oils– High boiling point– Not changing its specific gravity and viscosity on

exposure to atmosphere– Having low specific gravity

Pycnometer method

grainbydisplacedtolueneofwt

grainofwtCattolueneofgrsggravityspecific

.

.20..

Example

Consider the volume measurement for a sample of 16 corn kernels coated with Pliabond– Weight of sample = 4.4598 g– Weight of pycnometer = 55.6468 g– Weight of pycnometer+toluene = 78.2399 g– Weight of pycnometer+toluene+sample =

79.6226 g– Weight of pycnometer+water = 81.7709 g

Porosity

Void volume or pore volume (empty space) relative to total volume

),( sizeparticlecontentmoisturefporosity

porosityratiovoid

solidofvolume

voidofvolumeratiovoid

volumetotal

voidofvolumeporosity

Porosity tank

1

2

V

Vvolumevoid

Example

To determine the porosity of dry shelled corn, tank 2 of the apparatus is filled with a sample of this corn to a bulk density of 47 lb/ft3. The pressure readings were P1 = 15.2 and P2 = 10.4 in Hg

Porosity

Porosity is also referred to as packing factor (PF):

particlesofdensitysolid

packingofdensityparticlesofdensitysolidPF

Porosity and bulk density

Weight and surface area

32KWSAVW

Surface area

Leaf and stalk surface area Light planimeter Indirect estimation (projected area) Surface coating method

– Estimated by the weight of coating material– Material is coated on grains and glass beads of

known surface area (control).

Air permeability method

sampleglassbeads

beadsglasssample W

W

areasurfaceareaSurface

Shape, Size and Area

Using image analysis – The image analysis setup consists of a color CCD

camera and a circular lighting chamber connected to a host Pentium II 400 MHz computer.

Top view of the Image Analysis Set up

CCD Camera

Illumination Chamber

Image Analysis Software

Two image analysis software are available for extracting the dimensional feature of rice kernels

1. Image Tool 2: This program was developed at the University of Texas Health Science center at San Antonio, Texas and available from the internet (http://ddsdx.uthscsa.edu/dig/download.html).

2. Particle Image Analysis: This program was developed by Procure Vision AB Ltd., Stockholm, Sweden and the evaluation version is available from the internet (http://www.acoutronic.com).