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).