Fe-501 physical properties of food Materials

FE-501
PHYSICAL PROPERTIES OF
FOOD MATERIALS
ASSOC PROF. DR. YUS ANIZA YUSOF
DEPARTMENT OF PROCESS & FOOD ENGINEERING
FACULTY OF ENGINEERING
UNIVERSITI PUTRA MALAYSIA

INTRODUCTION
• Foods are characterized by their physical properties.
y
p y
p p
• Physical properties intensely affect the quality of foods
and can be used to classify/identify foods.
• Formerly, the quality of a food was given by its
geometric characteristics.
• Now quality of food evaluate as total quality and takes
Now, quality of food evaluate as total quality and takes
into account the entire spectrum of physical properties
of foods.
• Physical properties should be able to be measured
objectively, quickly, individually, at a low cost and in a
manner that will not destroy the foods.
manner that will not destroy the foods

SIZE, SHAPE, VOLUME AND
RELATED PHYSICAL
ATTRIBUTES

INTRODUCTION
• Size and shape are important physical
attributes of foods that are used in screening,
grading and quality control of foods.
• They are also important in fluid flow and heat
and mass transfer calculations.

SIZE, SHAPE, VOLUME AND RELATED PHYSICAL ATTRIBUTES

SIZE
• Size is an important attribute of foods used in
p
screening solids to separate foreign materials, grading
of fruits and vegetables, and evaluating the quality of
food materials
materials.
• In fluid flow, and heat and mass transfer calculations, it
y
p
is necessary to know the size of the sample.
• Size of the particulate foods is also critical. For
example, particle size of powdered milk must be large
enough to prevent agglomeration but small enough to
agglomeration,
allow rapid dissolution during reconstitution.


SIZE
• Particle size was found to be inversely proportional to
l
f
d b
l
l
dispersion of powder and water holding capacity of whey
p
protein powders (Resch & Daubert, 2001).
p
(
)
• Decrease in particle size also increased the steady shear and
complex viscosity of the reconstituted powder.
• The importance of particle size measurement has been widely
recognized, especially in the beverage industry, as the
distribution and concentration ratio of particulates present in
p
p
beverages greatly affect their flavor.
• It is easy to specify size for regular particles, but for irregular
particles the term size must be arbitrarily specified.
ti l th t
i
tb
bit il
ifi d

SIZE
• Particle sizes are expressed in different units depending on
l
d d ff
d
d
the size range involved.
• Coarse particles are measured in millimeters, fine particles in
Coarse particles are measured in millimeters, fine particles in
terms of screen size, and very fine particles in micrometers or
nanometers.
• Ultrafine particles are sometimes described in terms of their
surface area per unit mass, usually in square meters per gram
(
(McCabe, Smith & Harriot, 1993).
,
,
)


SIZE
• Size can b d
be determined using the projected area method. In
d
h
d
h d
this method, three characteristic dimensions are defined:
1. Major diameter, which is the longest dimension of the
maximum projected area;
2. Intermediate diameter, which is the minimum
diameter of the maximum projected area or the
maximum diameter of the minimum projected area;
3.
3 Minor diameter which is the shortest dimension of the
diameter,
minimum projected area.


SIZE
• Length, width, and thickness terms are commonly used that
correspond to major, i
d
j
intermediate, and minor di
di
d i
diameters,
respectively.
• The dimensions can be measured using a micrometer or
caliper (Fig. 1). The micrometer is a simple instrument used to
measure distances between surfaces. Most micrometers have
a frame anvil spindle sleeve thimble and ratchet stop They
frame, anvil, spindle, sleeve, thimble,
stop.
are used to measure the outside diameters, inside diameters,
the distance between parallel surfaces, and the depth of
holes.

Fig.1

SIZE
• Particle size of particulate foods can be determined by sieve
analysis (Fi 2) passage through an electrically charged
l i (Fig.2),
h
h
l
i ll
h
d
orifice, and settling rate methods.
• Particle size distribution analyzers (Fig.3), which determine
both the size of particles and their state of distribution, are
used for production control of powders.

Fig.3

Fig.2

SHAPE
• Shape is also important in heat and mass transfer
calculations, screening solids to separate foreign
materials, grading of fruits and vegetables, and
, g
g
g
,
evaluating the quality of food materials.
• The shape of a food material is usually expressed
in terms of its sphericity and aspect ratio.
• Sphericity is an important parameter used in fluid
flow and heat and mass transfer calculations.


SHAPE
• According to the most commonly used
definition, sphericity is the ratio of volume of
solid to the volume of a sphere that has a
diameter equal to the major diameter of the
object so that it can circumscribe the solid
sample. For a spherical particle of diameter
Dp,
Dp sphericity is equal to 1 (Mohsenin 1970)
(Mohsenin, 1970).


SHAPE
• Assuming that the volume of the solid sample
g
p
is equal to the volume of the triaxial ellipsoid
which has diameters equivalent to those of
the sample, then:


SHAPE
• In a triaxial ellipsoid, all three perpendicular
p
,
p p
sections are ellipses (Fig. 4). If the major,
,
, ,
intermediate, and minor diameters are 2a, 2b,
and 2c, respectively, volume of the triaxial
p
ellipsoid can be determined from the
following equation:
• Then, sphericity is

SHAPE

Fig.4 Triaxial ellipsoid


SHAPE
• Sphericity is also defined as the ratio of
p
y
surface area of a sphere having the same
j
volume as the object to the actual surface
area of the object (McCabe, Smith, & Harriot,
)
1993):
where,
where


SHAPE
• The equivalent diameter is sometimes defined as
the d
h diameter of a sphere h
f
h
having the same volume
h
l
as the particle.
• However for fine granular materials it is difficult
However,
materials,
to determine the exact volume and surface area
of a particle.
• Therefore, equivalent diameter is usually taken to
be the nominal size based on screen analysis or
microscopic examination in granular materials
materials.
• The surface area is found from adsorption
measurements or from the pressure drop in a
bed of particles.

SHAPE
• In general, diameters may be specified for any
g
,
y
p
y
equidimensional particle.
• Particles that are not equidimensional that is
equidimensional,
is,
longer in one direction than in others, are
often characterized by the second longest
major dimension.
• For example for needlelike particles
example,
particles,
equivalent diameter refers to the thickness of
the particles not their length
particles,
length.

SHAPE
• In a sample of uniform particles of diameter
p
p
Dp, the number of particles in the sample is:
where

• Total surface area of particles;


SHAPE
• Another definition of sphericity is the ratio of
p
y
the diameter of the largest inscribed circle (di )
to the diameter of the smallest circumscribed
circle (dc) (Mohsenin, 1970):
• Recently, Bayram (2005) proposed another
equation to calculate sphericity
equation to calculate sphericity as:


SHAPE
• Where

• According to this formula, equivalent diameter for irregular
shape material is accepted as the average dimension.
• Differences between average diameter and measured
dimensions are determined by the sum of square of
differences.
• When this difference is divided by the square of product of
the average diameter and number of measurements, it
gives a fraction for the approach of the slope to an
equivalent sphere which is sphericity
sphere,
sphericity.

SHAPE

• According to Eq. (1.9), if the sample sphericity value is close to
zero it can be considered as spherical
spherical.
• The aspect ratio (Ra) is another term used to express the
shape of a material. It is calculated using the length (a) and
the width (b) of the sample as (Maduako & Faborode, 1990):
• Certain parameters are important f the d
for h design of conveyors
f
for particulate foods, such as radius of curvature, roundness,
g
p
p
and angle of repose. Radius of curvature is important to
determine how easily the object will roll. The more sharply
rounded the surface of contact, the greater will be the
stresses developed
developed.

SHAPE
Where

• The minimum and the maximum radii of curvature for larger
objects such as apples are calculated using the larger and
smaller dial indicator readings, respectively.
• For smaller objects of relatively uniform shape, the radius of
curvature can be calculated using the major diameter and
either the minor or intermediate diameter.


• Where

SHAPE

• Roundness is a measure of the sharpness of the corners of
the solid. Several methods are available for estimating
roundness. The most commonly used ones are given below
(Mohsenin, 1970):

where

SHAPE

Fig. 5 Roundness
definitions.

• Roundness can also be estimated from Eq. (1.15):

where


SHAPE
• Angle of repose is another important physical property used
g
p
p
p y
p p y
in particulate foods such as seeds, grains, and fruits.
• When granular solids are piled on a flat surface, the sides of
the il
th pile are at a d fi it reproducible angle with th
t
definite
d ibl
l
ith the
horizontal.
• This angle is called the angle of repose of the material. The
g
g
p
angle of repose is important for the design of processing,
storage, and conveying systems of particulate material.
• Wh
When the grains are smooth and rounded, the angle of
h
i
h
d
d d h
l
f
repose is low. For very fine and sticky materials the angle of
repose is high.

PARTICLE SIZE DISTRIBUTION
• The range of particle size in foods depends on the cell
g
p
p
structure and the degree of processing.
• The hardness of grain is a significant factor in the particle size
distribution f flour. Th particle size di t ib ti of fl
di t ib ti of fl
The
ti l i distribution f flour i
is
known to play an important role in its functional properties
and the quality of end products.
• The relationship between the physicochemical properties of
rice grains and particle size distributions of rice flours from
different rice cultivars were examined (Chen Lii & Lu 2004)
(Chen, Lii, Lu, 2004).
• It was found that physical characteristics of rice grain were the
major factors but chemical compositions were also important
in affecting the particle size distribution of rice flour.

• Particles can be separated into fractions by using one of the
p
y
g
following methods:
1. Air elutriation method: In this method, the velocity of an air
stream is adjusted so that particles measuring less than a given
diameter are suspended. After the particles within the size range
are collected, the air velocity is increased and the new fraction of
particles is collected The process continues until the particulate
collected.
food is separated into different fractions.

Air classifier

2. Settling, sedimentation, and centrifugation method: In settling and
sedimentation, the particles are separated from the fluid by gravitational
forces acting on the particles. The particles can be solid particles or liquid
drops. Settling and sedimentation are used to remove the particles from
the fluid. It is also possible to separate the particles into fractions of
different size or density. Particles that will not settle by gravitational force
can be separated by centrifugal force. If the purpose is to separate the
particles i t f ti
ti l into fractions of diff
f different sizes, particles of uniform d it b t
t i
ti l
f if
density but
different sizes are suspended in a liquid and settle at different rates.
Particles that settle in given time intervals are collected and weighed.

Centrifuge

3. Screening: This is a unit operation in which various sizes of
g
p
solid particles are separated into two or more fractions by
passing over screen(s). A dispersing agent may be added to
improve sieving characteristics Screen is the surface
characteristics.
containing a number of equally sized openings. The openings
are square. Each screen is identified in meshes per inch.
Mesh is defined as open spaces in a network. The smallest
mesh means largest clear opening.


• A set of standard screens is stacked one upon the other with
p
the smallest opening at the bottom and the largest at the top
placed on an automatic shaker for screen analysis (sieve
analysis).
analysis) In screen analysis the sample is placed on the top
analysis,
screen and the stack is shaken mechanically for a definite
time. The particles retained on each screen are removed and
weighed. Then, the mass fractions of particles separated are
calculated. Any particles that pass through the finest screen
p
are collected in a pan at the bottom of the stack.


• Particle size analysis can be done in two different ways:
l
l
b d
d ff
– differential analysis
– cumulative analysis.
y

• In differential analysis, mass or number fraction in each size
increment is plotted as a function of average particle size or
particle size range. The results are often presented as a
ti l i
Th
lt
ft
t d
histogram as shown in Fig. 6 with a continuous curve to
approximate the distribution. If the particle size ranges are all
equal as in this figure, the data can be plotted directly.



Fig. 6 Particle size
g
distribution using
differential analysis.

• However it gives a false impression if the covered range of particle
However, it gives a false impression if the covered range of particle
sizes differs from increment to increment. Less material is retained
in an increment when the particle size range is narrow than when it
is wide. Therefore, average particle size or size range versus
is wide Therefore average particle size or size range versus
should be plotted, where is the mass fraction and
is the particle size range in increment i (McCabe et al., 1993).


• Cumulative analysis is obtained by adding consecutively the
adding, consecutively,
individual increments, starting with that containing the
smallest particles and plotting the cumulative sums against
the maximum particle diameter in the increment. In a
cumulative analysis, the data may appropriately be
represented by a continuous curve.
p
y
• Table 1 shows a typical screen analysis. Cumulative plots are
made using the second and fifth columns of Table 1 (Fig. 7)



Fig. 7 Particle size distribution using
cumulative analysis

• Calculations of average particle size, specific surface area, or
g p
, p
,
particle population of a mixture may be based on either a
differential or a cumulative analysis. In cumulative analysis,
the assumption of “all particles in a single fraction are equal in
all
size” is not required. Therefore, methods based on the
cumulative analysis are more precise than those based on
differential analysis.


• The specific surface area is defined as the total surface area of
p
a unit mass of particles.
• For constant density (ρp) and sphericity
, specific surface
area (A ) of th mixture i
(Aw f the i t
is:
where


• If the cumulative analysis is used, specific surface area of the
y
, p
mixture is found by integrating with respect to mass fraction
between the limits of 0 to 1 (McCabe & Smith, 1976):

• Average particle diameter of a mixture can be calculated in
Average particle diameter of a mixture can be calculated in
different ways. The most commonly used one is the volume
surface mean diameter (Sauter mean diameter). It is used if
the mass fraction of particles in each fraction is known. For
h
f
i
f
i l i
hf
i i k
F
differential analysis:


• For cumulative analysis:
y

• Mass mean diameter can also be calculated if the mass
fractions of particles in each fraction are known For
known.
differential analysis:



• If the number of particles in each fraction is known,
p
,
arithmetic mean diameter is used. For differential analysis:

where

For cumulative analysis:


• The number of particles in the mixture can be calculated from
p
either differential or cumulative analysis using Eqs. (1.25) and
(1.26), respectively:

• where is the volume shape factor, which is defined by the
p
,
y
ratio of volume of a particle (Vp) to its cubic diameter:


• Dividing the total volume of the sample by the number of
g
p y
particles in the mixture gives the average volume of a particle.
The diameter of such a particle is the volume mean diameter,
which is found from:
which is found from:

For the cumulative analysis, volume mean diameter is
determined by integrating with respect to mass fraction between
the limits of 0 and 1:


VOLUME
• Volume is defined as the amount of three‐dimensional space
p
occupied by an object, usually expressed in units that are the
cubes of length units, such as cubic inches and cubic
centimeters,
centimeters or in units of liquid measure such as gallons and
measure,
liters.
• In the SI system, the unit of volume is m3.
• Volume is an important quality attribute in the food industry.
• It appeals to the eye, and is related to other quality
parameters. F
For i
instance, i i i
it is inversely correlated with
l
l d ih
texture.


VOLUME
• Volume of solids can be determined by using the following
y
g
g
methods:
1. Volume can be calculated from the characteristic
dimensions in the case of objects with regular shape.
di
i
i th
f bj t ith
l h
2. Volumes of solids can be determined experimentally
by liquid, gas, or solid displacement methods.
y q ,g ,
p
3. Volume can be measured by the image processing
method. An image processing method has been recently
developed to measure volume of ellipsoidal agricultural
d l
d
l
f lli id l
i l
l
products such as eggs, lemons, limes, and peaches
(Sabliov, Boldor, Keener, & Farkas, 2002).

VOLUME
Liquid Displacement Method
• If the solid sample does not absorb liquid very fast the liquid
If the solid sample does not absorb liquid very fast, the liquid
displacement method can be used to measure its volume.
• In this method, volume of food materials can be measured by
y
pycnometers (specific gravity bottles) or graduated cylinders.
• The pycnometer has a small hole in the lid that allows liquid
to escape as the lid is fitted into the neck of the bottle (Fig. 8).
to escape as the lid is fitted into the neck of the bottle (Fig 8)

Fig. 8 Pycnometer (specific gravity
bottle)

VOLUME
• The bottle is precisely weighed and filled with a liquid of
The bottle is precisely weighed and filled with a liquid of
known density.
• The lid is placed on the bottle so that the liquid is forced out
p
q
of the capillary.
• Liquid that has been forced out of the capillary is wiped from
the bottle and the bottle is weighed again.
the bottle and the bottle is weighed again
• After the bottle is emptied and dried, solid particles are
p
placed in the bottle and the bottle is weighed again.
g
g
• The bottle is completely filled with liquid so that liquid is
forced from the hole when the lid is replaced.


VOLUME
• The bottle is reweighed and the volume of solid particles can
The bottle is reweighed and the volume of solid particles can
be determined from the following formula:

where


VOLUME
• The volume of a sample can be measured by direct measurement
of volume of the liquid displaced by using a graduated cylinder or
burette.
• The difference between the initial volume of liquid in a graduated
cylinder and the volume of liquid with immersed material gives us
the volume of the material.
• That is the increase in volume after addition of solid sample is
is,
equal to the solid volume.
• In the liquid displacement method, liquids used should have a low
surface tension and should be absorbed very slowly by the
surface tension and should be absorbed very slowly by the
particles.
• Most commonly used fluids are water, alcohol, toluene, and
tetrachloroethylene. For displacement, it is better to use a
tetrachloroethylene For displacement it is better to use a
nonwetting fluid such as mercury.

VOLUME
• For larger objects a platform scale can be used (Mohsenin
objects,
(Mohsenin,
1970) (Fig. 9). The sample is completely submerged in liquid
such that it does not make contact with the sides or bottom of
the beaker. Weight of the liquid displaced by the solid sample is
divided by its density. The method is based on the Archimedes
p
principle, which states that a body immersed in a fluid will
p ,
y
experience a weight loss in an amount equal to the weight of
the fluid it displaces. That is, the upward buoyancy force
exerted on a body immersed in a liquid is equal to the weight of
the displaced liquid.
Fig. 9 Platform scale for
measurement of volume of large
objects.

VOLUME

where


VOLUME
• Liquids having a density lower than that of sample should be
used if partial floating of the sample is observed. The sample
is forced into the liquid by means of a sinker rod if it is lighter
or it is suspended with a string if it is heavier than the liquid. If
the sample is forced into the fluid using a sinker rod, it should
be taken into account in the measurement as:


VOLUME
Gas Displacement Method
• Volumes of particulate solids and materials with irregular
shape can be determined by displacement of gas or air in
pycnometer (Karathanos & Saravacos, 1993).
• The most commonly used gases are helium and nitrogen.
• The pycnometer consists of two airtight chambers of nearly
equal volumes V1 and V2,that are connected with small
volumes,
that
small‐
diameter tubing (Fig. 10).

Fig. 10 Gas comparison
pycnometer.

VOLUME
• The material to be measured is placed in the second chamber
chamber.
• The exhaust valve (valve 3) and the valve between the two
chambers (valve 2) are closed.
(
)
• The inlet valve (valve 1) is opened and the gas is supplied to
the first chamber until the gauge pressure is increased up to a
suitable value (e g 700 1000 Pa)
(e.g., 700–1000 Pa).
• Then, the inlet valve is closed and the equilibrium pressure is
g
g
y
recorded. Assuming that the gas behaves ideally:


VOLUME
where

• After the equilibrium pressure is recorded the valve between
recorded,
the two chambers is opened (valve 2) and the gas within the
first chamber is allowed to fill the empty spaces (pores) in the
second chamber.
d h b
• The new pressure (P2) is recorded. When valve 2 is opened,
total mass of gas (m) is divided into two, one of which fills the
first tank (m1) and the other fills the pore space of the second
tank (m2).

VOLUME
• Assuming that the system is isothermal:
• where Va2 is the volume of the empty spaces within the
second chamber and can be expressed as:

• where Vs i the volume of the solid ( 3) and can b calculated
h
is h
l
f h
lid (m
d
be l l d
from the following equation:


VOLUME
• The errors in this method may come from not taking into
account the volumes of the tubing connecting the chambers.
• M
Moreover, although the calculation assumes an id l gas, the
lh
h h
l l i
ideal
h
air does not exactly follow the ideal gas law.
• In addition, the equalization in pressures between the two
chambers is not isothermal.
• To eliminate these errors, the instrument should be calibrated
by i
b using an object of precisely k
bj
f
i l known volume.
l


VOLUME
Solid Displacement Method
• The volume of irregular solids can also be measured by sand
sand,
glass bead, or seed displacement method.
• Rapeseeds are commonly used for determination of volume
p
y
of baked products such as bread.
• In the rapeseed method, first the bulk density of rapeseeds is
determined by filling a glass container of known volume
uniformly with rapeseeds through tapping and smoothing the
surface with a ruler.
• All measurements are done until the constant weight is
reached between the consecutive measurements.
• Th d iti of th seeds are calculated f
The densities f the
d
l l t d from th measured
the
d
weight of the seeds and volume of the container.

VOLUME
Solid Displacement Method
• The sample and rapeseeds are placed together in the
container. The container is tapped and the surface is
smoothed with a ruler. Tapping and smoothing are continued
until a constant weight is reached between three consecutive
measurements. The volume of the sample is calculated as
follows:

where


VOLUME
Expressions of Volume
• Volume can be expressed in different forms The form of the
forms.
volume must be well defined before the data are presented. The
most commonly used definitions are:
– Solid volume (Vs ) is the volume of the solid material (including water)
excluding any interior pores that are filled with air. It can be determined
by the gas displacement method in which the gas is capable of penetrating
all open pores up to the diameter of the gas molecule.
– A
Apparent volume (Vapp) i the volume of a substance i l di all pores
l
is h
l
f
b
including ll
within the material (internal pores). Apparent volume of regular
geometries can be calculated using the characteristic dimensions.
Apparent volume of irregularly shaped samples may be determined by
solid or liquid displacement methods.
– Bulk volume (Vbulk) is the volume of a material when packed or stacked in
bulk. It includes all the pores enclosed within the material (internal pores)
and also the void volume outside the boundary of individual particles
when stacked in bulk (external pores).

POROSITY
• Porosity is an important physical property characterizing the
texture and the quality of dry and intermediate moisture
foods.
• Porosity data is required in modeling and design of various
heat and mass transfer processes such as drying, frying,
baking, heating, cooling,
baking heating cooling and extrusion
extrusion.
• It is an important parameter in predicting diffusional
properties of cellular foods.
• Porosity (ε) is defined as the volume fraction of the air or the
void fraction in the sample and expressed as:


POROSITY


POROSITY
• There are different methods for determination of
porosity, which can b summarized as f ll
i
hi h
be
i d follows:
1. Direct method: In this method, porosity is determined from the
difference of bulk volume of a piece of porous material and its
volume after destruction of all voids by means of compression.
volume after destruction of all voids by means of compression
This method can be applied if the material is very soft and no
attractive or repulsive force is present between the particles of
solid.
2. Optical method: In this method, porosity is determined from the
microscopic view of a section of the porous medium. This method
is suitable if the porosity is uniform throughout the sample, that
is, the sectional porosity represents the porosity of whole
,
p
y p
p
y
sample. Pore size distribution can be determined if a suitable
software is used to analyze images.
3. Density method: In this method, porosity is calculated from the
measured densities:
measured densities:

POROSITY
DENSITY METHOD
• Porosity due to the enclosed air space within
the particles
is named apparent porosity (εapp) and defined as the ratio of
total enclosed air space or voids volume to the total volume.
It can
also be named internal porosity. Apparent
porosity is calculated from
the measured solid (ρx) and
apparent density (ρapp)data as:
pp
y
)
• or from the specific solid

and apparent

volumes as:


POROSITY
DENSITY METHOD
• Bulk porosity (εbulk) which can also be called external or
Bulk porosity (ε ), which can also be called external or
interparticle porosity, includes the void volume outside the
boundary of individual particles when stacked as bulk and
calculated using bulk and apparent densities as:
• or from the specific bulk
or from the specific bulk
volumes as:

and apparent
and apparent

• Then, total porosity when material is packed or stacked as
bulk is:


POROSITY
DENSITY METHOD

• Pores within the food materials (internal pores) can be
divided into three groups: closed pores that are closed from
all sides, blind pores that have one end closed, and open or
flow‐ through pores where the flow typically takes place (Fig.
1.11).

Fig. 11 Different kinds
of pores.


POROSITY
DENSITY METHOD
• Since the apparent porosity is due to the enclosed air space
within the particles and there are three different forms of
pores within the particles, it can be written as:
where

• Then total porosity can also be written as:
Then,


POROSITY
GAS PYCNOMETER METHOD
4.
4 Gas pycnometer method: Porosity can be measured
directly by measuring the volume fraction of air using the
air comparison pycnometer. Remembering Eq. (1.49):

Porosity can be calculated from Eq. (1.49) as:

5.
5 Using porosimeters: Porosity and pore size
distribution can be determined using porosimeters,
which are the instruments based on the principle of
either li id i
i h liquid intrusion i
i into pores or li id extrusion
liquid
i
from the pores.

POROSITY

• For extrusion porosimetry, wetting liquids are used to fill the pores in
the porous materials. Liquid is displaced from the pores by applying
differential pressure on the sample and volume of extruded liquid is
measured.
• Extrusion methods can be categorized as capillary flow porosimetry
and liquid extrusion porosimetry. Capillary flow porosimetry is a liquid
extrusion method in which the differential gas pressure and flow rates
g p
through wet and dry samples are measured (Fig. 12). Capillary flow
porosimetry can measure pore size between 0.013 and 500 μm (Jena &
Gupta, 2002).
Fig. 12 Principle of
capillary flow
capillary flow
porosimetry

POROSITY

• For large pore sizes, liquid extrusion porosimetry is preferred.
g p
, q
p
y p
Liquid extrusion porosimetry can be used for pore sizes of
0.06 to 1000 μm.

Fig. 13 Principle of liquid
extrusion prosimetry


POROSITY

• In intrusion porosimetry, as intrusion liquid mercury, oil, or
water is used.
• In intrusion porosimetry, liquid is forced into pores under
pressure and intrusion volume and pressure are measured.
• Mercury intrusion porosimetry can measure pores in the
size range of 0.03 to 200 μm while nonmercury intrusion
porosimetry can measure pores in the size range of 0.001
to 20 μm.
• This method can detect pore volume, pore diameter, and
surface area of through and blind pores.
g
p
• Since very high pressures are required in mercury
intrusion, the pore structure of the samples can be
distorted.

POROSITY
• Porosity may show a maximum or minimum as a function of
y
y
moisture content.
• It may also decrease or increase exponentially during drying
without showing an optimum point.
ith t h i
ti
i t
• The porosity of the apple rings increased linearly when
moisture content decreased during drying and then reached a
g y g
constant value (Bai, Rahman, Perera, Smith, & Melton, 2002).
• A linear increase in the bulk porosity was also observed during
drying f h
d i of the starch samples (M
h
l (Marousis & S
i
Saravacos, 1990)
1990).


POROSITY
• The drying method is also important in affecting porosity.
y g
p
gp
y
• Freeze drying was found to produce the highest porosity,
whereas in conventional air drying the lowest porosity was
observed as compared t vacuum, microwave, and osmotic
b
d
d to
i
d
ti
drying of bananas, apples, carrots, and potatoes (Krokida &
Maroulis, 1997).
• Rahman (2003) developed a theoretical model to predict
porosity in foods during drying assuming that volume of pores
formed is equal to the volume of water removed during
drying.


POROSITY
• The presence of pores and degree of porosity affect the
p
p
g
p
y
mechanical properties of food materials.
• It has been shown that mechanical properties of extruded
food
f d products are affected b porosity (G
d t
ff t d by
it (Guraya & T l d
Toledo,
1996).
• Mandala and Sotirakoglou (2005) mentioned that crumb and
g
(
)
crust texture of breads could be related to porosity.


POROSITY
• Porosity is also important in frying, since it affects oil uptake
y
p
y g,
p
of the product.
• A linear relationship was found between oil uptake during
frying and porosity prior to frying (Pinthus,Weinberg, & Saguy,
f i
d
it
i t f i (Pi th W i b
&S
1995).
• Porosity increased during frying of restructured potato
y
g y g
p
product and after a short initial period, it was found to be
linearly correlated with oil uptake.


DETERMINATION OF VOLUME OF
DIFFERENT KINDS OF PORES
• Total specific pore volume within the material
can be
calculated if the specific volume of all kinds of pores—closed
pores , blind pores,
pores
blind pores
,and flow‐through pores
and flow through pores
are known:
• Total specific pore volume within the material can be
calculated by measuring specific bulk
and the specific
solid volume determined after compacting the sample to
solid volume determined after compacting the sample to
exclude all the pores :


• The difference between the specific solid volume determined
by gas pycnometer
and specific solid volume after
compacting the sample , gives the volume of closed pores
compacting the sample
gives the volume of closed pores
since in a gas pycnometer, gas enters into the open and blind
pores but not the closed ones. From these results, the specific
volume of closed pores can be calculated:
• Volume of flow through or open pores of the sample
Volume of flow through or open pores of the sample,
,
can be measured directly using liquid extrusion porosimetry.
From Eq. (1.51), the specific volume of the blind pores is:

• Substituting Eqs. (1.52) and (1.53) into Eq. (1.54):
• The fraction of open, closed, or blind pores can be calculated
by dividing the specified pore volume by total pore volume.


SHRINKAGE
• Shrinkage is the decrease in volume of the food
S
age s t e dec ease
o u e o t e ood
during processing such as drying.
g
• When moisture is removed from food during
drying, there is a pressure imbalance between
inside and outside of the food.
• This generates contracting stresses leading to
material shrinkage or collapse (Mayor & Sereno,
2004).
2004)
• Shrinkage affects the diffusion coefficient of the
material and therefore has an effect on the drying
rate.

SHRINKAGE


SHRINKAGE
• Apparent shrinkage is defined as the ratio of
Apparent shrinkage is defined as the ratio of
the apparent volume at a given moisture
content to the initial apparent volume of
content to the initial apparent volume of
materials before processing:
when


SHRINKAGE
• Shrinkage is also defined as the percent
change from the initial apparent volume.
• Two types of shrinkage are usually observed in
food materials. If there is a uniform shrinkage
in all dimensions of the material it is called
material,
isotropic shrinkage.
• Th
The nonuniform shrinkage i
if
hi k
in diff
different
dimensions, on the other hand, is called
anisotropic shrinkage.
i
i hi k

REFERENCES
1.
2.
3.
4.
5.
6.

Bayram, M. (2005). Determination of the sphericity of granular food
materials. Journal of Food Engineering, 68, 385–390.
Karathanos,V.T.,&Saravacos, G.D. (1993). Porosity and pore size
distribution of starch materials. Journal of Food Engineering, 18, 259
distribution of starch materials Journal of Food Engineering 18 259–
280.
McCabe, W.L, Smith, J.C., & Harriot, P. (1993). Unit Operations of
Chemical Engineering, 5th ed. Singapore: McGraw‐Hill.
Mohsenin, N.N. (1970). Physical Properties of Plant and Animal
h
(
) h
l
f l
d
l
Materials. New York: Gordon and Breach.
Maduako, J.N.,&Faborode, M.O. (1990). Some physical properties of
p
p
yp
g f
f
gy, ,
cocoa pods in relation to primary processing. Ife Journal of Technology, 2,
1–7.
Sabliov, C.M., Boldor, D.,Keener, K.M.,&Farkas, B.E. (2002). Image
processing method to determine surface area and volume of axi‐
symmetric agricultural products. International Journal of Food
symmetric agricultural products International Journal of Food
Properties, 5, 641–653.

THANK YOU


MASS
• Mass is a measure for inertia and heaviness of a body.
Heaviness i caused b the E h’ gravitational attraction f
H i
is
d by h Earth’s
i i
l
i for
a body. The force between the body of interest and the planet
Earth is called the weight force of the body. Mathematically,
this force can be expressed as the product of the body’s mass
and the Earth’s acceleration due to gravity, as shown by
equation (3 1)
(3.1).
(3.1)

• where

MASS & DENSITY

MASS
• The density of planet Earth varies with location and the planet
is slightly pear shaped and not in the shape of a perfect
pear‐shaped
sphere, the value of gravitational acceleration differs slightly
with location on the Earth’s surface. Considering the rotation
of the planet a body resting at the equator will have a greater
planet,
tangential speed and centrifugal force than in regions far
north or south of the equator.
• The value of Earth’s gravitational acceleration in Zurich,
h
l
f
h’
l
l
h
Switzerland is used as a standard for calculations, and is called
standard gravitational acceleration having the value g =
2
9.80665m∙ s−2.When a balance which was adjusted in Zurich,
is taken to another place on the Earth, but is not corrected for
the local gravitational acceleration, the displayed weight may
be in error.
MASS & DENSITY

MASS
• Table 3.1 illustrates this concept for a body having a mass of
1kg. To avoid erroneous weight measurements of this type, a
1k T
id
i h
f hi
balance has to be recalibrated at the location in which it will
be used. For this purpose, commercial mass standards are
produced with the help of national standards organizations
around the world.
Table 3.1 Weighing a 1 kg mass in different place

MASS & DENSITY

WEIGHING AND ATMOSPHERIC BUOYANCY
• A balance is an instrument measuring the weighing force of a
g
g g
body. However, it usually does not display a force signal (e.g.
newtons), but a mass signal (e.g. kilograms).This is due to the
principle of calibration used for balances: A mass standard is
placed on the balance that causes a deformation, which can
be read as an angle, a distance or an electric voltage,
depending on the type of balance.
• A calibration has to be performed for every type of
sensing/measuring instrument For this purpose appropriate
instrument.
purpose,
respective standard materials and procedures are needed,
that make it possible to perform calibration of an instrument
in
i any l b t
laboratory.
MASS & DENSITY

• From a scientific point of view the calibration procedure described
for a balance is basically to use the instrument as a “force meter,”
then divide the force G measured by the value of the local
gravitational acceleration g, and display the result (equation volume
of h d
f hydrometer i m3)
t in ).
(3.2)

• Since the middle ages the weight of a body has been a manifold of
a reference weight. So weighing is simply a comparison to a given
mass standard. From this point of view weighing is dividing the
weight force of the given body and weight force of a mass standard
and the result is a dimensionless number. That is the principle of all
mechanical and electronic balances up to today, and a consequence
of lacking an expression for mass with fundamental natural
constants.
MASS & DENSITY

(3.3)

• where

MASS & DENSITY

• Most weight measurements are carried out with body and balance
surrounded by atmospheric air, which is a gaseous fluid possessing
density. Only bodies of material with density greater than
atmospheric air at the Earth’s surface can impart a force when
p
p
placed upon a balance.
• For example a rubber balloon filled with helium gas (less dense than
air) possesses mass but it will not rest on a balance It will rise
mass,
balance.
upward into the atmosphere in search of an altitude at which the
density of the atmosphere is in equilibrium with itself. His upward
force caused the density of the Earth’s atmosphere is known as
Earth s
buoyancy. This atmospheric buoyancy causes a body resting on a
balance when surrounded by atmospheric air to exhibit a slightly
smaller weight measurement than if it were in a vacuum (Figure
3.1).
MASS & DENSITY


Figure 3.1 A balance is adjusted to zero weight (picture I). A mass of 1 kg is weight
in atmosphere (picture II) and in vacuum (picture III)

MASS & DENSITY

• The calculation needed to correct for this buoyancy effect in
y y
order to yield the true mass of a body is called atmospheric
buoyancy correction. The true mass of a body mK is the
product of the displayed mass m*K and a correctional factor K
m
K.
The value of the correctional factor K depends on the density
of the air surrounding the balance. Because weight
measurement is a comparison of a body of interest and a
mass standard, the densities of both materials also influence
( q
( ) ( )
the correctional factor (equations (3.4) to (3.6):
(3.4)

MASS & DENSITY

(3.5)

(3.6)

• Wh
Where

MASS & DENSITY

• The density of air depends on its pressure, temperature,
y
p
p
,
p
,
humidity and its concentration of CO2.
• For practical purposes, the density of atmospheric air at
normal room t
l
temperature and sea l l ( t d d conditions)
t
d
level (standard
diti )
can be taken to be approximately 1.2 kg ∙ m−3. A simple
approach to calculate the density of air more precisely is given
by equation (3.7):
(3.7)

• where

MASS & DENSITY

• In contrast to air, the density of water is 1000 times greater
,
y
g
(1000 kg ∙ m−3). Therefore, the density range of most food,
agricultural and biological materials is in the same order of
3
magnitude as that of water about 1200 ± 300 kg ∙ m−3. The
water,
densities of materials with high water content are in a range
more closely to that of water (between 1000 and 1100 kg ∙
3
m−3) while dry materials like agricultural grains, seeds and dry
beans consisting of proteins, carbohydrates, starch or
g
g
cellulose are often in the range 1400–1600 kg ∙ m−3.

MASS & DENSITY

DENSITY
• The density of a substance is the quotient of mass over
y
q
volume. The standard international (SI) units for expressing
density are kg ∙ m−3.The same definition is valid for solid,
liquid,
liquid gaseous and disperse systems like foams bulk goods or
foams,
powders.
• The reciprocal of density is called specific volume and the
units are m3 ∙ kg−1 (equations (3.8) and (3.9).
(3.8)

(3.9)

MASS & DENSITY

DENSITY
• where

MASS & DENSITY

DENSITY
TEMPERATURE DEPENDENCY OF DENSITY
• Many materials undergo thermal expansion when heated,
meaning they increase in volume without any change in mass.
For this reason, the density of a given material often depends
on temperature. Since the volume of a material normally
increases with temperature, the density usually decreases
with t
ith temperature. Thi effect i much l
t
This ff t is
h larger i gaseous
in
systems than in liquid or solid systems.

MASS & DENSITY

DENSITY
TEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS
• For many engineering applications air can be assumed to
For many engineering applications air can be assumed to
behave as an ideal gas, meaning that the ideal gas law can be
used for calculating the density of air as a function of
temperature and pressure (equations (3.10) and (3.11).
(3.10)
(3.11)

• where

MASS & DENSITY

DENSITY
TEMPERATURE DEPENDENCY OF DENSITY – IDEAL GAS
• In case of low temperatures and humid air the ideal gas law
loses accuracy, and will lead to error. To calculate the density
of air more precisely as a function of water vapor partial
pressure and atmospheric pressure, equation (3.7) can be
used.

MASS & DENSITY

DENSITY
TEMPERATURE DEPENDENCY OF DENSITY – SOLID AND LIQUIDS
• The density of liquids and solids is a function of temperature.
Small changes in volume caused by temperature change can
be calculated with the aid of the thermal expansion
coefficient:
(3.12)

• where

MASS & DENSITY

DENSITY
• Water shows abnormal behavior in a narrow range of
temperature near its freezing point at atmospheric pressure.
When lowering the temperature of water from 4 ◦C and 0◦C,
C
0 C,
the density of water actually decreases rather than increases.
This abnormal behavior of water (see Figure 3.2 and Figure
3.3 is taken into
3 3 i t k i t account within th polynomial f ti of
t ithi the l
i l function f
Bertsch (1983) for calculation of the density of liquid water
(equation (3.13):
(3.13)

MASS & DENSITY

DENSITY

Fig. 3.2 Normal (N) and abnormal (H O)
Fig 3 2 Normal (N) and abnormal (H2O)
thermal expansion (schematic)

Fig. 3.3 Abnormality of water (H2O):
g
y
(
)
Temperature dependency of density
compared to normal behavior (N)
MASS & DENSITY

DENSITY
• A further abnormality of water is that the solid phase (ice) has
a lower density than the liquid phase at the same
temperature. This behavior has important consequences for
the biosphere. Because of this temperature dependency of
density, control or measurement and recording of
temperature i necessary when d it i measured f
t
t
is
h
density is
d for
process control and quality control purposes.

MASS & DENSITY

DENSITY
PRESSURE DEPENDENCY OF DENSITY
• Materials are compressible. On application of pressure their
volume decreases, causing the density to be a function of
pressure as well as temperature. Gases are far more
compressible than liquids and solids. Over a normal
temperature range many gases can be assumed to behave like
ideal
id l gases.

MASS & DENSITY

DENSITY
PRESSURE DEPENDENCY OF DENSITY – IDEAL GAS
• For ideal gases the density is directly proportional to the
pressure:
(
(3.14)
)
(3.15)
(3.16)

• so the density of the ideal gas is
(3.17)

MASS & DENSITY

DENSITY
PRESSURE DEPENDENCY OF DENSITY – IDEAL GAS
• The negative slope of the volume–pressure curve divided by
the initial volume is called the compressibility . It is the
inverse compression modulus K of a material.
(3.18)

(3.19)

MASS & DENSITY

DENSITY
PRESSURE DEPENDENCY OF DENSITY – LIQUIDS AND SOLIDS
• Ideal liquids and solids show an elastic behavior. That means
their volume can decrease by a certain amount when a
pressure is applied, but that it will fully recover to the initial
volume when the pressure is restored. For this type of
material the change in volume on increasing the pressure can
be l l t d based
b calculated b d on equation (3 20)
ti (3.20):
(3.20)

• with (2.8) and because of m = const the relative density is:
(3.21)
MASS & DENSITY

DENSITY
• where

MASS & DENSITY

DENSITY
• Liquids and solids with very low compressibility show a very
small volume reduction and often are treated in practice as
incompressible materials. Water has very low compressibility
with a value of ≈ 5x10−10 Pa−1. So, up to pressures in the order
of 10 MPa (100 bar), the reduction of the volume in water is
so small th t it can b neglected. Alth
ll that
be
l t d Although i hi h pressure
h in high
processing of food, where the pressure will range to some
100MPa, the compressibility of water cannot be neglected.

MASS & DENSITY

DENSITY
SPECIFIC GRAVITY (RELATIVE DENSITY)
• The ratio of the absolute density of a material to the density
of a reference material is called relative density d. Water at 4
°C or 20°C is most often used as the reference material for
C
20 C
this purpose. In the USA and Canada, when water is used as
the reference standard, the term“ relative density” is not
used, and i replaced b th t
d
d is
l d by the term“ specific gravity.” Si
“
ifi
it ” Since
water is nearly always chosen as the reference standard
world‐wide, for practical purposes the terms “relative
density” and “specific gravity” may be considered as
synonymous.
(3.22)
(3 22)
MASS & DENSITY

DENSITY
SPECIFIC GRAVITY (RELATIVE DENSITY)
• Where

• It is important to note that both density and specific gravity
(relative density) relate to the same physical property. However,
density
d i must b reported i di
be
d in dimensional units of mass per unit
i
l i
f
i
volume (e.g. g ∙ cm−3 or kg ∙ m−3), while specific gravity (relative
density) is a ratio of densities, and is always a dimensionless
number. In the case where density is being reported in dimensional
units of g ∙cm−3 and with the density of the reference material being
1 g ∙ cm−3 or nearly 1 g ∙ cm−3 it is interesting to note that numerical
values of both density and specific gravity (relative density)will be
the same, respectively.
MASS & DENSITY

DENSITY
METHODS FOR LABORATORY MEASUREMENT OF DENSITY
• Table 3.2 shows examples of different methods used for density
measurement.

MASS & DENSITY

DENSITY
PYCNOMETRIC MEASUREMENT

• By weighing a known volume of a liquid, the density of that
liquid can be measured in a simple way Glass bulbs with
way.
precisely known volume that are used for this purpose are
called pycnometers. A pycnometer can also be any other
instrument d i d f the same purpose that may h
i
designed for h
h
have
sample chambers of precisely known volume, but made of
other materials (not glass bulbs). The glass bulb or sample
chamber will have a marker to which the liquid sample must
be carefully filled. Then the density of the fluid can be
calculated by:
(3.23)
MASS & DENSITY

DENSITY

• Because of thermal expansion of the glass, the pycnometer
volume is known for the temperature at which it was
calibrated, only. So, for measurement of the absolute density,
pycnometers should be used at the same temperature at
which they were calibrated.
hi h h
lib
d
• Another way is to measure the relative density (specific
gravity) rather than the absolute density. For this purpose, the
pycnometer is weighed with the sample liquid and again
weighed with the reference liquid (often water).The ratio of
both weights gives the relative density d or specific gravity of
d,
the sample.
MASS & DENSITY

DENSITY
(3.24)
(3 24)

where

MASS & DENSITY

DENSITY

• Once the relative density d, or specific gravity, of the sample is
known,
known and the density of the reference material is known
from the literature, the absolute density of the sample can be
calculated:
(3.25)

MASS & DENSITY

DENSITY
• Fig. 3.4 and 3.5 show different designs of glass pycnometers

Fig. 3.4 Pycnometer designs: (a) Reischauer, (b) Bingham, (c) Gay‐Lussac,
(d) Sprengel,(e) Lipkin, (f) Hubbard

MASS & DENSITY

DENSITY

Fig. 3.5 Examples of pycnometers . The right one is for viscous samples
and powders

MASS & DENSITY

DENSITY
HYDROSTATIC BALANCES (BUOYANCY WEIGHING)

• The principle of a hydrostatic balance is based on Archimedes
law of buoyancy If a body is submersed in a fluid its weight
buoyancy.
will be lowered because of the buoyancy force. The buoyancy
force is directly proportional to the volume of the submersed
body d the density f the fluid. By
b d and th d it of th fl id B measurement of th
t f the
buoyancy force with the balance, the volume of the body can
be determined quite accurately, and together with the
measured mass of the body, the density is obtained.

MASS & DENSITY

DENSITY

• A simple technique for making this type of measurement is to
place a beaker partially filled with water on top of a top‐
top
loading balance, with the weight of beaker and water tared‐
out to read zero on the display. Then, fully submerge the solid
body beneath th water surface, t ki care th t it neither
b d b
th the
t
f
taking
that
ith
touches the bottom nor the sides of the beaker. The weight
reading shown on the display of the balance will be the
weight of the volume of water displaced by the solid body.
Since density of water is known, the precise volume of the
solid body is determined.
MASS & DENSITY

DENSITY
(3.8)
(3.26)

• with ∆m as the difference in weight (in kg) of the body before
and after submersion:
(3.27)
(3.28)
(3 28)
(3.29)
(3.30)
MASS & DENSITY

DENSITY

• where

• S th d it f b d
So the density of a body can be obtained by taking first the
b bt i d b t ki fi t th
weight prior to submersion (that means weighing in air) and
its weight when submersed in a fluid with a known density F
using equation (3.30).
MASS & DENSITY

DENSITY

• With the ratio
(3.31)
(3 31)

• the relative density d (specific gravity) of the body is
(3.32)

(3.33)

• That means d can be calculated very quickly after two
readings from the balance.
MASS & DENSITY

DENSITY

• If the weight in air mL is not corrected for atmospheric
buoyancy,
buoyancy the density obtained by hydrostatic weighing can
be called apparent density of the body. If that correction
made, then mL and K will be slightly higher, and can be called
true mass and t
t
d true d it
density.
• On the other hand when a body of known volume is
submersed in a fluid, the difference in weight of the body in
,
g
y
air and the weight of fluid displaced by the body can be used
to determine the density of the fluid, and can be calculated
with equation (3 34):
(3.34):
(3.34)
MASS & DENSITY

DENSITY

• Figure 3.6 shows a special design of hydrostatic balance that is
suitable for measuring the density of a solid or the density of
suitable for measuring the density of a solid or the density of
the liquid in the reservoir when used with a solid body of
precisely known volume.

Fig. 3.6 Hydrostatic balance design.
1: balance, 2: platform, 3: small
beaker,
beaker 4: large beaker 5: support
beaker,
bracket, 6: pan, 7: thermometer
MASS & DENSITY

DENSITY
• To obtain the density of a solid, the sample is weighed first in air, and
then it is submersed and the weight is taken again. As can be seen in
Figure 3.6 there is a small pan mounted on the weighing plate of the
balance. A small beaker on a cable is suspended within a larger beaker
containing the fluid of interest. The large beaker is resting on a raised
platform so its weight is not transmitted to the balance.
• To obtain the fluid density in the large beaker, a test body with known
p
p
g
volume is first placed on the pan and its weight in air is measured.
Then the test body is placed into the small beaker, submersed in the
fluid and weighed once again. Then the density of the liquid is
g q
(
)
calculated using equation (3.34). It should be remembered that the
density of the fluid is dependent on temperature so the temperature
must be controlled and recorded.

MASS & DENSITY

DENSITY
MOHR‐WESTPHAL BALANCE

• The Mohr–Westphal balance (see Figure 3.7) is another type
of hydrostatic balance. It is designed as a nonsymmetric beam
of hydrostatic balance It is designed as a nonsymmetric beam
balance for measuring the density of liquids.

Fig. 3.7 Mohr‐Westphal balance 1:
beam, 2: weights, 3: buoyancy body, 4:
beam 2: weights 3: buoyancy body 4:
liquid sample
MASS & DENSITY

DENSITY

• At the free end of the arm of the balance a “buoyancy body”
is suspended in air The buoyancy body is normally made of
air.
glass and can have a built‐in thermometer. Then the buoyancy
body is submersed into the liquid of interest.
• Because of the effect of buoyancy, the weight of the
submersed glass body will appear lower than it was in air, and
will bring the balance out of zero.
g
• The buoyancy force can be measured by successively adding
small weights to the arm until the balance is restored to zero.
The
Th measurement i th repeated with water as a reference
t is then
t d ith t
f
liquid.
MASS & DENSITY

DENSITY

• The ratio of both readings provides the relative density or
specific gravity of the liquid as can be shown below. With the
specific gravity of the liquid as can be shown below With the
buoyancy force
(3.40)
(3.41)

• With the fluid of interest
(3.42)

• With water as reference material
(3.43)
(3 43)
MASS & DENSITY

DENSITY
• So the ratio is
(3.44)

• Because the volume of the glass body is the same for both readings,
then
(3.45)

• So the specific gravity is simply
(3.46)
(3 46)
MASS & DENSITY

DENSITY

• where

MASS & DENSITY

DENSITY

• The result should be recorded along with the temperature of
the measurement. Often both readings are taken at 20 C and
the measurement Often both readings are taken at 20 ◦C and
the result is written as d20/20. The quantity d20/4 would mean
that the density of the liquid was compared to the density of
water at 4°C:
t
t 4°C

MASS & DENSITY

DENSITY

• The Mohr–Westphal balance can also be used to measure the
density of a solid sample which is submersed in a fluid with
known density. For this purpose, equation (3.37) would be
used to calculate the volume of the sample.

MASS & DENSITY

DENSITY
HYDROMETER

• Hydrometers (Fig 3.8) are hollow glass bodies with the shape
of a buoy
buoy.
• Hydrometers are designed with a volume to mass ratio in such
a way that the glass body will float at a certain depth in the
liquid under investigation.
• Depending upon the density of that liquid the hydrometer will
float at a higher or lower position The upper part of the
position.
hydrometer has a scale for reading the nonsubmersed part h
of the floating glass body.

MASS & DENSITY

DENSITY
HYDROMETER

• The nonsubmersed length of the hydrometer can be read with
the aid of a scale on the upper part of the hydrometer
hydrometer.
• A weight at the bottom of the hydrometer acts like the keel of
a sailboat to ensure that it will float in the liquid in a vertical
orientation.
• The scale can be calibrated directly in units of density or, e.g.
in concentration units (Fig 3 9)
3.9).

MASS & DENSITY

DENSITY
HYDROMETER

Fig. 3.8 Hydrometer. 1:scale, 2: body
(with and without thermometer), 3: keel

Fig. 3.9 Reading of a hydrometer scale at
the liquid surface (example)

MASS & DENSITY

DENSITY
HYDROMETER

• The floating depth position of the hydrometer depends on
weight force and interfacial force (force due to surface
weight force and interfacial force (force due to surface
tension). It is
(3.47)

• Which means:
(3.48)

• so
(3.49)

MASS & DENSITY

DENSITY
HYDROMETER

• The nonsubmersed part of the hydrometer has the length
(3.50)

• Which means
(3.51)

• Sometimes the combination of two physical properties will
give the information needed about a process or a product. For
example, by knowing both the density and refractive index of
beer wort, the alcohol content can be calculated, and by this,
the progress of fermentation
MASS & DENSITY

DENSITY
HYDROMETER

MASS & DENSITY

DENSITY
HYDROMETER

• Without consideration of interfacial tension effects the
hydrometer equation simplifies to
hydrometer equation simplifies to
(3.52)

• There are hydrometers available which are corrected for
interfacial tension offered in different range categories called
– L (l
L (low, 15–35mN ∙m−1),
15 35 N
1)
– M(medium, 35–65 mN ∙ m−1) and
– H (high, for higher values).

MASS & DENSITY

DENSITY
SUBMERSION TECHNIQUE

• Pycnometers and hydrometers do not work very well with
liquids of high viscosity
viscosity.
• For highly viscous liquids, measurement of density can be
performed with the submersion technique (see Fig 3.10).
• A beaker with the viscous liquid sample is put on a balance.
The display value is recorded, or the display may be set to
zero (tare)
(tare).
• Then a test body with known volume is pressed into the
sample.
MASS & DENSITY

DENSITY

Fig. 3.10 Submersion technique
for density measurement. 1:
depth mark, 2: liquid sample, 3:
buoyancy body of known volume

MASS & DENSITY

DENSITY

• The buoyancy force caused by the submerged test body is
transferred to the balance and appears on the display as an
apparent increased weight m.
• This increased weight force is the buoyancy force, and is the
weight of the displaced liquid, which is equal in volume to the
volume of the submersed solid body:
(3.53)

• and
(3.54)

MASS & DENSITY

DENSITY

• So
(3.55)

• where

MASS & DENSITY

DENSITY

• For precision measurement, the buoyancy body can be a
hollow metal sphere with calibrated volume To avoid errors
volume.
from buoyancy of the mounting rod there is normally a depth
mark on the rod which indicates the right depth position for
immersion so th t th submerged section of rod i accounted
i
i
that the b
d
ti
f d is
t d
for in the calibrated volume.

MASS & DENSITY

DENSITY
DENSITY OF SOLIDS

• Many agricultural materials and food and feed ingredients are
in the form of granular materials (grains meals and powders)
(grains,
powders),
which are bulk solids made up of small particles.
• The weight or size of the individual particles within any of
these types of materials may vary over a large range e.g. from
frozen diced vegetables to corn cornels to fine powder
p
particles.
• The term “solid density” means the density of the solid
material of which a particle is made, no matter what type of
fluid
fl id or other material may exist b t
th
t i l
i t between th particles.
the
ti l
MASS & DENSITY

DENSITY
DENSITY OF SOLIDS

• Solid particles contain pores or hollow cavities filled with
gases or liquids this contributes to the density of the solid
liquids,
solid.
• When pores or cavities occur, it is important to state whether
they are closed or open. If they are closed, meaning they are
located completely within the solid particle, they belong to
the solid. If they are open to the surroundings at the particle
surface, e.g. the atmosphere, they do not belong to the solid
, g
p
,
y
g
body.
• To avoid communication errors the density of solids should be
given with a note lik “i l di pore volume” or “ ith t
i
ith
t like “including
l
”
“without
pore volume.”
MASS & DENSITY

DENSITY
DENSITY OF SOLIDS

• This can be accomplished by how the system boundaries are
defined, and can be calculated as follows:
defined and can be calculated as follows:
(3.8)

• where

MASS & DENSITY

DENSITY
DENSITY OF SOLIDS

• To measure the density of a solid particle often simply means
to measure its volume, because its mass is known upon
to measure its volume because its mass is known upon
weighing.
• To get the volume of the solid sample without its open pores,
a pycnometer technique with an appropriate liquid can be
used.
• The liquid must not alter or dissolve the sample For this
The liquid must not alter or dissolve the sample. For this
purpose, a sequence of weighings is conducted as indicated in
Figure 3.11.

MASS & DENSITY

DENSITY
DENSITY OF SOLIDS

• After weighing the empty pycnometer m0 the pycnometer is
weighed with the sample m
weighed with the sample mP.
• Then the pycnometer is filled up to a designated mark with an
appropriate reference liquid of known density and weighed
again mP,F.
• Finally, the pycnometer is weighed when filled to the same
mark with only the reference liquid m
mark with only the reference liquid mF:

MASS & DENSITY

DENSITY
DENSITY OF SOLIDS

Fig. 3.11 Pycnometer measurement of the density of a solid granular material, e.g. a
powder

MASS & DENSITY

DENSITY
DENSITY OF SOLIDS

• The density of the solid material then is
(3.8)
(3.56)
(3.57)
(3.58)
(3 58)

MASS & DENSITY

DENSITY
DENSITY OF SOLIDS
(3.59)

(3.60)

(3.61)

MASS & DENSITY

DENSITY
DENSITY OF SOLIDS
(3.62)

(3.63)

• where

MASS & DENSITY

DENSITY
BULK DENSITY

• Powders and bulk goods contain hollow spaces or voids filled
with gas normally air The density of that type of bulk
gas,
air.
material, including the void spaces, is called bulk density.
• Using equation (3.8) the bulk density can be calculated by
weighing a sample of the bulk material and measurement of
its volume.
• The volume of the whole bulk material must be taken “as is ”
as is.
To measure this volume, the sample material can be poured
into a beaker or cylinder up to a known volumetric mark.

MASS & DENSITY

DENSITY
BULK DENSITY

• Different technique in filling the beaker or cylinder may lead
to different distributions of solid particles and hollow spaces
spaces.
So, to get repeatable results the technique of filling has to be
standardized.
• To overcome problems with repeatable filling technique, the
bulk material can be tapped before reading of the volume. By
tapping the material, the solid particles will “settle” into the
pp g
,
p
most stable situation they can reach. The void spaces will get
smaller as the solid particles settle step by step into a spatial
situation where the bulk density will reach a maximum The
maximum.
time needed to reach this maximum depends on tapping
MASS & DENSITY
speed and tapping amplitude.

DENSITY
BULK DENSITY

Figure 3.12. Device for tapping of bulK goods:
1: rotating cam, 2: housing, 3: powder sample,
y
g
4: cylinder, 5: overring

MASS & DENSITY

DENSITY
BULK DENSITY

• Figure 3.12 shows an example of a device which can be used
to measure bulk density and tapped bulk density
subsequently.
• First the bulk material is filled into a 1000 cm3 cylinder until it
is overflowing under repeatable technique conditions. Then
with aid of a flat spatula, the excess overflow of sample
material is scraped away from the top of the cylinder to leave
p
y
p
y
the sample perfectly level at the top, and the 1000 cm3
sample is weighed to get the bulk density.

MASS & DENSITY

DENSITY
BULK DENSITY

• Now a cylindrical extension overring is slipped onto the 1000
cm3 cylinder and more sample material is filled in The
in.
cylinder is mounted on the tapping device and moved for a
fixed number of tappings. In German testing standards a
number of 2500 with a f
b
f
ith frequency of 250 s−1 i specified.
f
1 is
ifi d
• After this the sample material is adjusted to 1000 cm3 again
and weighed. The tapped bulk density should be recorded
g
pp
y
with the parameters of its measurement.

MASS & DENSITY

DENSITY
BULK DENSITY

• The difference between bulk density and maximum tapped
bulk density provides information about the ability of the bulk
material to be compressed by gravity or pressure. Powders
can be characterized for this property by the Hausner ratio,
which i th quotient of t
hi h is the
ti t f tapped b lk d it over untapped
d bulk density
t
d
bulk density (see Table 3.3).

Table 2.7.
Characterization of
Characterization of
powder flowability
by Hausner ratio
MASS & DENSITY

DENSITY
POROSITY

• Also the volume of the hollow void space (pores) can be
calculated.
calculated The ratio of the volume of the void space (pores)
and the total volume of the bulk is called porosity ɛ:
(3.64)
(3 64)
(3.65)

• because mB ≈ mS = m
(3.66)
MASS & DENSITY

DENSITY
POROSITY

• So
(
(3.67)
)

• With ɛ as the relative volume of the hollow pore space, and α
as the relative volume of the solid particle space it is evident
that:
(3.68)

MASS & DENSITY

DENSITY
POROSITY

• where

MASS & DENSITY

THE END
THE END

RHEOLOGICAL PROPERTIES OF FOODS

Fe-501 physical properties of food Materials

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Fe-501 physical properties of food Materials