T.C. MARMARA UNIVERSITY

FACULTY OF ENGINEERING METALLURGICAL AND MATERIALS ENGINEERING

DEPARTMENT

DIFFUSION PROPERTIES OF SELECTED MATERIALS

Münevver BAYAZITLI

(Metallurgical and Materials Engineering)

SENIOR PROJECT

ADVISOR

Prof.Dr. Ersan KALAFATOĞLU

İSTANBUL 2005

2

TABLE OF CONTENTS

I. INTRODUCTION

II. BACKGROUND Diffusion Mechanisms

Steady-state Diffusion

Non-steady state Diffusion

Diffusion in gases

Diffusion in Liquids

Diffusion in solids

Diffusion Coefficient Measurements

III. PROCEDURE

IV. RESULTS

V. DISCUSSION OF RESULTS

VI. CONCLUSION

VII. REFERENCES

3

I.INTRODUCTION

The fragrance of flowers in a corner of a room drifts even to far distances.

When one droplet of ink is dripped into a cup of water, the ink soon spreads, even

without stirring, and quickly becomes invisible. These facts show that even if there is

no macroscopic flow in a gas or a liquid, molecular movement can take place, and

different entities can mix with each other.

It can be seen that examples of diffusion in everyday life are to much; the

diffusion of sugar in a cup of tea, the vaporization of water in a teakettle, cloud

formation, clothes drying, etc.

Engineers are concerned with diffusion when studying lots of subjects; such

as: gas absorption, seperation, crystallization and extraction, production and heat

treatment of metals, drying, cutting and welding metals, mass transfer in waste

treatment.

Many reactions and processes which are mentioned above, rely on the transfer

of mass either within a specific solid or from a liquid, a gas, or another solid phase.

This is accomplished by diffusion. The purpose of this project is to study the

properties of diffusion process, to observe the diffusion mechanisms and the diffusion

in gases, liquids and solids, to find the diffusion coefficient of selected materials by

doing experiments and using the formulas of diffusion.

4

II. BACKGROUND

DIFFUSION MECHANISMS

From an atomic perspective, diffusion is just the stepwise migration of atoms

from lattice site to lattice site. In fact, the atoms in solid materials are in constant

motion, rapidly changing positions. For an atom to make such a move, two

conditions must be met:

1. There must be an empty adjacent site.

2. The atom must have sufficient energy to break bonds with its neighbor

atoms and then cause some lattice distortion during the displacement (1).

This energy is vibrational in nature. At a specific temperature some small

fraction of the total number of atoms is capable of difusive motion, by virtue of the

magnitudes of their vibrational energies. This fraction increases with rising

temperature. Several different models for this atomic motion have been proposed; of

these posibilities, two dominates for metallic diffusion.

Vacancy Diffusion

One mechanism involves the interchange of an atom from a normal lattice

position to an adjacent vacant lattice site or vacancy, as represented in Figure 1. This

process necessitates the presence of vacancies, and the extent to which vacancy

diffusion can occur is a function of the number of these defects that are present;

significant concentrations of vacancies may exist in metals at elevated temperatures.

Since diffusing atoms and vacancies exchange positions, the diffusion of atoms in one

direction corresponds to the motion of vacancies in the opposite direction. Both self-

diffusion and interdiffusion occur by this mechanism.

Instertitial Diffusion

The second type of diffusion involves atoms that migrate from an instertitial

position to a neighboring one that is empty. This mechanism is found for

interdiffusion of impurities such as hydrogen, carbon, nitrogen, and oxygen, which

have atoms that are small enough to fit into the interstitial positions. Host or

5

substitutional impurity atoms rarely form instertitials and do not normally diffuse via

this mechanism. This phenomenon is appropriately termed instertitial diffusion,

shown in Figure 1.

Figure 1 schematic representation of vacancy and instertitial diffusion.

In most metal alloys, instertitial diffusion occurs much more rapidly than

diffusion by the vacancy mode, since the instertitial atoms are smaller, and thus more

mobile. Furthermore, there are emptier instertitial positions than vacancies; hence,

the probability of instertitial atomic movement is greater than for vacancy diffusion.

STEADY-STATE DIFFUSION

Diffusion is a time-dependent process that is, in macroscopic sense, the

quantity of an element that is transprted within another is a function of time. Often it

is necessary to know how fast diffusion occurs, or the rate of mass transfer. This rate

is frequently expresses as a diffusion flux (J), defined as the mass (or equivalently, the

number of atoms) M diffusing through and perpendicular to a unit cross-sectional area

of solid per unit time. In mathematical form, this may be represented as;

J = tA

M.

(Equation 1.a)

Where A denotes the area across which diffusion is occuring and t is elapsed diffusion

time. In differential form, this expression becomes;

J = dt

dMA1 (Equation 1.b)

6

The units for J are kilograms or atoms per meter squared per second (kg/m2-s or

atoms/m2-s).

If the diffusion flux does not change with time, a steady-state condition exists.

One common example of steady-state diffusion is the diffusion of atoms of a gas

through a plate of metal for which the concentrations (or pressures) of the diffusing

species on both surfaces of the plate are held constant. This is represented

schematically in Figure 2.a.

When concentration C is plotted versus position (or distance) within the solid

x, the resulting curve is termed the concentration profile; the slope at a particular

point on this curve is the concentration gradient:

Concentration gradient = dxdC (Equation 2.a)

Thin metal plane

PA>PB

and constant Gas at pressure PB

Gas at pressure PA Direction of diffusion of gaseous species Area, A Figure 2.a Steady-state difusion across a thin plane

Concentration of diffusing Species (C) CA CB Position (x) xA xB

Figure 2.b A linear concentration profile for the diffusion situation

7

In the present treatment, the concentration profile is assumed to be linear, as depicted

in Figure 2.b, and

Concentration gradient = xC∆∆ =

BA

BA

xxCC

−−

(Equation 2.b)

For diffusion problems, it is sometimes convenient to express concentration in terms

of mass of diffusing species per unit volume of solid (kg/m3 or g/cm3).

The mathematics of steady-state diffusion in a single (x) direction is

relatively simple, in that the flux is proportional to the concentration gradient through

the expression;

J = dxdCD− (Equation 3)

The constant of proportionality D is called diffusion coefficient, which is expressed

in square meters per second. The negative sign in this expression indicates that the

direction of diffusion is down the concentration gradient, from a high to a low

concentration. Equation 3 is sometimes called Fick’s first law.

Sometimes the term driving force is used in the contex of what compels a

reaction to occur. For diffusion reactions, several such forces are possible; when

diffusion is according to Eguation 3, the concentration gradient is the driving force.

One practical example of steady-state diffusion is found in the purification

of hydrogen gas. One side of a thin sheet of palladium metal is exposed to the impure

gas composed of hydrogen and other gaseous species such as nitrogen, oxygen, and

water vapor. The hydrogen selectively diffuses through the sheet to the opposite side,

which is maintained at a constant and lower hydrogen pressure.

NONSTEADY-STATE DIFFUSION

Most practical diffusion situations are nonsteady-state. That is diffusion

flux and the concentration gradient at some particular point in a solid varies with time,

with a net accumulation or depletion of the diffusing species resulting. Under

8

conditions of nonsteady-state, use of Equation 3 is no longer convenient; instead, the

partial differential equation;

tC∂∂ = ⎟

⎠⎞

⎜⎝⎛

∂∂

∂∂

xCD

x. (Equation 4.1)

Known as Fick’s second law, is used. If the diffusion coefficient is independent of

composition, Equation 4.1 simplifies to;

tC∂∂ = 2

2

xCD

∂∂ (Equation 4.2)

Solutions to this expression are possible when physically meaningful boundary

conditions are specified. Comprehensive collections of these are given by Crank,

Carslaw and Jaeger.

One practically important solution is for a semi-infinite solid in which the

surface concentration is held constant. Frequently, the source of the diffusing species

is a gas phase, the partial pressure of which is maintained at a constant value.

Furthermore, the following assumptions are made (1):

1. Before diffusion, any of diffusing solute atoms in the solid are uniformly

distributed with concentration of C0.

2. The value of x at the surface is zero and increases with distance into the

solid.

3. The time is taken to be zero the instant before the diffusion process

begins.

DIFFUSION IN GASES

Diffusion through a Stagnant Gas Film

The Arnold diffusion cell of Figure 3, which is often used to measure mass

diffusivities experimentally, contains a pure liquid A which vaporizes and diffuses

into the stagnant column of gas B(3). Right at the liquid-gas interface the gas phase

9

concentration of A, expressed as mole fraction, is xA1. This is taken to be the gas

phase concentration of A corresponding to equilibrium with the liquid at the interface;

that is, xA1 is the vapor pressure of A divided by the total pressure, provided that A

and B from an ideal gas mixture. We further assume that the solubility of B in liquid

A is negligible (4).

At the top of the tube (z=z2) a stream of gas mixture A-B of concentration

xA2 flows past slowly; thereby the mole fraction of A at the top of the column is

maintained at xA2. The entire system is presumed to be held at constant temperature

and pressure. Gases A and B are assumed to be ideal.

Figure 3 Arnold diffusion cell

When the evaporating system attains a steady-state, there is a net motion of

A away from the evaporating surface and vapor B is stationary. Hence the expression

can be used for NAz:

AzN = dzdx

xcD A

A

AB

−−

1 (Equation 5.1)

A mass balance over an incremental column height ∆z states that at steady state;

0=− ∆+ zzAZzAz SNSN (Equation 5.2)

z = z1

z = z2

Liquid A

Gas stream of A and B

∆z

10

in which S is the cross sectional area of the column. Division by S∆z and taking the

limit as ∆z approaches zero gives;

0=−dz

dN Az (Equation 5.3)

Substitution of Eq.5.1 into Eq.5.3 gives;

01

=⎟⎟⎠

⎞⎜⎜⎝

⎛− dz

dxx

cDdzd A

A

AB (Equation 5.4)

For an ideal-gas mixture at constant temperature and pressure, c is constant,

and DAB is very nearly independent of concentration. Hence cDAB can be taken

outside the derivative to get;

01

1=⎟⎟

⎠

⎞⎜⎜⎝

⎛− dz

dxxdz

d A

A

(Equation 5.5)

This is a secon-order equation for the concentration profile expressed as mole fraction

of A. Integration with respect to z gives;

111 C

dzdx

xA

A

=−

(Equation 5.6)

A second integration then gives;

( ) 211ln CzCxA +=−− (Equation 5.7)

The two constants of integration may be determined by the use of the boundary

conditions;

B.C.1: at 1zz = , 1AA xx = (Equation 5.8)

B.C.2: at 2zz = , 2AA xx = (Equation 5.9)

11

When the constants so obtained are substituted into Eq.5.7, the following expressions

for the concentration profiles are obtained:

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

111

A

A

xx =

12

1

1

2

11 zz

zz

A

A

xx −

−

⎟⎟⎠

⎞⎜⎜⎝

⎛−− (Equation 5.10)

Although the concentration prıofiles are helpful in picturing the diffusion

process, in engineering calculations it is usually the average concentration or the mass

flux at some surface that of interest(4).

The rate of mass transfer at the liquid-gas interface, which is the rate of

evaporation, is obtained by using Eq.5.1:

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=+=−

−==1

2

1211

ln11

B

BABB

B

ABA

A

ABzzAz x

xzz

cDdz

dxx

cDdz

dxx

cDN (Equation 5.11)

DIFFUSION IN LIQUIDS

Mass diffusion in liquids is important to many industrial seperation

processes such as distillation and extraction. Often the largest resistance to overall

mass transfer is in the liquid phase. Diffusion coefficients in liquid systems are very

low when compared to gas systems. The low rates of diffusion in the liquid phase

make small effects, such as the volume change upon mixing, very important; the

precence of a concentratin gradient causes mass diffusion, but that rate may be

equally dependent upon other factors(2).

DIFFUSION IN SOLIDS

Diffusion coefficients in solids are much less than those in gases and range

from slightly less than those in liquids to very small. Diffusion in solids often occurs

in conjunction with adsorption and chemisorption phenomena. Metallurgists have

been interested in solid diffusion because of its importance in such problems as

degassing of metals and graphite, carburization, nitriding and phosphorizing of steel,

12

and desulfurization of steel. An example of diffusion coupled with adsorption is the

sulfur-iron system. It has been suggested that sulfur diffuses in iron by an alternate

dissociation and formation of sulfides, rather than by interpenetration or by place

change (2).

There have been many studies of the interdiffusion of metals. For instance,

it was known before 1900 that at 300 °C gold diffuses more rapidly through lead than

does sodium chloride through water at 18 °C. Radioactive tracers are convenient in

following interdiffusion in metals. Diffusion in polymers is another active research

area. The precence of vapors or gases sometimes alters the internal structure and

external dimensions of a polymer solid. Diffusion in polumers is of interest in the

drying dyeing of textiles, in the air or water permeability of paint films and packaging

materials, and the migration of plasticizers (2).

Diffusion in solid may be divided into two classes: structure-insensitive and

structure-sensitive diffusion. Structure-insensitive diffusion refers to the case in

which the solute is dissolved so as to form a homogeneous solution. An example is

the interdiffusion of metals, where the solute is part of the solid structure. The

copper-zinc system behaves in this manner, as does the lead-gold system. In contrast,

structure-sensitive diffusion occurs in the case of liquids and gases flowing through

the interstices and capillary passages in a solid; an example is the diffusive flow of

fluids through the sintered metal, such as that used in catalysts(2).

The Kirkendall Effect

An experiment which shows that, in a binary solid solution, each of the two

atomic forms can move with a different velocity. In the original experiment, as

performed by Smigalskas and Kirkendall, the diffusion of copper and zinc atoms was

studied in the composition range where zinc dissolves in copper and the alloy still

retains the face-centered cubic crystal structure characteristics of copper. Since their

original work, many other investigators have found similar results using a large

number of different binary alloys.

13

Figure 4 Kirkendall diffusion couple

Figure 4 is a schematic representation of a Kirkendall diffusion couple: a

three dimesional view of a block of metal formed by welding together two metals of

different compositions. In the plane of the weld, shown in the center of Figure 4, a

number of fine wires (usually of some refractory metal that will not dissolve in the

alloy system to be studied) are incorporated in the diffusion couple. These wires

serve as markers with which to study the diffusion process. For the sake of the

argument, assuming that the metals seperated by the plane of the weld are originally

pure metal A and pure metal B. In order to that a total amount of diffusion, which is

large enough to be experimentally measurable, can be obtained in a specimen of this

type, it is necessary that it be heated to temperature close to the melting point of the

metals comrising the bar, and maintained there for a relatively long time, usually of

the order of days, for diffusion in solids is much slower than in gases or liquids.

Upon cooling the specimen to room temperature, it is placed in a lathe and thin layers

parallel to the weld interface are removed from the bar. Each layer is then analyzed

chemically and the results plotted to give a curve showing the composition of the bar

as a function of distance along the bar (5).

DIFFUSION COEFFICIENT MEASUREMENTS

Marrero and Mason provide an excellent review of measurement techniques

for gas-phase diffusion coefficients. The Stefan method for the measurement of the

diffusion coefficient in gases uses the rate of evaporation of a liquid in a narrow tube.

The first component must be a liquid, while the second gas is passed across the top of

Metal A Metal B

Wire

Weld

14

the tube. The inside capillary diameter is known, and from the evaporation rate the

diffusion coefficient can be determined. Precision is poor at high or low vapor

pressures, and so the range of temperatures for a given system is restricted (2).

In the Loschmidt method, two gaseous components are olaced in a tube that

is divided into two sections by a removable partition. The partition is removed for a

time and the gases are allowed to diffuse under unsteady-state conditions. The

partition is reinserted and the contents of each chamber are analyzed. From this, the

diffusion coefficient can be calculated. The method often yields diffusion coefficients

that are in error because of convection currents. If the gases have different densities,

then there may be appreciable mass transfer by natural convection currents (2).

The point source method fo gases, developed by Walker and Westenberg,

has been used to measure diffusion coefficients at temperatures up to 1200 K with a

precision of about 1 percent. The point source method injects a trace sample of one

gas into the laminar flow of a second gas stream. In a flow system it is relatively easy

to control the temperature by adding a constant amount of heat to a constant flow of

gas. In the region of the injection probe, the total pressure may be asumed constant,

and the injected species diffuses along the direction of flow as well as in a radial

direction. The concentration of the injevted gas is measured by a special sampling

technique in which the gas ample is continually withdrawn and passed through a

thermal conductivity cell. The point source technique appears to be the most

satisfactory technique developed so far for measurements of diffusion coefficients

over wide ranges of temperature and pressure. The Stefan method was severely

limited by the requirement that one component be a liquid with vapor pressure neither

too high or too low, and the Loschmidt method, while capable of high temperature

measurements, is relatively imprecise even with the best available constant-

temperature equipment(2).

Diffusion coefficients in liquids are of interest not only to engineers

designing mass transfer equipment but also to physical chemists and others studying

the proporties of proteins and other high molacular weight polymer and colloid

solutions(2).

15

III. PROCEDURE

Experimental Plan for Gas Diffusion

Three laboratory solvents will be used in this experiment. These are water,

ethanol, methanol and isopropyl alcohol.

The solvents are put into the graduated cylinder which is on a proper mass

balance device. When the liquid is evaporating into the air, we can say the liquid

level at z=z1 as shown in Figure 5;

z = z2 2AA xx =

z = z1 1AA xx =

Liquid A Figure 5 Schematic illustration of the diffusion cell

The system is presumed to be held at constant temperature and pressure. With

time there is a net motion of liquid away from the surface and the weight and the

height of the liquid in the graduated cylinder decreases.

The mass change and the height of the liquid with increasing time will be

recorded. Temperature and pressure will be measured.

Vapor pressure of the liquid A is a function of temperature and will be found.

The mass diffusivity (cm2sec-1) of the selected solvent will be obtained by

using some formulas which are shown in the calculation part.

16

IV. RESULTS Measured values which are obtained from the experiment with water, ethanol,

isopropyl alcohol and methanol; are shown in the Table 1, Table 2, Table 3, and Table

4, respectively.

Decrease in the mass of substance with time and the increase in the height of

the graduated cylinder from the top to the level of liquid, with time are shown in the

graphs below (Figures 6, 7, 8, 9, 10, 11, 12, 13)

17

Result of experiment with pure water: Table 1 Results of pure water

t (min) Mass (g) H (mm) Temperature (°C) Humidity (%) 0 108.5235 142.5 22 49

60 108.5146 143 20 49 120 108.5099 143.5 20 49 180 108.5035 144 20 49 240 108.5005 144.1 20 49 300 108.4977 144.2 20 49

pure water

108,5235

108,5146108,5099

108,5035108,5005

108,4977y = -0,00008462x + 108,52097619

108,4900

108,4950

108,5000

108,5050

108,5100

108,5150

108,5200

108,5250

108,5300

0 60 120 180 240 300

Time (min.)

Mas

s (g

ram

Figure 6 Measured mass-time graph of pure water

pure water

142,5

143

143,5

144 144,1 144,2y = 0,0059x + 142,67

142

142,5

143

143,5

144

144,5

145

0 60 120 180 240 300

Time (min.)

Hei

ght o

f the

cyc

linde

r(m

m)

Figure 7 Measure height-time graph for pure water

18

Result of experiment with ethanol: Table 2 Results for ethanol

t (min) Mass (g) H (mm) Temperature (°C) 0 92.8393 159.5 20

30 92.8303 160 20 60 92.8234 160.1 20 90 92.8166 160.5 20 120 92.8105 160.6 20 150 92.8049 160.7 20 210 92.7942 160.7 20 270 92.7830 161 20 300 92.7765 161.3 20 330 92.7694 161.5 20

Ethanol

92,8393

92,8303

92,8234

92,816692,8105

92,8049

92,7942

92,783

92,7765

y = -0,0002x + 92,836

92,77

92,78

92,79

92,8

92,81

92,82

92,83

92,84

92,85

92,86

0 30 60 90 120 150 180 210 240 270 300 330

Time (min.)

Mas

s (g

ram

)

Figure 8 Measured mass-time graph for ethanol

Ethanol

159,5

160 160,1

160,5 160,6 160,7 160,7

161

161,3y = 0,005x + 159,784

159,4159,6159,8

160160,2160,4160,6160,8

161161,2161,4161,6

0 30 60 90 120 150 180 210 240 270

Time (min.)

Hei

ght o

f the

cyc

linde

r(m

m)

Figure 9 Measured height-time graph for ethanol

19

Result of experiment with isopropyl alcohol:

Table 3 Results for isopropyl alcohol

t(min) Mass (g) H (mm) Temperature (°C) 0 87.5235 171 20

30 87.5078 171.2 20 60 87.5020 171.3 20 90 87.4974 171.4 20 120 87.4903 171.5 20 150 87.4848 171.6 20 180 87.4768 171.65 20 210 87.4715 171.7 20 240 87.4647 171.75 20 270 87.4623 171.8 20

Figure 10 Measured mass-time graph for isopropyl alcohol

Izopropyl Alcohol

171

171,2171,3

171,4171,5

171,6171,65

171,7171,75

171,8y = 0,0028x + 171,11

170,9171

171,1171,2171,3171,4171,5171,6171,7171,8171,9

172

0 30 60 90 120 150 180 210 240 270

Time (min.)

Hei

ght o

f the

cyl

inde

r(m

m)

Figure 11 Measured height-time graph for isopropyl alcohol

Izopropyl Alcohol

87,5235

87,507887,502

87,497487,4903

87,484887,4768

87,471587,464787,4623y = -0,0002x + 87,5174

87,44

87,46

87,48

87,5

87,52

87,54

0 30 60 90 120 150 180 210 240 270

Time (min.)

Mas

s (g

ram

)

20

Result of experiment with methanol: Table 4 Results for methanol

t (min) Mass (g) Height (mm) Temperature (°C) 0 94.8647 152.5 20 60 94.8160 153.5 20 90 94.7967 153.6 20 120 94.7768 153.7 20 150 94.7641 153.8 20 180 94.7380 154 20 240 94.6985 154.1 20 300 94.6613 154.2 20 360 94.6232 154.5 20

Methanol

94,8647

94,816

94,7768

94,738

94,6985

94,6613

94,6232y = -0,0007x + 94,85994,6

94,65

94,7

94,75

94,8

94,85

94,9

0 60 120 180 240 300 360 420

Time (min.)

Mas

s (g

ram

)

Figure 12 Measured mass-time graph for methanol

Methanol

152,5

153,5153,7

154 154,1 154,2

154,5y = 0,0046x + 152,95

152

152,5

153

153,5

154

154,5

155

0 60 120 180 240 300 360 420

Time (min.)

Hei

ght o

f the

cyc

linde

r(m

m)

Figure 13 Measured height-time graph for methanol

21

Calculations of Diffusion Coefficients:

Before calculation the diffusion coefficients of these solvents, some

calculations should be done. To calculate the diffusion flux, which is shown in the

Equation 6, the slope of the mass-time graph ( tM ∆∆ ) can be used. AM is the

molecular weight of the substances and A is the cross-sectional area of the graduated

cylinder which has a radius of 1 cm.

AtMMN A

.∆∆

= (Equation 6)

To obtain a diffusion coefficient, the equilibrium concentration (c) on the

liquid level should be known. It can be calculated by dividing the total atmospheric

pressure which is assumed as 1 atm, to the constant R ( KmolcmatmR ..06.82 3= )

times temperature (K).

At the top of the graduated cylinder, the concentration ( 2Ax ) of the ethanol,

isopropyl alcohol and methanol is zero. The concentration of pure water at the top, is

not zero. To calculate the concentration, the humidity should be known. As it can be

seen from Table1, humidity is %49 and this value can be used when calculating the

concentration at the top.

z∆ can be found from the difference between 2z and 1z level of the tube.

Finally, the diffusion coefficient of the laboratory solvents at 20°C can be

calculated from the equation below;

( )12ln..

BBAB xxc

zND ∆= (Equation 7)

All calculations and the results are shown in Table 5.

22

Table 5 Results of the experiment

Calculated Values

Pure Water

Ethanol

Isopropyl

Alcohol

Methanol

tM ∆∆ 0.0000846 0.0002 0.0002 0.0007

3cmgM A = 18 46 60 32

A ( 2cm ) 7.065 7.065 7.065 7.065

N (flux)

91008.11 −× 91025.10 −× 91086.7 −× 9106.51 −×

c (equilibrium concentration)

510159.4 −× 510159.4 −× 510159.4 −× 510159.4 −×

Vapor Pressure at 20°C 0.023079atm 0.05824atm 0.04367atm 0.12722atm

PPx AA =1 0.023079 0.05824 0.04367 0.12722

2Ax 0.00113087 0 0 0

11 1 AB xx −= 0.97692 0.94176 0.956 0.8727

22 1 AB xx −= 0.98869 1 1 1

( )12ln BB xx 0.0119 0.060 0.0449 0.136

z∆ (cm) 14.4 16.15 17.19 15.45

( )12ln..

BBAB xxc

zND ∆=

sec2cm

0.322 0.0663 0.0724 0.140

23

V. DISCUSSION OF RESULTS

Measurements and the diffusion coefficient values from the literature are

shown in the Table 6. Results of the experiment show that the measurements for pure

water and methanol can be possible at 20°C, but the measurements for ethanol and

isopropyl alcohol lower than the expected value. There can be lots of reasons for this

situation; temperature change in the atmosphere during the experiment, total

atmospheric pressure can be said.

Table 6 Diffusion Coefficients

Diffusion

Coefficient

Pure Water

Ethanol

Isopropyl Alcohol

Methanol

Experiment (at

20°C)

0.322 0.0663 0.0724 0.140

Literature(6) (at

0°C)

0.220 0.102 0.0808 0.132

VI. CONCLUSION

In conclusion, by studying with four laboratory solvents, the diffusion

properties of these substances were discussed. The basic diffusion mechanisms and

diffusion coefficient calculations were learned.

24

VII. REFERENCES

1. William D. CALLISTER; JR, Materials Science and Engineering an

Introduction, p.94, Fifth Edition, John Wiley Sons, Inc.

2. Robert S. BRODKEY, Harry C. HERSHEY; Transport Phenomena, A

Unified Approach; p.179, McGraw-Hill International Editions.

3. Leighton E. SISSOM, Donald R. PITTS; Elements of Transport

Phenomena; p.200, McGraw-Hill Book Company.

4. R. Byron BIRD, W.L. Stewart, and E.N. Lightfoot, Transport Phenomena,

p.525, John Wiley & Sons, Inc.

5. Physical Metallurgy Principles, p.386

6. John H. PERRY, Chemical Engineer’s Handbook, p.14-23, Fourth edition.