Jordan University of Science and Technology
Deanship of Research
Research Grant Application
A- General Information:
1- Applicant (s) :
I - Name (Principal Researcher) Dr. Abdalla A.
Obeidat---------------------Rank Lecturer-----Dept./College-Physics/Faculty of Science---------------Ii - Name (Co-researcher) - Safwan Jaradat --Rank
Master Student Dept. of Applied
Physics/College of
Science and Arts /JUST----------2- Title of Research Proposal : -“Binary Nucleation Rates Of Water-Ethanol using an
Equation of state”
3- Type of Research:
1
Ph.D. Thesis (Name of student
..................................................)
M.Sc. Thesis (Name of student ...
Safwan Jaradat.
Student
Number
20073092003......................)
Joint Research (Name of other
partner ….................................)
Commissioned Research (Name of
sponsor .............................)
Individual Research
Competitive Awarded Research
B- Research Project Description :
1.
Abstract ( 100 – 150 words on a separate sheet):
2
The first Gradient Theory (GT) was devised by Van der
Waals to describe the structure of planer interfaces. To apply
GT, one needs a well-behaved Equation of State (EOS). It
should have the form of cubic equation, similar in spirit to the
Van der Waals EOS, which describes the system as a single
homogeneous phase whose density varies continuously
through out the two-phase region. A chain of rotators EOS
will be used with GT to predict the binary nucleation rates of
fluids such as Water-Ethanol. The results will be compared
with Classical Nucleation Theory and with experimental
results.
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2.
Research Objectives:
The principle goal of this research is to apply gradient theory
[1] to study the binary nucleation rate of Water-Ethanol using
a cubic equation of state and compare it with the different
form of classical nucleation theory [2, 3]. The usual forms of
CNT are well-known to provide a poor quantitative
description
of
temperature
dependence
of
measured
nucleation rates, although the predicted dependence on
supersaturation is generally quite satisfactory. To explore this,
GT and Gibbs’s original formula will be used to calculate
binary
nucleation
rates
for
Water-Ethanol.
The
implementation of GT and of Gibbs’s original formula
requires the use of an accurate equation of state for the liquid
4
properties. In our case, an exact equation of state, chain of
rotators EOS [4] will be used.
3.
Review of Related Literature:
The first comprehensive treatment of the thermodynamics of
nucleation process is due to Gibbs [2]. Gibbs showed that the
reversible work required to form a nucleus of the new
phase consists of two terms: a bulk (volumetric) term and
surface term. Later, in 1926 Volmer and Weber [5] developed
the first nucleation rate expression, by arguing that the
nucleation rate should be proportional to the frequency of
collisions between condensable vapor molecules and small
droplets of the new phase of a size, critical size, which just
permits spontaneous growth. The theory of Volmer and
Weber was extended later by Frenkel, Zelodivich, and Becker
5
and during [3, 6-7] and known as classical nucleation theory
(CNT) [8]. The most fundamental approach to improving
CNT is through the development of microscopic theories such
as molecular dynamic (MD), Monte Carlo (MC) computer
simulation, and Hybrid approach [9-14]. Another approach is
known as density functional theory (DFT) [15-17]. Because
DFT involves the use of realistic intermolecular potentials, it
is considerable more difficult to use than CNT. Gradient
theory is a methodological less demanding, but more
approximate relative of DFT. Whereas DFT depends on the
intermolecular potentials as it main ingredient, the GT,
instead, requires a well-behaved mean-field EOS.
6
Theoretical background:
Cahn and Hilliard [17] were the first who developed a
type of DFT for nucleation theory. They proposed the
Helmholtz potential to be
F [  (r )] 

3
2
d
r
f
[

(
r
)]

c
[


(
r
)]
0


Where f 0 is the Hemholtz free energy density of the
homogeneous fluid density  , c is so-called the influence
parameter related to the intermolecular potential, and

is the
gradient of the density. And for Two-component Fluid as in
Water-Ethanol to find  we need to solve two equations with
two conditions.
c11 (d2 1/dx2) +c12 (d2  2/dx2) =o1() - 1= 1()
c21 (d2 1/dx2) +c22 (d2  2/dx2) =o2() - 2= 2()
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And
1/2cαβ (dα/dx)(dβ/dx)=ω()
Where the conditions are
* c11= c12
,
c11 c22 - c12 c21  0
** (c11)1/21() = (c11)1/22()
Because of Hemholtz potential above depends on the gradient
of the density, minimizing the above equation will obtain a
differential Euler-Lagrange equation. This theory is called
gradient theory (GT). The density distribution that makes F
extremum is determined by the Euler-Lagrange equation
  0  c 2 
Where

is the constant chemical potential of the
inhomogeneous fluid, and 0 is the chemical potential of the
homogeneous fluid at density  .
8
The work of formation is defined as the difference in the free
energy containing the droplet and that of the homogeneous
system, which is equivalent to the original result of Cahn and
Hilliard [17]
W GT 
c





 
2
Where    (  )   ( e ) , 
 f 0  
2

 dV

and  e is the equilibrium
density of either bulk phase. The nucleation rate is given by
2   Pv 
W GT
vl  
J  J 0 exp( 
) With a pre-exponential factor J 0 
m  kT 
kT
2
Where m is the mass of a condensable vapor molecule, v is the
l
molecular volume, and
4.
Pv
is the vapor pressure.
Significance of the Project:
In this research we will be able to get more insight and to
hope to understand the binary nucleation rates of some fluids
such as Water-Ethanol. All theories behind studying binary
9
nucleation rate for Water-Ethanol gave some defected to
predict rates regarding the T-dependence [18-20]. This will be
the first time to apply chain of rotators equation of state for
Water-Ethanol to study the rates using the exact Gibbs
formula and gradient theory. This research is very important
in the area of cloud physics, industry and in the
environment, especially in forests.
5.
Description of Research Program:
I - Methodology and Parameters to be investigated:
1- The work of formation
droplet of critical size
n*
W*
required to form a
for binary Water-Ethanol.
2- Binary Nucleation rates of Water-Ethanol.
3- Comparison with experimental data and other
models.
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Ii - Location and Safety Considerations:
Iii - Expected Duration and Time Schedule:
1st 2nd 3rd 4th 5th 6th 7th 8th
mo mo mo mo mo mon mo mo
nth nth nth nth nth th nth nth
Reading x
x
x
x
x
Set up
x
x
the
equation
s
Calculat
x
x
x
ions
Discussi
x
x
x
on
Writing
x
x
x
6.
References:
[1] J. D. van der Waals, Verh.-k. Ned. Akad. Wet. Afd.
Natuurkd., Reeks Eerste 1, 1(1893)
[2] J.W.Gibbs, the scientific papers of J. W. Gibbs, Vol I,
(Dover, New York, 1961) P.253.
[3] R. Becker and W. During, Ann. Phys.24, 719 (1935)
11
[4]
[5] M. Volmer and A. Weber, Z. Phys. Chem. 119, 227
(1926)
[6] J. Frenkel, J. Chem. Phys. 7, 538 (1939)
[7] J. B. Zelividch, Zh. Eksp. Theor. Fiz. 12, 525 (1942)
[8] F.F. Abraham, Homogeneous Nucleation Theory,
Academic Press, Inc, New York and London, 1974.
[9] D.J. Lee, M.M. Telo de Gama, and K.E.Gubbins,
J.Chem.Phys.85, 490(1986)
[10] M. Tarek and M.L. Klein, J. Phys. Chem. 101, 8639
(1997)
[11]
J.K.Lee,
J.A.
Barker
and
F.
J.Chem.Phys.58, 3166 (1973)
[12] B.N. Hale, Aust. J.Phys.49, 425(1996)
12
F.
Abraham,
[13] I. Kusaka and D. W. Oxtoby, J. Chem.Phys. 110, 5249
(1999)
[14] C. L. Weaklien and H. Reiss, J. Chem. Phys. 101, 2398
(1994)
[15] R. Evans, Adv. Phys.28, 143 (1979)
[16] F.F. Abraham, Phys. Rep. 53, 93 (1979)
[17] J. W. Cahn and J. E. Hillard, J. Chem. Phys. 31, 688
(1959)
[18] R. Strey, P.E.Wagner and T. Schmeling, J. Chem. Phys.
84, 2325 (1986)
[19] T.F. Sun, J. A. Schouten and S.N. Biswas, Int. J.
Thermophys. 12, 381 (1991)
[20] A. Obeidat, and G. Wilemski, Atmos. Res., submitted
(2004)
13
[21] Carey, B.S., Scriven, L.E., and David, HT 1978.AIChE
j., 24, 1076
[22] Carey, B.S., Scriven, L.E., and David, HT 1978.AIChE
j., 26,705.
7. Experience of Applicant(s) in the Area of the
Proposed Research Project ( Mention
Previous published or supervised work, and the
main findings.)
1-Gradient theory of nucleation in polar fluids
Obeidat, A and Wilemski, G., Atoms. Res., submitted (2004)
2-Nuleation of polar fluids from Gradient Theory.
Obeidat, A. and Wilemski, G., in Nucleation and Atmospheric
Aerosols, 2004, Ed. M. Kasahara and M. Kulmala, (Kyoto
University Press, Kyoto, 2004) pp. 186-189.
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3-Binary Nucleation of Nonideal System from Classical and
Density
Functional
Theories.
Obeidat, A., Li, J.-S .and Wilemski, G., in Nucleation and
Atmospheric Aerosols, 2004, Ed. M. Kasahara and M.
Kulmala, (Kyoto University Press, Kyoto, 2004) pp. 81-84.
8. Current and Previous Research Grants by Applicant
(s):
Number Year of completion
JD
Source of funding
Grant
amount,
----------------------------------------------------------------------------- ---------- ----------------------------------------------------------------------------- --------------------------------------------------------------------9. Applicant(s) Contribution (Briefly describe the role of
each applicant):
15
I - The Role of the Principal Researcher.
Safwan will setup the equations and calculate the
vapor and liquid densities for binary Water-Ethanol, and
then he will write the equations required to calculate the
work of formation and the binary nucleation rates.
Finally, he will setup the code and run it on the computer.
C- Budget Details
Item
Estimated Cost
1- Manpower
a- Research Assistant (Salary and Duration):
………………………………………………... bIncentives:
…………………………….…………………………………
……………………
2-
Equipment (List major needed equipment):
16
3- Supplies & Materials (List major needed items):
4-
Travel (National & International):
------------------
5Other Expenses :
-----------------_________________________________________________
__________________________________
Total:
--
---------------
Signature(s) of Researcher(s)
----------------------
D- Department Evaluation
17
Date: -
-
-
Name
of
the
Researcher…………………….…
……...………….
Dept.
Principal
/Faculty
Title
of
research
project:
........................................................…….....…...................
..........…
- Research Type:
M.Sc. thesis
Ph.D. thesis
Joint Research
Commissioned research
Individual work
Competitive Awarded research
- Does the Principal Researcher have a personal
computer?
Yes
No
- Main equipment needed for this research which is
available in the Department:
1.......................................................................…………………
…..............................................
2...............................................................................……………
………......................................
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3...................................................................................................
..........……………………........
-
Research Project Evaluation:
Excell Very
ent good
Good Wea
k
Chairman
of
Department
Committee...................Signature
.......................Date................
E- Approval:
Research
Evaluation
Item
Research methodology
Research objectives
Research originality
Research contribution
Research applicability and
relevance
An overall evaluation
-
Recommendations of the Department Chairman
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Approved
Disapproved
Signature-------------------------------------------------Date-------------------------------------------------------_________________________________________________
__________________________________
Recommendation of the Faculty Research Committee
---------------------------------------------------------------------------------------------------------------------------------------------------------------------Chairman of Faculty Research Committee:
Signature----------------------Date---------------------
_________________________________________________
__________________________________
- Recommendation of the Dean of the Faculty
Approved
Disapproved
Signature--------------------------------------------Date-------------------------------------------------------_________________________________________________
__________________________________
University Review Committee for Research on
Humans (Any research on humans should
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Be approved by this committee before approving this
research work).
Approved
Approved on
conditions
(Use an additional
sheet for details)
Disapproved
Chairman of University Review Committee for
Research on Humans -------------------------------Signature-----------------------Date --------------------_________________________________________________
__________________________________
- University Research Committee:
Approved & Amount of grant
-----------------JD
Disapproved
Postponed
Directed to -------------------------------------------------------Dean of Research---------------------------- Signature---------------------- Date --------------------------
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