Environmental Engineering Reference
In-Depth Information
v
w
o
RT
]
2
ˇ
w
o
=
[
ʴ
w
(
T
)
−
ʴ
o
(
T
)
,
(32)
v
eo
RT
]
2
ˇ
eo
=
[
ʴ
e
(
T
)
−
ʴ
o
(
T
)
,
(33)
and, in fact, taking the square root of any two of these equations (say, the first two),
adding them together, and assuming
v
e
w
=
v
w
o
=
v
eo
≡
v
m
, we can have a very
good estimate for the third one
√
ˇ
e
w
+
√
ˇ
e
w
2
v
m
RT
]
2
=
[
ʴ
e
(
T
)
−
ʴ
o
(
T
)
≡
ˇ
eo
.
(34)
Although we have assumed heretofore that DPD particles mix randomly, and that
the particles of a given type are indistinguishable, this model predicts very well the
major trends in the behaviour of real polymer solutions and is used to predict new
behaviour in polymers in current research of (Gama Goicochea et al.
2009
; Mayoral
and Nahmad-Achar
2014
; Gonzalez-Melchor et al.
2006
; Mayoral and Nahmad-
Achar
2012
).
4 Applications
4.1 Interfacial Tension
Interfacial tension arises from the contact between immiscible fluids. It is a measure
of the cohesive (excess) energy present, arising from the imbalance of forces between
molecules at the interface. This excess energy is called
surface free energy
and is a
measurement of the energy required to increase the surface area of the interface by
one unit. Equivalently, it may be quantified as a force/length measurement: the force
which tends to minimise the surface area. Interfacial tension plays an important role
in the formation of colloids or emulsions: as each phase tries to maintain as small
an interface as possible, they do not easily mix. Similarly, it is important for the
dispersion of insoluble particles in a liquid medium, the penetration of molecules
through membranes, adsorption, and stability.
The measure or determination of the interfacial tension then allows us to study
the hydrodynamics and morphology of multiphase systems, and this in turn is a most
important aspect of the understanding of natural processes and of product design.
The conservative force allows us to calculate the average kinetic energy
E
k
via
the virial theorem
N
F
i
C
E
k
=−
1
·
r
i
,
2
(35)
i
=
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