Environmental Engineering Reference
In-Depth Information
Fig. 1
Sketch of the
dissipative and stochastic
forces applied in a pair of
fluid particles in the DPD
thermostat. The forces are
applied in the direction
connecting both particles in
such a way that all added
“thermostating” forces
vanish
F
R
F
D
F
D
F
R
the velocity Verlet algorithm (Murtola et al.
2009
; Frenkel and Smit
2002
; Allen and
Tildesley
1987
).
3 Interaction Models: Soft and Hard Potentials
3.1 DPD with Soft Potentials
From the very inception of the DPD method by Hoogerbrugge and Koelman (
1992
),
the spatial dependence of the conservative force (
F
ij
) was chosen to be a short range,
linearly decaying function:
a
ij
1
r
ij
R
c
F
ij
=
−
e
ij
,
dž
(7)
where
r
ij
e
ij
is the unit vector in
the direction of
r
ij
, with
r
i
being the position of particle
i
. The constant
a
ij
is
the strength of the conservative force between particles
i
and
j
and
R
c
is a cutoff
distance. This force becomes zero for
r
ij
>
=
r
i
−
r
j
is the relative position vector and
dž
R
c
. It should be remarked that this choice
of the distance-dependent force is not arbitrary, as it has been shown to arise from
properly averaged, microscopic interactions, such as the Lennard-Jones potential
(Forrest and Suter
1995
). As for the interaction constant,
a
ij
, Groot and Warren
(
1997
) have provided a guide to calculate it using the Flory-Huggins model for like-
unlike particles, and the isothermal compressibility of water for like-like interactions.
The standard procedure to choose the conservative force parameter for particles of
the same type,
a
ii
, is given by
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