Dissipative Particle Dynamics: A Method to Simulate Soft Matter Systems in Equilibrium and Under Flow - Selected Topics of Computational and Experimental Fluid Mechanics - page 61

and Fig. 5 ). By integrating the contribution to the total wall force from each parti-
cle on the surface it is possible to obtain an exact expression for the effective DPD
surface force, which is given by the following polynomial (Gama Goicochea and
Alarcón 2011 ):

1

4

6 z
z c

2

8 z
z c

3

3 z
z c

F i (

) = − + − dž ,

z a w , i z (14)

where the symbols have the same meaning as in Eq. ( 13 ), except that the strength of
the interaction is given in this case by the relation:

12 ˁ w R c a ij .

a w , i = (15)

ˁ w is the density of the wall, R c is the usual cutoff radius, and a ij is
the conservative force strength between the particle i in the fluid and j on the wall.
The surface force in Eq. ( 14 ) is appealing for several reasons: it is exact, it is soft
and short—ranged as the other DPD forces, and its strength is defined through the
interaction strength of the conservative force as expressed in Eq. ( 15 ). Using this
effective surface force, GCMC simulations have been performed to calculate the full
solvation force that the walls exert on a simple monomeric DPD fluid. This solvation
force, which is equal to the change in the free energy of the system between two
compression states, per unit area, is surprisingly of relatively long range, as shown in
Fig. 6 , even though the surface—fluid particle force is of short range. This phenom-

In Eq. ( 15 )

Fig. 5 Model to derive an effective DPD surface force ( left ). The resulting force is a polynomial
(see Eq. 14 ) which is also of short range, as are the other forces that make up the DPD model ( right ).
Adapted from Gama Goicochea and Alarcón ( 2011 )