Dissipative Particle Dynamics: A Method to Simulate Soft Matter Systems in Equilibrium and Under Flow - Selected Topics of Computational and Experimental Fluid Mechanics - page 72

ˁ = . ʵ/˃

where is the external

body force applied on each bead to produce the flow, D w is the channel width and
z 0 indicates the position at which the velocity profile extrapolates to 0 velocity. The
viscosity

is the number density of the fluid at bulk, f x 0 008

is the only parameter in Eq. ( 18 ) that is not measured directly from the
simulation. It can be obtained from the fit of the profile with Eq. ( 18 ).
These examples illustrate the use of DPD with hard potentials, in which the struc-
tural properties of the liquid, flow properties (slip length and slip velocity, velocity
profile) and rheological properties (viscosity, regions of non-newtonian behavior) of
these soft matter systems can be obtained from the simulations using the two simplest
hydrodynamic flows, i.e. Couette (linear) and Poiseuille (quadratic) flows. Velocity
fields, together with density profiles can be studied globally (Pastorino et al. 2006 ,
2009 ; Müller et al. 2009 ; Léonforte et al. 2011 ), locally (for example inside a droplet)
(Servantie and Müller 2008 ; Tretyakov et al. 2013 ; Tretyakov and Müller 2013 )or
for a given type of molecule (Pastorino and Müller 2014 ).

ʷ

5 The Conservation of Temperature in Flow Simulations

Under conditions of high flow, the DPD thermostat can have problems to maintain a
constant temperature across the fluid (Pastorino et al. 2007 ). A particular complicated
case takes place for good solvent conditions in polymeric or other soft matter system.
An important difference between Langevin and DPD thermostat is that Langevin
forces act on every particle, independently of the cut-off radius of the potential or
the density of the system. DPD, however, acts on pairs of interacting particles, those
that are within the cut-off radius. For systems with short cut-off radii as it is the case
of the Kremer-Grest model for polymers in good solvent conditions, the number of
thermostated pairs per time step can be pretty low, reducing the ability of the DPD
thermostat to extract a given amount of heat per unit time in the system. This behavior
is illustrated in Fig. 16 for Poiseuille-flow simulations. Figure 16 b shows the velocity
profile across the channel for different external forces. There is a quadratic behavior,
but some deformation is observed, as compared to Fig. 15 . The reason for that can
be noticed in Fig. 16 a, which shows the temperature profile across the channel.These
are extracted from the mean quadratic velocity in the directions without flow ( y dž

1 1

v y = and

2 k B T , from which a local
temperature can be extracted. For higher forces, starting in f x

z ). The equipartition theorem implies dž

2 m

,the
temperature is not conserved and heating of the liquid occurs in the regions of higher
shear rate. There, the heat production per unit time is higher than the maximum
removed by the thermostat and the temperature cannot be maintained at the defined
value k B T

= 0 . 014 ʵ/˃

.
In these situations various strategies can be adopted to maintain the constant
temperature. The simplest choice would be increasing the friction constant of the
thermostat. This can be perfectly done if the short-time dynamics of the molecules is
not of interest. This means also increasing the amplitude

= 1 . 68 ʵ

˃ R of the stochastic force
(see Eq. 3 ). Another alternative is to change the weight functions in the forces of the