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Heffelfinger et al.
1987
), thus providing novel properties to that system. It also creates
layers near the walls hence affecting crystallization on the system (Alba-Simionesco
et al.
2006
). Confinement also induces a non-uniform distribution of the particles'
density (Magda et al.
1985
). As one can see, confinement may provide new char-
acteristics to constrained interacting systems, hence the necessity of studying them.
Recent theoretical and computational works studying the influence of confinement
on interacting fluids are given by Karbowniczek and Chrzanowska (
2013
), Das and
Singh (
2013
), Hartkamp et al. (
2012
).
In this research we use Molecular Dynamics simulations to study the effect of
interactions and confinement (walls) on particles diffusion. We extend previous stud-
ies by analyzing the mean squared displacement of an interacting fluid constrained
to a circular, square and triangular cavity. The interactions among particles and walls
are modeled by means of three classic interaction potentials namely, Lenard-Jones
(CLJ), soft Lenard-Jones (SLJ) and hard Lenard-Jones (HLJ) potentials, and whose
differences in the interaction they produce are also analyzed. This work is organized
as follows. In Sect.
2
we set up the problem and detailed information on the sim-
ulations is given. Section
3
presents the obtained results, and finally we offer our
conclusions in Sect.
4
.
2Model
Consider a fluid made up of spherical interacting particles of mass
m
, diameter
˃
, and confined in a two-dimensional closed cavity of three prototypical shapes
(circular, square and triangular, as shown in Fig.
1
). Particle-particle and particle-
wall interactions are modeled via the Lennard-Jones potential. Thus we formally
solve for a set of coupled first order differential equations for the position
r
i
and
momentum
p
i
of the
i
-particle
(a)
(b)
(c)
σ
σ
σ
σ
σ
Fig. 1
(Color online) Schematics of the three cavities studied. Note that the spherical particles
forming the walls and the fluid particles, have the same diameter
˃
for all cavities.
a
circular
cavity;
b
square
cavity;
c
triangular
cavity
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