The Nature of Fluid Flow - Fluid Properties at Nano/Meso Scale: A Numerical Treatment - page 35

centres is exchanged, while the component of velocity perpendicular to this line
remains the same for both spheres. The velocities of both spheres are updated and
can be used to update the prediction table for the next collision time for the pair.
There is no need to update the table for all the molecules, as only the colliding pair
experience a change in velocity. The updated tables can then be used to predict
the time step to the next collision.
1.4.5 Soft sphere model
The soft sphere model of molecular interactions considers molecules to interact
by exerting a force on each other relative to the distance between them. These
interactions occur continually, with each molecule having a 'zone' in which any
other molecule present is influenced. Hard spheres will only interact when contact
is made.
The initialization stage starts as stated above, where the initial positions and
velocities have been defined for all molecules in the system. Force calculation for
soft sphere models is more complex due to the addition of long-range interactions.
Particles in the system continually attract and repel their neighbours through a
predefined potential function, as opposed to the instantaneous and perfectly elastic
collisions of the binary collisions described above.
This is best described with the use of Figure 1.18, where the centre particle
is interacting with particles within a set radius, R C . The most common potential
used is the Lennard-Jones 12-6 potential, which provides an approximation of the
attractive and repulsive forces experienced by nonbonded molecules.
R N
R C
Figure 1.18 Soft sphere interaction detection.