Molecular and Particle Modelling of Laminar and Turbulent Flows

6.8. Particle Equations of Motion

6.8. Particle Equations of Motion

We assume for two particles P i, P j the potential

(6.14)

in which R ij is the distance in centimeters between the particles. Thus, the force which particle P j exerts on particle P i is

(6.15)

Our first problem is to determine A and B. Let . Then in consistency with the way the particle positions were generated, let F(0.05) = 0, so that

(6.16)

In order to determine a second equation, some relevant observations must be made first.

Note that the number N of molecules which can be arranged in the 0.4 cm by 17.6 cm rectangle using a regular triangular grid is

(6.17)

Also, note that since the mass M of a water molecule is (30.103)10 -24 gr, the total mass of the water molecules inside the rectangle is

(6.18)

Distributing this mass over the 3500 particles lor conservation of total mass yields an individual particle mass m of

(6.19)

The total potential energy P M of the molecular configuration is, approximately,

(6.20)

In order to determine the kinetic energy K M of the molecular system, we now fix the temperature at 15 C, at which temperature the modal speed of a water molecule is 3.65 /ps, or, equivalently, 3.65(10) 4 cm/sec. Hence, the kinetic energy of the molecular system is


Thus, from (6.20), the total energy E M of the molecular system is

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