The Nature of Fluid Flow - Fluid Properties at Nano/Meso Scale: A Numerical Treatment - page 10

Figure 1.4 Left: continuous and infinitely divisible. Right: finite number of molecules,
mass and energy localized and not continuously distributed.

number of molecules, when it is divided up even in a finite number of sections,
some will contain mass (a molecule) and energy and some will not (Figure 1.4).
Thermodynamic Equilibrium. To maintain the assumption of continuum
mater with an infinite number of molecules, there must also be an approxi-
mately infinite number of intermolecular interactions occurring over length and
time scales in the system. This means that there is a continuous propagation
of energy throughout the system. Discontinuities cannot occur as the fluid is
continuous (infinitely divisible) and an infinite number of infinitely small in-
termolecular energy exchanges smooth out and propagate fluid properties and
energy through the system.
This is also essential to maintain the linear relationship between the stress
and strain rate and the heat flux and temperature gradient. The thermodynamic
equilibrium condition also states that there are sufficient interactions or colli-
sions to smooth out any statistical variations occurring from the molecular scale
(Figure 1.5).

Continuum Molecular

x x

Figure 1.5 Statistical variations in properties arising from a finite number of molecules
in the system,