Variables and equations for phase transitions (illustrated for momentum transports), by Douglas R. White

V = convective velocity, in units of length/time.

m (mu) = (shear) viscosity, in units of force/velocity ((mass/time²)/(length/time)= mass/length*time), the mass that can be moved per distance traversed in time in random collisional movement.

r (rho) = mass density of an atomism in units of mass/length³.

n (nu) = m/r = kinematic viscosity for simple systems, the area traversed in Brownian motion per unit time (length²/time).

v_d = _Ým/rD = n/D = diffusive velocity for simple systems, the distance traveled away from an origin in Brownian motion per unit time (length/time), where the distance travelled is a function of the square root of time.

Re = V / v_d = VD/n = Reynolds number (dimensionless) for simple systems.

l (lambda) = bulk viscosity, in units of force/velocity, the mass that can be moved per distance traversed in time-delayed absorption into the internal processes (typically of variable densities) of an atomism (mass/length*time).

v_d = (m+l)/rD = diffusive velocity for (complex) systems with bulk viscosity, the distance traveled away from an origin in Brownian motion per unit time (length/time), where the distance travelled is a function of the square root of time.

n* (nu*) = (m+l)/r = kinematic viscosity for (complex) systems with bulk viscosity, the area traversed in Brownian motion (including internal processes) per unit time (length²/time).

Re = V / v_d = VD/n* = VD/(m+l)/r = VD/ (1+l/m)m/r = VD/n(1+l/m) = Reynolds number (dimensionless) for (complex) systems with bulk viscosity.Ý

Phase transitions

ÝÝÝÝÝÝ Re < 1, diffusion time can handle convective flow, no phase transition.

ÝÝÝÝÝÝ Re = 1, transition is reached from microscopic transport to macroscopic transport

ÝÝÝÝÝÝ Re > 1, diffusion time is too short to handle convection,

ÝÝÝÝÝ structural change occurs in the form of convective superatomisms (fluid cells).

ÝÝÝÝÝÝ Re >> 1, turbulence begins.

Structure transitions

ÝÝÝÝÝÝ Bonding may occur within fluid superatomisms, and bonding energies are emitted (e.g., as accompany transitions from gas to liquid to solid).

Figure 1: Summary of the Physics of Phase Transitions