## 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/time^{2})/(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/length^{3}.

n (nu) = m/r = *kinematic viscosity for simple systems*,
the area traversed in Brownian motion per unit time (length^{2}/time).

v_{d}
= _{н}m/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 (length^{2}/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*.н

## Phase transitions

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

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

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

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

нннннн Re >> 1, turbulence begins.

##

## Structure
transitions

нннннн 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**