Transport properties of matter express the way a current of a certain quantity is created
by an imposed gradient of another conjugate quantity.
For example, a gradient of temperature causes an entropy current which is perceived
as a flow of heat.

The analysis of any transport property always follows the same pattern:
Assume a given gradient and deduce the current thus produced.
(The scale of observation makes the number of microscopic components large
enough for statistical physics to be relevant.)

(2006-09-14) Viscosity
The capability to transport microscopic momenta.

In 1860, James Clerk Maxwell (1831-1879) analyzed the viscosity of ideal gases
as microscopic transfers of horizontal momenta in response to a vertical gradient
in the average horizontal velocity of particles.
He obtained a surprising theoretical result, which he confirmed experimentally
with the help of his wife: The vicosity of a gas has little to
do with its density and it increases in direct proportion with the
square root of the absolute temperature.

This remarkable result is in sharp contrast with the common knowledge about
liquids (whose viscosity clearly decreases with temperature).
Maxwell's result was one of the great early successes of the
kinetic theory of gases.

(2006-10-01) Brownian Motion:
Brown (1827) & Einstein (1905)
The motion of microscopic grains led Einstein to gauge molecular sizes.

The constant microscopic motion of very small particles was first noticed by
the Scottish botanist Robert Brown (1773-1858) in the summer of 1827,
as he observed under the microscope colloidal
suspensions of pollen grains (from a type of evening primrose
called Clarkia Pulchella).

By repeating the observation with other types of small particles, including mineral dust,
Brown ruled out any biological origin for that microscopic agitation, now known as
Brownian motion. This would remain a mystery for 78 years.

In his celebrated "Miracle Year" (1905), Albert Einstein proposed that Brownian motion
could be explained in terms of the kinetic theory of fluids and
could serve to estimate the size of the molecules
involved.

The actual experimental measurements were first carried out in 1908 by the
team of the French physical chemist Jean Perrin (1870-1942;
Nobel 1926).

The microscopic grains are in thermal equilibrium (at temperature T)
with the molecules of the colloid in which they are suspended.
Thus, the average (translational) kinetic energy of each grain is (3/2) kT.
The speed of the grains can't be measured directly by the overall diffusion
can be: It behaves according to the rules of kinetic theory
as if the grains formed a gas of very heavy molecules.

(2006-09-14) Thermal
Conductivity Thermal conductivity is the capability to transport random energy.

(2006-09-17) Diffusivity
The transport of chemical concentration.

(2012-08-17) Boltzmann Transport Equation
Linear stochastic partial differential equation.

(2006-09-14) Speed of Sound
Reversible propagation of a disturbance in the pressure of a fluid.

In a fluid, the square of the speed of sound is the
isentropic derivative of pressure (p) with respect to mass density
(r) :

Speed of
Sound (u) in a Fluid

u^{ 2}_{ } =

_{ }(

¶p

)_{S}

¶r

r may be defined as the ratio M/V
of the constant molar mass (M is roughly
0.002 kg/mol for hydrogen) to the variable
molar volume (V).

John James Waterston
(1811-1883) was a Scottish physicist (hailing from Edinburgh) whose
pioneering work on the kinetic theory of gases remained
obscure until
that theory was firmly established (by Clausius and Maxwell).

Many of Waterston's early results
(including a special case of the theorem of equipartition of energy)
remained hidden in a book with a very misleading title:
Thoughts on the Mental Functions (1843).
In 1851, Waterston explained Laplace's formula for the speed of sound in terms of the kinetic
theory of gases, in a paper which, unfortunately,
remained buried in the archives of the Royal Society
until Lord Rayleigh arranged for its publication, in 1891.