Diffusion:
general
Principle
Diffusion is the net action of particles
(molecules, atoms, electrons,
etc.), heat, momentum, or light whose end is to minimize a concentration
gradient. A concentration gradient is the difference between the high concentration
and the low concentration. It also includes the speed of the process. Diffusion
can be quantified by measuring the concentrations gradient.
More formally, diffusion is defined as the process
through which speed a thermodynamic
system at local thermodynamic equilibrium returns to global
thermodynamic equilibriums, through the homogenization of the values of its intensive
parameters (or bulk parameters, such as viscosity, density, melting point etc.).
In all cases of diffusion, the net flux of the transported
quantity (atoms, energy, or electrons) is equal to a physical property
(diffusivity, thermal conductivity, electrical conductivity) multiplied by a
gradient (a concentration, thermal, electric field gradient). So:
Diffusion ≡
some conductivity times a gradient.
Noticeable transport occurs only if there is a gradient.
For example, if the temperature is constant, heat will move as quickly in one
direction as in the other, producing no net heat transport or change in
temperature.
The process of diffusion minimizes free energy and is
thus a spontaneous process. An example of diffusion is the swelling of
pasta, where water diffuses into the sponge-like structure of the dry and stiff
pasta.
The different forms of diffusion can be modeled
quantitatively using the diffusion equation, (see More Info) which goes by different names depending on the physical
situation. For instance - steady-state bi-molecular diffusion is governed by Fick's law, steady-state thermal diffusion is
governed by Fourier's law. The generic
diffusion equation is time dependent, and as such applies to non-steady-state
situations as well.
The second law of thermodynamics states that in a
spontaneous process, the entropy of the universe increases. Entropy is a
measure of how far a spontaneous physical process of smoothing-out differences
has progressed, for instance a difference in temperature or in concentration (see further Entropy).
Change in entropy of the universe is equal to the sum of the change in entropy
of a system and the change in entropy of the surroundings. A system refers to
the part of the universe being studied; the surrounding is everything else in
the universe. Spontaneous change results in dispersal of energy. Spontaneous
processes are not reversible and only occur in one direction. No work is
required for diffusion in a closed system. Reversibility is associated with
equilibrium. Work can be done on the system to change equilibrium. Energy from
the surroundings decrease by the amount of work expended from surroundings.
Ultimately, there will be a greater increase in entropy in the surroundings
than the decrease of entropy in the system working accordingly with the second
law of thermodynamics.
Types of
diffusion
Diffusion includes all transport phenomena occurring
within thermodynamic systems under the influence of thermal fluctuations (i.e.
under the influence of disorder; this excludes transport through a hydrodynamic
flow, which is a macroscopic, ordered phenomenon). Well known types are the
diffusion of atoms and molecules, of electrons, (resulting in electric current),
Brownian motion (e.g. of a single
particle in a solvent), collective diffusion (the diffusion of a large number
of (possibly interacting) particles), effusion of a gas through small holes, heat
flow (thermal diffusion), osmosis, isotope separation with gaseous
diffusion.
Application
Application, i.e. occurrence, in nature, dead and alive,
can be found nearly everywhere. In living bodies it is found interstitionally
as well as in living cells. Many man made apparatus, also for medical purposes,
make use of the principle of diffusion. Some very obvious examples of
applications are in the techniques of chromatography,
electrophoresis, oxygen analysis, spectroscopy,
thermography, the calculation of body
heat conduction and dissipation (see Body heat conduction and
Diffusion
in biological systems
Specific examples in biological systems
are diffusion across biological membranes, of ion through ion
channels, in the alveoli of mammalian lungs across the alveolar-capillary
membrane. In the latter process the diffusion is Knudson-like diffusion, in
other words it is also dependent on space restrictions (the small size of the
providing (alveoli) and recipient (capillaries) volumes. Another type is facilitated
diffusion (passive transport across a membrane, with the assistance of
transport proteins)
Numeric example
By knowing the diffusion coefficient of oxygen in watery
tissue, the distance of diffusion and the diffusion gradient, then the time
required for the diffusion of oxygen from the alveoli to the alveolar
capillaries can be calculated. It appears to be some 0.6 ms (see More Info).
More Info
Diffusion
equation
The diffusion equation is a partial differential equation, which
describes the density fluctuations in a material undergoing diffusion. It is
also used in population genetics to describe the 'diffusion' of alleles in a
population.
The equation is usually written as:
(1)
where φ is the density of the diffusing material, t is time, D is the collective diffusion
coefficient, 
is the spatial coordinate and the nabla symbol φ represents the vector
differential operator
, (2)
also called the heat
equation.
Diffusion
displacement
The diffusion displacement can be described by the
following formula:
<rk2>
= 2kD’t,
where k is the
dimensions of the system and can be one, two or three. D’ is the diffusion
coefficient, but now also per unit of concentration difference of the particles
and t is time. For the three-dimensional
systems the above equation will be:
<x2> +
<y2> + <z2>
= <r32> = 6D’t,
where < > indicates the mean of the squared
displacement of the individual particles.
Biological numeric example
Calculate the time required for O2 diffusion across the
alveolar-capillar membrane. By knowing D’ of oxygen in watery tissue (suppose 15x10-10
m2s-1bar-1), the 1D-distance of diffusion x (suppose
the distance between alveolar and capillary volume is0.4 μm) and the O2
diffusion gradient Δp is
t = x2/(2DΔp) = 0.16x10-12/(2x15x10-10x0.09)
= 0.6x10-3 s.
See further Fick's laws, for
the diffusion equations and Grahams Law
for particle velocity of diffusing particles.