Diffusion coefficient of spherical Brownian particles from temperature and dynamic viscosity
============================================================================================

Brownian motion is the random motion of microscopic visible suspended particles of a solid
substance in a liquid or gas caused by the thermal motion of particles of a liquid or gas.
The *diffusion coefficient* is a quantitative characteristic of the diffusion rate, equal to
the amount of matter passing per unit time through a section of a unit area as a result of
the thermal motion of molecules with a concentration gradient equal to one (corresponding to
a change from :math:`1 \frac{\text{mol}}{\text{L}}` to :math:`0 \frac{\text{mol}}{\text{L}}`
per unit length). The diffusion coefficient is determined by the properties of the medium and
the type of diffusing particles. This law is also known as the *Stokes—Einstein—Sutherland relation*.

**Notation:**

#. :math:`R` (:code:`R`) is :attr:`~symplyphysics.quantities.molar_gas_constant`.
#. :math:`N_\text{A}` (:code:`N_A`) is :attr:`~symplyphysics.quantities.avogadro_constant`.

**Conditions:**

#. Particle displacements are equally likely in any direction.
#. The inertia of a Brownian particle can be neglected compared to the influence of friction forces.
#. Particles are spherical.
#. Low Reynolds number, i.e. non-turbulent flow.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Einstein_relation_(kinetic_theory)>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.diffusion_coefficient_of_spherical_brownian_particles_from_temperature_and_dynamic_viscosity

.. py:data:: diffusion_coefficient

    :attr:`~symplyphysics.symbols.chemistry.diffusion_coefficient` of the particles.

Symbol:
    :code:`D`

Latex:
    :math:`D`

Dimension:
    :code:`area/time`


.. py:data:: temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the system.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: particle_radius

    :attr:`~symplyphysics.symbols.classical_mechanics.radius` of the particles.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: dynamic_viscosity

    :attr:`~symplyphysics.symbols.classical_mechanics.dynamic_viscosity` of the particles.

Symbol:
    :code:`mu`

Latex:
    :math:`\mu`

Dimension:
    :code:`pressure*time`


.. py:data:: law

    :code:`D = R * T / (6 * N_A * pi * r * mu)`


    Latex:
        .. math::
            D = \frac{R T}{6 N_\text{A} \pi r \mu}