Diffusion flux from diffusion coefficient and concentration gradient
====================================================================

*Fick's first law* relates the diffusion flux to the gradient of the concentration.
It postulates that the flux goes from regions of high concentration to regions of
low concentration, with a magnitude that is proportional to the concentration gradient
(spatial derivative), or, in simplistic terms, the concept that a solute will move from
a region of high concentration to a region of low concentration across a concentration
gradient. The minus sign in the law indicates that the directions of the diffusion
flow and the gradient are opposite: the gas diffuses towards a lower concentration,
and the gradient is directed towards a higher concentration.

**Conditions:**

#. The mixture is ideal.

**Links:**

#. `Wikipedia, first formula <https://en.wikipedia.org/wiki/Fick%27s_laws_of_diffusion#Fick's_first_law>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.diffusion_flux_from_diffusion_coefficient_and_concentration_gradient

.. py:data:: position

    :attr:`~symplyphysics.symbols.classical_mechanics.position` of particles.

Symbol:
    :code:`x`

Latex:
    :math:`x`

Dimension:
    :code:`length`


.. py:data:: diffusion_flux

    :attr:`~symplyphysics.symbols.classical_mechanics.diffusion_flux` as a function of :attr:`~position`.

Symbol:
    :code:`J(x)`

Latex:
    :math:`J{\left(x \right)}`

Dimension:
    :code:`amount_of_substance/(area*time)`


.. py:data:: diffusion_coefficient

    :attr:`~symplyphysics.symbols.classical_mechanics.diffusion_coefficient`.

Symbol:
    :code:`D`

Latex:
    :math:`D`

Dimension:
    :code:`area/time`


.. py:data:: concentration

    :attr:`~symplyphysics.symbols.chemistry.molar_concentration` of particles as a function of :attr:`~position`.

Symbol:
    :code:`c(x)`

Latex:
    :math:`c{\left(x \right)}`

Dimension:
    :code:`amount_of_substance/volume`


.. py:data:: law

    :code:`J(x) = -D * Derivative(c(x), x)`


    Latex:
        .. math::
            J{\left(x \right)} = - D \frac{d}{d x} c{\left(x \right)}