Put variable definitions in a table

Fluid Equations

Fluid Variables

===============

We define the following fluid variables:

where :math:`\rho_g =` fluid density (assumed to be constant in the absence of reactions)

where :math:`\varepsilon_g =` volume fraction of fluid (accounts only for displacement of fluid by particle, does not account for the EB walls)

where :math:`U_g =` fluid velocity

where :math:`p_g =` fluid pressure

where :math:`tau =` viscous stress tensor

   +-----------------------+--------------------------------------------------+

   | Variable              | Definition                                       |

   +=======================+==================================================+

   | :math:`\rho_g`        | Fluid density                                    |

   +------------+-------------------------------------+-----------------------+

   | :math:`\varepsilon_g` | Volume fraction of fluid (= 1 if no particles)   |

   +------------+-------------------------------------+-----------------------+

   | :math:`U_g`           | Fluid velocity                                   |

   +------------+-------------------------------------+-----------------------+

   | :math:`\tau`          | Viscous stress tensor                            |

   +------------+-------------------------------------+-----------------------+

   | :math:`g`             | Gravitational acceleration                       |

   +------------+-------------------------------------+-----------------------+

where :math:`g =` gravitational acceleration 

where :math:`\beta_p =` drag coefficient associated with a particle

where :math:`V_p =` velocity associated with a particle

Below are the governing equations for the fluid:

Fluid Equations

===============

Conservation of fluid mass:

.. math:: \frac{ \partial (\varepsilon_g \rho_g U)}{\partial t} + \nabla \cdot (\varepsilon_g \rho_g U_g U_g) + \varepsilon_g \nabla p_g = \nabla \cdot \tau

           + \sum_{part} \beta_p (V_p - U_g) + \rho_g g

where :math:`\sum_p \beta_p (V_p - U_g)` is the drag term in which :math:`V_p` represents the particle velocity.

where :math:`\sum_p \beta_p (V_p - U_g)` is the drag term in which :math:`V_p` represents the particle velocity and 

      :math:`\beta_p` is the drag coefficient associated with that particle

Conservation of fluid volume: