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We define the following fluid variables:

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

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

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

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

 :math:`U_g = ` fluid velocity

.. :math:`U_g = ` fluid velocity

 :math:`p_g = ` fluid pressure

.. :math:`p_g = ` fluid pressure

 :math:`tau = ` viscous stress tensor

.. :math:`tau = ` viscous stress tensor

 :math:`g = ` gravitational acceleration 

.. :math:`g = ` gravitational acceleration 

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

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

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

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

Below are the governing equations for the fluid: