From 506a8ef1d0a15552fe9b4b3bb1c070e18bafc374 Mon Sep 17 00:00:00 2001
From: Ann Almgren <asalmgren@lbl.gov>
Date: Wed, 17 Oct 2018 19:36:14 -0700
Subject: [PATCH] Define variables

---
 docs/source/FluidEquations.rst | 26 ++++++++++++++++++++++----
 1 file changed, 22 insertions(+), 4 deletions(-)

diff --git a/docs/source/FluidEquations.rst b/docs/source/FluidEquations.rst
index dca9b8d..2ad1374 100644
--- a/docs/source/FluidEquations.rst
+++ b/docs/source/FluidEquations.rst
@@ -1,6 +1,24 @@
 Fluid Equations
 ===============
 
+We define the following fluid variables:
+
+: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:`U_g = ` fluid velocity
+
+:math:`p_g = ` fluid pressure
+
+:math:`tau = ` viscous stress tensor
+
+:math:`g = ` gravitational acceleration 
+
+:math:`\beta_p = ` drag coefficient associated with a particle
+
+:math:`V_p = ` velocity associated with a particle
+
 Below are the governing equations for the fluid:
 
 Conservation of fluid mass:
@@ -9,12 +27,12 @@ Conservation of fluid mass:
 
 Conservation of fluid momentum:
 
-.. 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 + {\bf g} 
-           + \sum_{part} \beta (V_{part} - U_g)
+.. 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
 
-Conservation of fluid volume:
+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_{part} \beta (V_{part} - U_g)` is the drag term in which :math:`V_{part}` represents the particle velocity.
+Conservation of fluid volume:
 
 .. math:: \frac{\partial \varepsilon_g}{\partial t} + \nabla \cdot (\varepsilon_g  U_g)  = 0
 
-- 
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