From e10e48d20d9bce4309ba36e41f1f182541706d02 Mon Sep 17 00:00:00 2001
From: Deepak Rangarajan <deepak.rangarajan@netl.doe.gov>
Date: Tue, 27 Aug 2024 11:52:00 -0400
Subject: [PATCH 1/6] Add doc for suspension viscosity models

---
 docs/source_docs/refs.bib                     | 53 +++++++++++++++++++
 .../user_guide/inputs/fluid_model.rst         | 36 ++++++++++++-
 2 files changed, 88 insertions(+), 1 deletion(-)

diff --git a/docs/source_docs/refs.bib b/docs/source_docs/refs.bib
index 0693753..92e5c82 100644
--- a/docs/source_docs/refs.bib
+++ b/docs/source_docs/refs.bib
@@ -82,6 +82,15 @@ pages = {379-402}
   url = {https://www.sciencedirect.com/science/article/pii/S0021999120305945},
 }
 
+@article{brinkman52,
+  author = {Brinkman, H.C.},
+  title = {The viscosity of concentrated suspensions and solutions},
+  journal = {The Journal of Chemical Physics},
+  year = {1952},
+  volume = {20},
+  pages = {571}
+}
+
 @book{Burden10,
   title={Numerical Analysis},
   author={Burden, R.L. and Faires, J.D.},
@@ -101,6 +110,14 @@ pages = {379-402}
   pages = {1-31}
 }
 
+@article{cheng03,
+  author = {Nian-Sheng Cheng and Adrian Wing-Keung Law},
+  title = {Exponential formula for computing effective viscosity},
+  journal = {Powder Technology},
+  year = {2003},
+  volume = {129},
+  pages = {156--160}
+}
 
 @techreport{chern87,
   author      = {Chern, I.-L., and Colella, P. },
@@ -190,6 +207,15 @@ pages = {379-402}
   publisher={Oxford University Computing Laboratory Oxford, UK}
 }
 
+@article{einstein11,
+  title={Eine neue bestimmung der moleküldimensionen},
+  author={Einstein, A},
+  journal={Ann. Physik},
+  volume={19},
+  pages={289--306},
+  year={1911},
+}
+
 @article{elhilo12,
 author = {M. El-Hilo and R.W. Chantrell},
 title = {Rationalisation of distribution functions for models of nanoparticle magnetism},
@@ -238,6 +264,15 @@ url = {https://www.sciencedirect.com/science/article/pii/S0304885312002132},
   publisher={Elsevier}
 }
 
+@article{gibilaro07,
+  author = {Gibilaro L.G., Gallucci K., Felice R. Di. and Pagliai P.},
+  title = {On the apparent viscosity of a fluidized bed},
+  journal = {Chemical Engineering Science},
+  year = {2007},
+  volume = {62},
+  pages = {294--300}
+}
+
 @article{Gid83,
   author = {Gidaspow, D. and Ettehadieh, B. },
   title = {Fluidization in Two-Dimensional Beds with a Jet; 2. Hydrodynamic Modeling},
@@ -290,6 +325,15 @@ doi = {https://doi.org/10.1016/j.jcp.2022.111305},
   pages = {843-855}
 }
 
+@article{krieger59,
+  author = {Krieger, I.M. and Dougherty, T.J. },
+  title = {A mechanism for non-newtonian flow in suspensions of rigid spheres},
+  journal = {Trans. Soc. Rheol},
+  year = {1959},
+  volume = {3},
+  pages = {137--152}
+}
+
 @article{Lat011,
   author = {Lathouwers, D. and Bellan, J. },
   title = {Modeling of dense gas-solid reative mixtures applied to biomass pyrolysis in a fluidized bed},
@@ -384,6 +428,15 @@ doi = {https://doi.org/10.1016/j.jcp.2022.111305},
   volume = {32}
 }
 
+@article{roscoe52,
+  author = {Roscoe, R.},
+  title = {The viscosity of suspensions of rigid spheres},
+  journal = {British Journal of Applied Physics},
+  year = {1952},
+  volume = {3},
+  pages = {267}
+}
+
 @article{Sch33,
   author = {Schiller, L. and Naumann, A. },
   title = {A drag coefficient correlation},
diff --git a/docs/source_docs/user_guide/inputs/fluid_model.rst b/docs/source_docs/user_guide/inputs/fluid_model.rst
index 374b671..7f1ef78 100644
--- a/docs/source_docs/user_guide/inputs/fluid_model.rst
+++ b/docs/source_docs/user_guide/inputs/fluid_model.rst
@@ -35,11 +35,45 @@ The following inputs are defined using the ``fluid`` prefix.
 | viscosity.eddy.Smagorinsky-Lilly.constant  | Smagorinsky-Lilly constant which usually has values        | Real   | None     |
 |                                            | between 0.1 and 0.2.                                       |        |          |
 |                                            |                                                            |        |          |
-|                                            | A value is required when using the ``Samgorinsky-Lilly``   |        |          |
+|                                            | A value is required when using the ``Smagorinsky-Lilly``   |        |          |
 |                                            | eddy viscosity model.                                      |        |          |
 +--------------------------------------------+------------------------------------------------------------+--------+----------+
 | viscosity.eddy.WALE.constant               | WALE eddy viscosity model constant.                        | Real   | 0.325    |
 +--------------------------------------------+------------------------------------------------------------+--------+----------+
+| viscosity.suspension                       | Specify suspension viscosty model.                         | String | None     |
+|                                            |                                                            |        |          |
+|                                            | Available options include:                                 |        |          |
+|                                            |                                                            |        |          |
+|                                            | * ``None`` No eddy viscosity model                         |        |          |
+|                                            | * ``Einstein`` :cite:p:`einstein11`                        |        |          |
+|                                            | * ``Brinkman`` :cite:p:`brinkman52,gibilaro07`             |        |          |
+|                                            |                                                            |        |          |
+|                                            |      :math:`\mu_{susp}=\mu_{mol} (1-\varepsilon_s)^{-n}`   |        |          |
+|                                            |                                                            |        |          |
+|                                            | * ``Roscoe`` :cite:p:`roscoe52,krieger59`                  |        |          |
+|                                            |                                                            |        |          |
+|                                            |      :math:`\mu_{susp}=\mu_{mol} \mu^*`, where             |        |          |
+|                                            |      :math:`\mu^*=(max(c1-\varepsilon_s,e^{-9})/c1)^{-c2}` |        |          |
+|                                            |                                                            |        |          |
+|                                            | * ``ChengLaw`` :cite:p:`cheng03`                           |        |          |
+|                                            |                                                            |        |          |
++--------------------------------------------+------------------------------------------------------------+--------+----------+
+| viscosity.suspension.Brinkman.constant     | Constant for exponent in Brinkman suspension expression.   | Real   | None     |
+|                                            |                                                            |        |          |
+|                                            | A value is required when using the model ``Brinkman``.     |        |          |
++--------------------------------------------+------------------------------------------------------------+--------+----------+
+| viscosity.suspension.Roscoe.c1             | Constant for max packing in Roscoe suspension expression.  | Real   | None     |
+|                                            |                                                            |        |          |
+|                                            | A value is required when using the model ``Roscoe``.       |        |          |
++--------------------------------------------+------------------------------------------------------------+--------+----------+
+| viscosity.suspension.Roscoe.c2             | Constant for exponent in Roscoe suspension expression.     | Real   | None     |
+|                                            |                                                            |        |          |
+|                                            | A value is required when using the model ``Roscoe``.       |        |          |
++--------------------------------------------+------------------------------------------------------------+--------+----------+
+| viscosity.suspension.ChengLaw.constant     | Constant for exponent in ChengLaw suspension expression.   | Real   | None     |
+|                                            |                                                            |        |          |
+|                                            | A value is required when using the model ``ChengLaw``.     |        |          |
++--------------------------------------------+------------------------------------------------------------+--------+----------+
 | species                                    | Specify the species that constitute the fluid.             | String |  None    |
 |                                            |                                                            |        |          |
 |                                            | All listed species must be properly defined. See the       |        |          |
-- 
GitLab


From 010db8b93359481042fe590175e8cfbc63fe4863 Mon Sep 17 00:00:00 2001
From: Deepak Rangarajan <deepak.rangarajan@netl.doe.gov>
Date: Tue, 27 Aug 2024 11:56:53 -0400
Subject: [PATCH 2/6] fix

---
 docs/source_docs/user_guide/inputs/fluid_model.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/source_docs/user_guide/inputs/fluid_model.rst b/docs/source_docs/user_guide/inputs/fluid_model.rst
index 7f1ef78..237dac7 100644
--- a/docs/source_docs/user_guide/inputs/fluid_model.rst
+++ b/docs/source_docs/user_guide/inputs/fluid_model.rst
@@ -53,7 +53,7 @@ The following inputs are defined using the ``fluid`` prefix.
 |                                            | * ``Roscoe`` :cite:p:`roscoe52,krieger59`                  |        |          |
 |                                            |                                                            |        |          |
 |                                            |      :math:`\mu_{susp}=\mu_{mol} \mu^*`, where             |        |          |
-|                                            |      :math:`\mu^*=(max(c1-\varepsilon_s,e^{-9})/c1)^{-c2}` |        |          |
+|                                            |      :math:`\mu^*=(max(c1-\varepsilon_s,10^{-9})/c1)^{-c2}`|        |          |
 |                                            |                                                            |        |          |
 |                                            | * ``ChengLaw`` :cite:p:`cheng03`                           |        |          |
 |                                            |                                                            |        |          |
-- 
GitLab


From 6831df4659a33c99a87817fe2933160813cd99a2 Mon Sep 17 00:00:00 2001
From: Deepak Rangarajan <deepak.rangarajan@netl.doe.gov>
Date: Tue, 27 Aug 2024 13:58:56 -0400
Subject: [PATCH 3/6] add another reference

---
 docs/source_docs/refs.bib                          | 8 ++++++++
 docs/source_docs/user_guide/inputs/fluid_model.rst | 2 +-
 2 files changed, 9 insertions(+), 1 deletion(-)

diff --git a/docs/source_docs/refs.bib b/docs/source_docs/refs.bib
index 92e5c82..a250d50 100644
--- a/docs/source_docs/refs.bib
+++ b/docs/source_docs/refs.bib
@@ -374,6 +374,14 @@ doi = {https://doi.org/10.1016/j.jcp.2022.111305},
   publisher   = {NOAA/NCAR Boulder Atmospheric Observatory},
 }
 
+@article{maron56,
+  author = {Samuel H Maron and Percy E Pierce},
+  title = {Application of ree-eyring generalized flow theory to suspensions of spherical particles},
+  journal = {Journal of Colloid Science},
+  year = {1956},
+  volume = {11},
+  pages = {80--95}
+}
 
 @article{Massoudi03,
   author = {Mehrdad Massoudi},
diff --git a/docs/source_docs/user_guide/inputs/fluid_model.rst b/docs/source_docs/user_guide/inputs/fluid_model.rst
index 237dac7..a8f2a71 100644
--- a/docs/source_docs/user_guide/inputs/fluid_model.rst
+++ b/docs/source_docs/user_guide/inputs/fluid_model.rst
@@ -50,7 +50,7 @@ The following inputs are defined using the ``fluid`` prefix.
 |                                            |                                                            |        |          |
 |                                            |      :math:`\mu_{susp}=\mu_{mol} (1-\varepsilon_s)^{-n}`   |        |          |
 |                                            |                                                            |        |          |
-|                                            | * ``Roscoe`` :cite:p:`roscoe52,krieger59`                  |        |          |
+|                                            | * ``Roscoe`` :cite:p:`roscoe52,krieger59,maron56`          |        |          |
 |                                            |                                                            |        |          |
 |                                            |      :math:`\mu_{susp}=\mu_{mol} \mu^*`, where             |        |          |
 |                                            |      :math:`\mu^*=(max(c1-\varepsilon_s,10^{-9})/c1)^{-c2}`|        |          |
-- 
GitLab


From f6d778129dd5b4e2123ab59eb80e8733cb1def81 Mon Sep 17 00:00:00 2001
From: Deepak Rangarajan <deepak.rangarajan@netl.doe.gov>
Date: Wed, 28 Aug 2024 10:58:52 -0400
Subject: [PATCH 4/6] update readme

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 585f536..8a510fe 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,7 @@ can be built locally by:
 1. Install sphinx:
 
 ```shell
-> pip install sphinx sphinx_rtd_theme sphinx-tabs
+> pip install sphinx sphinx_rtd_theme sphinx-tabs sphinxcontrib-bibtex
 ```
 
 2. Build the documentation:
-- 
GitLab


From 035d45627b67de1c42e4b7592fa921bb6689d758 Mon Sep 17 00:00:00 2001
From: Deepak Rangarajan <deepak.rangarajan@netl.doe.gov>
Date: Wed, 28 Aug 2024 14:04:57 -0400
Subject: [PATCH 5/6] apply review changes

---
 .../user_guide/inputs/fluid_model.rst         | 19 +++++++++++--------
 1 file changed, 11 insertions(+), 8 deletions(-)

diff --git a/docs/source_docs/user_guide/inputs/fluid_model.rst b/docs/source_docs/user_guide/inputs/fluid_model.rst
index a8f2a71..9d5581a 100644
--- a/docs/source_docs/user_guide/inputs/fluid_model.rst
+++ b/docs/source_docs/user_guide/inputs/fluid_model.rst
@@ -39,23 +39,26 @@ The following inputs are defined using the ``fluid`` prefix.
 |                                            | eddy viscosity model.                                      |        |          |
 +--------------------------------------------+------------------------------------------------------------+--------+----------+
 | viscosity.eddy.WALE.constant               | WALE eddy viscosity model constant.                        | Real   | 0.325    |
-+--------------------------------------------+------------------------------------------------------------+--------+----------+
-| viscosity.suspension                       | Specify suspension viscosty model.                         | String | None     |
+--------------------------------------------+------------------------------------------------------------+--------+----------+
+| viscosity.suspension                       | Specify suspension viscosty model of the form              | String | None     |
+|                                            | :math:`\mu_{susp}=\mu_{mol}(\mu^* - 1)`                    |        |          |
 |                                            |                                                            |        |          |
 |                                            | Available options include:                                 |        |          |
 |                                            |                                                            |        |          |
-|                                            | * ``None`` No eddy viscosity model                         |        |          |
+|                                            | * ``None`` No eddy suspension model                        |        |          |
+|                                            |   :math:`\mu^*=1`                                          |        |          |
+|                                            |                                                            |        |          |
 |                                            | * ``Einstein`` :cite:p:`einstein11`                        |        |          |
-|                                            | * ``Brinkman`` :cite:p:`brinkman52,gibilaro07`             |        |          |
+|                                            |   :math:`\mu^*=1 + 2.5\varepsilon_s`                       |        |          |
 |                                            |                                                            |        |          |
-|                                            |      :math:`\mu_{susp}=\mu_{mol} (1-\varepsilon_s)^{-n}`   |        |          |
+|                                            | * ``Brinkman`` :cite:p:`brinkman52,gibilaro07`             |        |          |
+|                                            |   :math:`\mu^*=(1-\varepsilon_s)^{-c}`                     |        |          |
 |                                            |                                                            |        |          |
 |                                            | * ``Roscoe`` :cite:p:`roscoe52,krieger59,maron56`          |        |          |
-|                                            |                                                            |        |          |
-|                                            |      :math:`\mu_{susp}=\mu_{mol} \mu^*`, where             |        |          |
-|                                            |      :math:`\mu^*=(max(c1-\varepsilon_s,10^{-9})/c1)^{-c2}`|        |          |
+|                                            |   :math:`\mu^*=(1-\varepsilon_s/c_1)^{-c_2}`               |        |          |
 |                                            |                                                            |        |          |
 |                                            | * ``ChengLaw`` :cite:p:`cheng03`                           |        |          |
+|                                            |   :math:`\mu^*=e^{2.5(1/(1-\varepsilon_s)^c-1)/c}`         |        |          |
 |                                            |                                                            |        |          |
 +--------------------------------------------+------------------------------------------------------------+--------+----------+
 | viscosity.suspension.Brinkman.constant     | Constant for exponent in Brinkman suspension expression.   | Real   | None     |
-- 
GitLab


From 7c91212f0e809c684cdc2b433df80b5b6947b2e8 Mon Sep 17 00:00:00 2001
From: Deepak Rangarajan <deepak.rangarajan@netl.doe.gov>
Date: Wed, 28 Aug 2024 14:06:36 -0400
Subject: [PATCH 6/6] fix format

---
 docs/source_docs/user_guide/inputs/fluid_model.rst | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/source_docs/user_guide/inputs/fluid_model.rst b/docs/source_docs/user_guide/inputs/fluid_model.rst
index 9d5581a..7e1430d 100644
--- a/docs/source_docs/user_guide/inputs/fluid_model.rst
+++ b/docs/source_docs/user_guide/inputs/fluid_model.rst
@@ -39,7 +39,7 @@ The following inputs are defined using the ``fluid`` prefix.
 |                                            | eddy viscosity model.                                      |        |          |
 +--------------------------------------------+------------------------------------------------------------+--------+----------+
 | viscosity.eddy.WALE.constant               | WALE eddy viscosity model constant.                        | Real   | 0.325    |
---------------------------------------------+------------------------------------------------------------+--------+----------+
+---------------------------------------------+------------------------------------------------------------+--------+----------+
 | viscosity.suspension                       | Specify suspension viscosty model of the form              | String | None     |
 |                                            | :math:`\mu_{susp}=\mu_{mol}(\mu^* - 1)`                    |        |          |
 |                                            |                                                            |        |          |
-- 
GitLab