CoolProp/doc/transport_table/table.tex

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\author{Ian Bell, Vincent Lemort, ULg}
\begin{document}

\centering
\begin{tabular}{ccp{3in}p{8	in}}
\hline\hline
Fluid & Reference & $\eta^0$ & $\eta^r$ \\
\hline
H2S & Quinones-Cisneros 2012 & $\eta^0 = 0.87721\dfrac{\sqrt{T}}{S^*(T^*)}$ \newline $S^*(T^*) = \sum_i \frac{\alpha_i}{T^{*i}}$ & FRICTION THEORY\\\hline
\hline \multicolumn{4}{c}{DONE below this line}\\ \hline\hline
Propane & (data) Vogel 1998 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta_h = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_1(1+g_2\tau^{1/2})$\\\hline
n-Butane & (RP) Vogel 1999 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta_h = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_1(1+\displaystyle\sum_{l=2}g_l\tau^{(l-1)/2})$ \\\hline
Isobutane & (RP) Vogel 2000 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta_h = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_1(1+\displaystyle\sum_{l=2}g_l\tau^{(l-1)/2})$  \\\hline
Octane, nonane, decane & (data) Huber 2004 &  $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+c_1\left(\frac{\delta}{\delta_0-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=c_2 +c_3\sqrt{\tau}+c_4\tau$\\\hline
n-Dodecane & (data) Huber 2004 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+c_1\left(\frac{\delta}{\delta_0-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=c_2 +c_3\sqrt{\tau}$\\\hline
R125 & (data) Huber 2006 & $\eta^0 = \dfrac{5}{16}\sqrt{\dfrac{MkT}{\pi N}}\dfrac{1}{\sigma^2\Omega^*(T^*)}$\newline $\Omega(T^*)$ from Neufeld & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+c_1\left(\frac{\delta}{\delta_0-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=c_2 +c_3\sqrt{\tau}$\\\hline
Carbon Dioxide & (data) Fenghour 1998 & $\eta^0 = \dfrac{1.00697\sqrt{T}}{\sigma^2\mathfrak{S}(T^*)}$ \newline $\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ &  $\Delta\eta = d_{11}\rho + d_{21}\rho^2+\frac{d_{64}\rho^6}{(T^*)^3}+d_{81}\rho^8+\frac{d_{82}\rho^8}{T^*}$ \newline $\Delta\eta = d_{11}\rho_c\delta + d_{21}\rho_c^2\delta^2+\frac{d_{64}\rho_c^6(\varepsilon/k)^3\delta^6\tau^3}{(T_c)^3}+\rho_c^8d_{81}\delta^8+\frac{\rho_c^8d_{82}\delta^8(\varepsilon/k)\tau}{T_c}$\\\hline
Nitrogen, argon, oxygen air & (data) Lemmon and Jacobsen 2004 & $\eta^0 = \dfrac{0.0266958\sqrt{MT}}{\sigma^2\Omega(T^*)}$\newline$\Omega(T^*)=\exp\left(\sum_{i=0}^{4}b_i[\ln T^*]^i\right)$ & $\eta^r = \sum_{i=1}^NN_i\tau^{\tau_i}\delta^{d_i}\exp(-\gamma_i\delta^{l_i})$\\\hline
R134a & (RP) Huber 2003 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = c_1\delta+\left(\frac{c_2}{\tau^6}+\frac{c_3}{\tau^2}+\frac{c_4}{\sqrt{\tau}}+c_5\tau^2\right)\delta^2+c_6\delta^3+c_7\left(\frac{1}{\delta_0-\delta}-\frac{1}{\delta_0}\right)$ \newline $\delta_0(\tau)=\frac{c_{10}}{1+c_8\tau+c_9\tau^2}$\\\hline
Dimethyl Ether & (exp. data) Meng 2012 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \Delta\eta$\newline$\Delta\eta = \sum_{i=0}^{1}n_i\tau^{t_i}\delta^{d_i} + \sum_{i=2}^{6}n_i\tau^{t_i}\delta^{d_i}\exp(-\delta^{p_i})$\\\hline
R123 & (data) Tanaka 1996 & $\eta^0 = \displaystyle\sum_{i}a_iT_i$ & $\eta^r = \eta^1\rho+\Delta\eta$ \newline $\eta^1 = b_0+b_1T$\newline$\Delta\eta = \frac{a_0}{\rho-\rho_0}+\frac{a_0}{\rho_0}+a_1\rho+a_2\rho^2+a_3\rho^3$\newline$\Delta\eta = \frac{a_0/\rho_c}{\delta-\delta_0}+\frac{a_0/\rho_c}{\delta_0}+a_1\rho_c\delta+a_2\rho_c^2\delta^2+a_3\rho_c^3\delta^3$\\\hline
R152A & (data) Krauss 1996 & $\eta^0 = \dfrac{5}{16}\sqrt{\dfrac{MkT}{1000\pi N}}\dfrac{10^{24}}{\sigma^2\Omega^*(T^*)}=\dfrac{0.2169614\sqrt{T}}{\sigma^2\Omega(T^*)}$\newline $\Omega(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\dfrac{\Delta\eta}{H_c} = \displaystyle\sum_{i=1}^{4}E_i\left(\frac{\rho}{\rho_c}\right)^i + \frac{E_5}{\rho/\rho_c-E_6}+\frac{E_5}{E_6}$\\\hline
Ethanol & (RP) Kiselev 2005 & $\eta^0 = \sum_i a_i T^{n_i}$ & $\eta^r = B_{RF}\rho\eta^0(T)+\Delta \eta$ \newline $\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_2+g_3\sqrt{\tau}$\\\hline
Water & (data) Huber 2009 & & \\\hline
Hydrogen & (from v5) Muzny 2013 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S^*(T^*)}$\newline$S^*(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = B_{RF}\rho\eta^0(T) + \Delta\eta$\newline$\Delta\eta = c_1\rho_r^2\exp\left[c_2T_r+c_3/T_r+\frac{c_4\rho_r^2}{c_5+T_r}+c_6\rho_r^6\right]$\\\hline
n-Hexane & (data) Michailidou 2013 &$\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S(T^*)}$\newline$S(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$& $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = (\rho_r^{2/3}T_r^{1/2})\left\lbrace\dfrac{c_0}{T_r}+\dfrac{c_1}{c_2+T_r+c_3\rho_r^2}+\dfrac{c_4(1+\rho_r)}{c_5 + c_6T_r+c_7\rho_r+\rho_r^2+c_8\rho_rT_r} \right\rbrace$ \\\hline
SF6 & (data) Quinones-Cisneros 2012 & $\eta^0 = \sum_i d_i T_r^{n_i}$ & FRICTION THEORY\\\hline
R404A, R410A, R507, R407 & (data) Geller 2000 & $\eta^0 = \sum_i A_iT^i$&$\eta^r = \sum_j b_j\rho^j$ \\\hline
Helium & (data) Arp 1998 & hardcoded & hardcoded \\\hline
R23 & (data) Shan 2000 & $\eta^0 = \frac{5}{16}\sqrt{\frac{MkT}{1000\pi N}}\frac{10^{24}}{\sigma^2\Omega^*(T^*)}$\newline $\Omega(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$  & \\\hline
Ethane & (data) Friend 1991 & $\eta^0 = \dfrac{12.0085\sqrt{t}}{\Omega^{(2,2)*}(t)}$ \newline $\Omega^{(2,2)*}(t) = \left[\sum_i C_it^{(i-1)/3-1} \right]^{-1}$& $\Delta\eta = 15.977\left[\displaystyle\sum_i g_i\delta^{r_i}\tau^{s_i}\right]\left[1+\displaystyle\sum_{i=10}^{11}g_i\delta^{r_i}\tau^{s_i}\right]^{-1}$\\\hline
Ammonia & (data) Fenghour 1995 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\Game(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ &  $\eta^r = B_{BV}\rho\eta^0(T) + \Delta\eta$\newline$\Delta\eta = \sum_i b_i(T)\rho^i$\\\hline
\hline\hline
\end{tabular}

For a description of the conversion between $\mathfrak{S}$ and $\Omega$, see Vesovic 1990 ($CO_2$).  Basically $\Omega = (5/4)\mathfrak{S}$.

\clearpage

\centering
\begin{tabular}{cccp{3in}p{8in}p{3in}}
\hline\hline
Fluid & Data & Reference & Dilute & Residual & Critical \\ \hline
Ammonia & & Tufeu 1984 \\
Helium & & Hands Cryo 1981\\
R23 & & Shan ASHRAE 2000 \\

\hline\hline STANDARD BELOW THIS LINE \\ \hline\hline
R404A, R407C, R401A, R507A & & Geller IJT 2001 \\

\hline\hline DONE BELOW THIS LINE\\ \hline\hline
Water & & Huber JPCRD 2012\\
Nitrogen, Argon, Oxygen, Air & & Lemmon 2004 & & &\\
Ethane & & Friend JPCRD 1991 \\
CO2 & & Vesovic JPCRD 1990 \\
R123 & & Laesecke IJR 1996 \\
R152A & & Krauss IJT 1996 \\
R1234ze(E) & & Perkins JCED 2011 \\
Propane & & Marsh JCED 2002\\
Dodecane & & Huber EF 2004 \\
Octane, Nonane, Decane & & Huber FPE 2005\\
Isobutane & & Perkins JCED 2002\\
Butane & & Perkins  JCED 2002 \\
R125 & & Perkins JCED 2006 \\
Normal-/Parahydrogen & & Assael JPCRD 2011\\
SF6 & & Assael JPCRD 2012\\
Toluene & & Assael JPCRD 2012\\
Heptane & & Assael JPCRD 2013\\
Benzene & & Assael JPCRD 2012 \\
Hexane & & Assael JPCRD 2013\\
Ethanol & & Assael JPCRD 2013 \\

\hline\hline
\end{tabular}


\end{document}