assael_1987
===========

M\. J\. Assael, S\. Mixafendi and W\. A\. Wakeham, "The Viscosity of Normal Deuterium in the Limit of Zero Density", J\. Phys\. Chem\. Ref\. Data 16, 189 \(1987\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/assael_1987.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1063/1\.555778 <https://doi.org/10.1063/1.555778>`__

**Source kind:** fit

**Recorded technique:** A correlation of the zero\-density viscosity of normal deuterium from 30 K to 2200 K\. Above 350 K, hydrogen's correlation \(the authors' earlier work, their ref\. 2\) scaled by the square root of the mass ratio \(Eq\. 3\), expected to hold to better than 0\.1 % above 300 K; below 350 K, the same form times a function f\(T\*\) fitted to four primary sets of oscillating\-disc and capillary measurements \(Table 1\: Kestin et al\. 200\-300 K, \+\-0\.2 %; Coremans et al\. 30\-80 K, \+\-2 %; Menabde 80\-300 K, \+\-2 %; Michels et al\. 290\-350 K, \+\-0\.2 %\)\. Table 2 tabulates the correlation\.

**Materials in structured entries:** D2

**Dataset quantities:** dilute\_viscosity

**Contents:** 1 dataset; 1 formula.

Curation notes
--------------

Identity VALIDATED\_WITH\_WARNINGS by the library\. Printed pp\. 189\-192 \(pdf pages 1\-4\)\.

THE CORRELATION \(pp\. 190\-191, checked against a 400 dpi rendering of the pages, 2026\-09\-30\)\: Eq\. \(1\), eta = \(5/16\) \(m k T / pi\)^\(1/2\) / \(sigma^2 Omega\*\(T\*\)\); Eq\. \(4\), ln Omega\* = 0\.46649 \- 0\.57015 ln T\* \+ 0\.19164 \(ln T\*\)^2 \- 0\.03708 \(ln T\*\)^3 \+ 0\.00241 \(ln T\*\)^4 \(0\.6 \< T\* \< 66\), T\* = kT/epsilon \(Eq\. 5\) with sigma = 0\.2968 nm and epsilon/k = 33\.3 K; below 350 K, eta\_D2 \(m\_H2/m\_D2\)^\(1/2\) / eta\_H2 = f\(T\*\) \(Eq\. 6\), f = 1 \- exp\(\-2\.8105 T\*^\(1/3\)\) \(Eq\. 7, 0\.9 \< T\* \< 10\.5\)\. Valid 30\-2200 K \(p\. 191\)\.

EQUATION AND TABLE DISAGREE\. Eqs\. \(1\) and \(4\)\-\(7\) as printed, with m the D2 molecular mass, do not reproduce Table 2\: \-12 % at 30 K, \-0\.6 % at 100 K, \+1\.5 % at 250 K, \+1\.3 % at 300 and 350 K, \-1\.9 % at 1000 K, \-2\.9 % at 2200 K \(computed 2026\-09\-30\)\. The table is smooth\.

RESOLVED \(TC\-760\)\. The printed Eq\. \(4\) is the authors' universal corresponding\-states functional \(assael\_1986, Eq\. 13\), not their hydrogen correlation \(assael\_1986, Eq\. 3 with its Table 2\)\. With the latter, the D2 mass and Eq\. \(7\)'s f\(T\*\) applied at every temperature \(not only below 350 K, as the text says\: f departs from 1 by 2e\-3 at 360 K and 1e\-4 at 1000 K\), Table 2 is reproduced within 1\.5 units of its last printed digit \(5\.1e\-4 relative, 140 of 224 cells within half a unit\), except at 90 K \(6\.5 units, 1\.2e\-3; computed 2026\-09\-30\)\. The 90 K cell is degraded in the scan and reads 5\.410 where the correlation and its neighbours give 5\.416; it is kept as printed\. Against a modern normal\-hydrogen dilute viscosity \(Muzny et al\. 2013, muzny\_2013\) times \(m\_D2/m\_H2\)^\(1/2\), Eq\. \(3\)'s scaling, it lies 0\.1\-1\.1 % below from 350 K to 2000 K and 0\.04 % above at 300 K; lower down, where the scaling is not expected to hold \(Eq\. 6\), it departs by up to \+0\.8 % \(120 K\) and \-2\.8 % \(30 K\)\. optmat serves Table 2 \(TC\-760\)\.

UNCERTAINTY \(p\. 191\)\: \+\-1 % from 250 K to 350 K, from the errors of the experimental data; \+\-2 % below; above 350 K, where the correlation rests on corresponding states, 'no more than \+\-4 % at the highest temperatures'\. The dataset takes 4 % throughout 350\-2200 K, a bound\. The primary data depart from the correlation by no more than \+\-0\.7 % over the whole range \(p\. 191\)\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

assael\_1987/table2
~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2",
     "material": "D2",
     "file": "D2/assael_1987__table2.csv",
     "table": "tbl_8b226138c853",
     "quantity": "dilute_viscosity",
     "unit": "Pa s",
     "scale": 1e-06,
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "relative": 0.04,
       "level": "not stated",
       "relative_rows": {
         "30": 0.02,
         "35": 0.02,
         "40": 0.02,
         "45": 0.02,
         "50": 0.02,
         "55": 0.02,
         "60": 0.02,
         "65": 0.02,
         "70": 0.02,
         "75": 0.02,
         "80": 0.02,
         "85": 0.02,
         "90": 0.02,
         "95": 0.02,
         "100": 0.02,
         "110": 0.02,
         "120": 0.02,
         "130": 0.02,
         "140": 0.02,
         "150": 0.02,
         "160": 0.02,
         "170": 0.02,
         "180": 0.02,
         "190": 0.02,
         "200": 0.02,
         "210": 0.02,
         "220": 0.02,
         "230": 0.02,
         "240": 0.02,
         "250": 0.01,
         "260": 0.01,
         "270": 0.01,
         "280": 0.01,
         "290": 0.01,
         "300": 0.01,
         "310": 0.01,
         "320": 0.01,
         "330": 0.01,
         "340": 0.01,
         "350": 0.01
       }
     }
   }

Table 2 \(p\. 191\)\: the viscosity of normal deuterium in the limit of zero density, eta/\(uPa s\), 30\-2200 K \(5 K steps to 100 K, 10 K above\)\. Four cells of the extracted table corrected from the page image \(the extraction script\)\.

Formulas
--------

assael\_1987/eq1\_eq4\_eq7
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "eq1_eq4_eq7",
     "material": "D2",
     "equation": "Eqs. (1), (4)-(7), pp. 190-191",
     "printed": "eta = (5/16)(m k T/pi)^(1/2)/(sigma^2 Omega*(T*)); ln Omega* = sum_i a_i (ln T*)^i; f(T*) = 1 - exp(-2.8105 T*^(1/3)) below 350 K",
     "variable": "T* = k T / epsilon; eta in Pa s with m in kg, sigma in m",
     "range": "30-2200 K",
     "coefficients": {
       "a0": "0.46649",
       "a1": "-0.57015",
       "a2": "0.19164",
       "a3": "-0.03708",
       "a4": "0.00241",
       "sigma_nm": "0.2968",
       "epsilon_k": "33.3",
       "f": "2.8105"
     },
     "check": "Does not reproduce Table 2 (notes); Table 2 is the dataset."
   }

Corrections
-----------

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register </register>` for the checks and decisions.