Diffusion Coefficients of Water

Olaf Dietrich <od@dtrx.net>, Munich, Germany


To provide exact values of self-diffusion coefficients of water (H216O) over a broad range of temperatures as reference values for testing and calibrating diffusion measurements, e. g., in diffusion-weighted magnetic resonance imaging (MRI).


Several publications provide values of self-diffusion coefficients of water at different temperatures [1–9]. These data points (listed below in the Data section) can be interpolated and extrapolated using the dependence between log D and 1/T (Arrhenius plot).

Here, an interactive interface is provided to calculate self-diffusion coefficients of water at different temperatures (or, alternatively, to calculate the temperature corresponding to a given diffusion coefficient). The (default) list of measured data points, i. e., of pairs (temperature, diffusion coefficient), used for these calculations consists of the results summarized in Tables 1–5 below. The list of data points can be extended or shortened (e. g, it may be advisable to remove data of low (≤ 5 °C) and high (≥ 50 °C) temperatures if interested in the intermediate range between 15 and 40 °C).

Diffusion coefficients of water do not follow an exact linear relationship in the Arrhenius plot. This is accounted for by the quadratic fit option that results in a very good agreement of measured data points and fit function. It is strongly recommended to use the quadratic fit when calculating diffusion coefficients. (In an earlier version of this document, only the linear fit was available; calculated diffusion coefficients based on this linear interpolation must be expected to be systematically too low by about 0.4 % in the range between 15 and 30 °C.)

All diffusion coefficients are given in μm2/ms = 10–3 mm2/s = 10–9 m2/s.

Arrhenius plot

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quadratic fit linear fit
Add to list (e. g., “20.5, 2.05”):
Temperature (°C): Diff. coefficient (10–3 mm2/s):


Table 1 shows data measured with a diaphragm-cell technique; the estimated error is “a few tenths of a per cent” [1]. Newer results measured with a diaphragm cell are presented in Table 2; the listed values are calculated from the published results for H218O using the relation D(H216O) = 1.0105 D(H218O); the estimated error is ±0.2 % [2]. Table 3 shows data from NMR measurements on a 19.8-MHz (0.47 T) spectrometer with an estimated experimental error of ±1 % [3]. Data from NMR measurements on a Bruker MSL200 (4.7 T) spectrometer with a total uncertainty (95 % confidence limit) of 1.5 % are shown in Table 4 [4]. Diffusion coefficients of water measured with a Bruker AM 300 instrument (300 MHz, i. e., 7 T) with error limits ≤ 1 % are shown in Table 5 [5]. Diffusion coefficients of supercooled liquid water down to –31 °C are presented in Table 6; the measurements were performed with an NMR spectrometer and the errors were estimated to be ±5 % (95 % confidence limits) [6]. Data from various publications are summarized in Table 7 [7–9].

Table 1: Diffusion coefficients D, diaphragm cell; R. Mills (1973) [1]
1 °C274.15 K1.149
4 °C277.15 K1.276
5 °C278.15 K1.313
15 °C288.15 K1.777
25 °C298.15 K2.299
35 °C308.15 K2.919
45 °C318.15 K3.575
Table 2: Diffusion coefficients D, diaphragm cell; A.J. Easteal et al. (1989) [2]
0 °C273.15 K1.130
10 °C283.15 K1.536
20 °C293.15 K2.022
25 °C298.15 K2.296
30 °C303.15 K2.590
40 °C313.15 K3.240
50 °C323.15 K3.968
60 °C333.15 K4.772
70 °C343.15 K5.646
80 °C353.15 K6.582
90 °C363.15 K7.578
100 °C373.15 K8.623
Table 3: Diffusion Coefficients D, NMR; K.R. Harris and L.A. Woolf (1980) [3]
4 °C277.15 K1.27
10 °C283.15 K1.55
25 °C298.15 K2.30
45 °C318.15 K3.55
60 °C333.15 K4.70
Table 4: Diffusion coefficients D, NMR; P.S. Tofts et al. (2000) [4]
15 °C288.15 K1.756
20 °C293.15 K2.023
25 °C298.15 K2.317
30 °C303.15 K2.616
Table 5: Diffusion coefficients D, NMR; Holz et al. (2000) [5]
15 °C288.15 K1.766
20 °C293.15 K2.025
25 °C298.15 K2.299
30 °C303.15 K2.597
35 °C308.15 K2.895
40 °C313.15 K3.222
45 °C318.15 K3.601
50 °C323.15 K3.983
56 °C329.15 K4.444
Table 6: Diffusion coefficients D, NMR; K.T. Gillen et al. (1972) [6]
–30.65 °C242.5 K0.187
–28.75 °C244.4 K0.219
–26.85 °C246.3 K0.263
–24.95 °C248.2 K0.321
–23.15 °C250.0 K0.341
–21.35 °C251.8 K0.395
–19.15 °C254.0 K0.438
–17.35 °C255.8 K0.477
–14.45 °C258.7 K0.553
–11.65 °C261.5 K0.633
–9.45 °C263.7 K0.700
0.35 °C273.5 K1.05  
12.15 °C285.3 K1.58  
25.05 °C298.2 K2.23  
Table 7: Diffusion Coefficients D, NMR; various studies
18.4 °C291.55 K 1.98 ± 0.14[7]
18.5 °C291.65 K 1.95 ± 0.02[8]
18.5 °C291.65 K 2.03 ± 0.01[8]
25.0 °C298.15 K 2.36 ± 0.04[8]
25.0 °C298.15 K 2.23 ± 0.06[9]


A simple application based on these data is the calibration of an MRI system with an ice-water phantom [10]. For water at 0 °C, a diffusion coefficient of 1.12 μm2/ms is estimated using the default data from Tables 1–5, but after removal of all measurements performed at temperatures > 30 °C.


[1] R. Mills. Self-diffusion in normal and heavy water in the range 1–45°. The Journal of Physical Chemistry, Vol. 77, No. 5, 685–688 (1973). DOI: 10.1021/j100624a025

[2] A.J. Easteal, W.E. Price, L.A. Woolf. Diaphragm cell for high-temperature diffusion measurements. Journal of the Chemical Society: Faraday Transactions 1, Vol. 85, No. 5, 1091–1097 (1989). DOI: 10.1039/F19898501091

[3] K.R. Harris, L.A. Woolf. Pressure and temperature dependence of the self diffusion coefficient of water and oxygen-18 water. Journal of the Chemical Society: Faraday Transactions 1, Vol. 76, 377–385 (1980). DOI: 10.1039/F19807600377

[4] P.S. Tofts, D. Lloyd, C.A. Clark, G.J. Barker, G.J.M. Parker, P. McConville, C. Baldock, J.M. Pope. Test liquids for quantitative MRI measurements of self-diffusion coefficient in vivo. Magnetic Resonance in Medicine, Vol. 43, No. 3, 368–374 (2000). DOI: 10.1002/(SICI)1522-2594(200003)43:3<368::AID-MRM8>3.0.CO;2-B

[5] M. Holz, S.R. Heil, A. Sacco. Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate 1H NMR PFG measurements. Physical Chemistry Chemical Physics, Vol. 2, 4740–4742 (2000). DOI: 10.1039/B005319H

[6] K.T. Gillen, D.C. Douglass, M.J.R. Hoch. Self-diffusion in liquid water to –31°C. The Journal of Chemical Physics, Vol. 57, No. 12, 5117–5119 (1972). DOI: 10.1063/1.1678198

[7] J.S. Murday, R.M. Cotts. Self-diffusion in liquids: H2O, D2O, and Na. The Journal of Chemical Physics, Vol. 53, 4724–4725 (1970). DOI: 10.1063/1.1674011

[8] C.R. Becker, L.R. Schad, W.J. Lorenz. Measurement of diffusion coefficients using a quick echo split NMR imaging technique. Magnetic Resonance Imaging, Vol. 12, No. 8, 1167–1174 (1994). DOI: 10.1016/0730-725X(94)90082-3

[9] D.E. O'Reilly, E.M. Peterson. Self-diffusion coefficients and rotational correlation times in polar liquids. II. The Journal of Chemical Physics, Vol. 55, No. 5, 2155–2163 (1971). DOI: 10.1063/1.1676386

[10] T.L. Chenevert, C.J. Galbán, M.K. Ivancevic, S.E. Rohrer, F.J. Londy, T.C. Kwee, C.R. Meyer, T.D. Johnson, A. Rehemtulla, B.D. Ross. Diffusion coefficient measurement using a temperature-controlled fluid for quality control in multicenter studies. Journal of Magnetic Resonance Imaging, Vol. 34, No. 4, 983–987 (2011). DOI: 10.1002/jmri.22363

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