Du Noüy ring method

The method involves slowly lifting a ring, often made of platinum, from the surface of a liquid. The force, {{mvar|F}}, required to raise the ring from the liquid's surface is measured and related to the liquid's surface tension {{mvar|γ}}:

: $F\; =\; w\_\backslash text\{ring\}\; +\; 2\backslash pi\; \backslash cdot\; (r\_\backslash text\{i\}\; +\; r\_\backslash text\{a\})\; \backslash cdot\; \backslash gamma,$

where {{math|r{{sub|i}}}} is the radius of the inner ring of the liquid film pulled, and {{math|r{{sub|a}}}} is the radius of the outer ring of the liquid film.{{cite journal | title = Physics and Chemistry of Interfaces | url = https://archive.org/details/physicschemistry00butt | url-access = limited | author1 = Butt, Hans-Jürgen | author2 = Graf, Karlheinz | author3 = Kappl, Michael | year = 2003 | pages = [https://archive.org/details/physicschemistry00butt/page/n28 14]–15}}{{dead link|date=October 2023}} {{math|w{{sub|ring}}}} is the weight of the ring minus the buoyant force due to the part of the ring below the liquid surface.{{Cite journal |last1=Zuidema |first1=H. |last2=Waters |first2=George |date=1941-05-01 |title=Ring Method for the Determination of Interfacial Tension |url=https://doi.org/10.1021/i560093a009 |journal=Industrial & Engineering Chemistry Analytical Edition |volume=13 |issue=5 |pages=312–313 |doi=10.1021/i560093a009 |issn=0096-4484|url-access=subscription }}

When the ring's thickness is much smaller than its diameter, this equation can be simplified to

: $F\; =\; w\_\backslash text\{ring\}\; +\; 4\backslash pi\; R\; \backslash gamma,$

where {{mvar|R}} is the average of the inner and outer radius of the ring, i.e. $(r\_\backslash text\{i\}\; +\; r\_\backslash text\{a\})/2.${{Cite web |title=Total Weight of Ring using Ring-Detachment Method Calculator {{!}} Calculate Total Weight of Ring using Ring-Detachment Method |url=https://www.calculatoratoz.com/en/total-weight-of-ring-using-ring-detachment-method-calculator/Calc-30889 |access-date=2024-05-29 |website=www.calculatoratoz.com |language=en}}

The maximum force is used for the calculations, and empirically determined correction factors are required to remove the effect caused by the finite diameter of the ring:

: $F\; =\; w\_\backslash text\{ring\}\; +\; 4\backslash pi\; R\; \backslash gamma\; f,$

with {{mvar|f}} being the correction factor.

File:Du Nouy tensiometer.jpg

The most common correction factors include Zuidema–Waters correction factors (for liquids with low interfacial tension), Huh–Mason correction factors (which cover a wider range than Zuidema–Waters), and Harkins–Jordan correction factors (more precise than Huh–Mason, while still covering the most widely used liquids).{{Cite book |url=https://books.google.com/books?id=dOSZ2LsBJKgC&pg=PA19 |title=Effect of Temperature and Impurities on Surface Tension of Crude Oil |last=Udeagbara |first=Stephen Gekwu |date=2010-07-30 |publisher=Universal-Publishers |isbn=9781599423555 |language=en}}

The surface tension and correction factors are expressed by

: $\backslash gamma\; =\; \backslash frac\{F\}\{4\; \backslash pi\; R\}\; f,$

where {{mvar|γ}} is surface tension, {{mvar|R}} is the average radius of the ring, and {{mvar|f}} is correction factor.

H. H. Zuidema and George W. Waters introduced the following correction factor in 1961:

: $(f\; -\; a)^2\; =\; \backslash frac\{4b\}\{\backslash pi\; ^2\}\; \backslash frac\{1\}\{R^2\}\; \backslash frac\{\backslash gamma\_\backslash text\{measured\}\}\{\backslash rho\_\backslash text\{lower\}\; -\; \backslash rho\_\backslash text\{upper\}\}\; +\; C,$

where

: {{mvar|F}} = maximum pull of rings [dyn/cm],

: {{mvar|ρ}} = density of the lower and upper phases,

: $C\; =\; 0.04534\; -\; 1.679\; \backslash frac\{r\}\{R\},$

: {{math|1=a = 0.7250}},

: {{math|1=b = 0.0009075}} [s²⋅cm⁻¹],

: {{mvar|r}} = Du Noüy wire radius,

: {{mvar|R}} = Du Noüy ring radius.

C. Huh and S. G. Mason{{Cite journal|last1=Huh|first1=C.|last2=Mason|first2=S. G.|date=1975-07-01|title=A rigorous theory of ring tensiometry|url=https://doi.org/10.1007/BF01753960|journal=Colloid and Polymer Science|language=en|volume=253|issue=7|pages=566–580|doi=10.1007/BF01753960|s2cid=94325517 |issn=1435-1536|url-access=subscription}}{{Cite journal|last1=Huh|first1=C.|last2=Mason|first2=S. G.|date=1977-05-01|title=A rigorous theory of ring tensiometry: Addendum on the wall effect|url=https://doi.org/10.1007/BF01536462|journal=Colloid and Polymer Science|language=en|volume=255|issue=5|pages=460–467|doi=10.1007/BF01536462|s2cid=97555566 |issn=1435-1536|url-access=subscription}} described the correction factors as a function of $\backslash tfrac\{R\}\{r\}$ and $\backslash tfrac\{R^3\}\{V\}.$ See the references.

William Draper Harkins and Hubert F. Jordan{{Cite journal|last1=Harkins|first1=William D.|last2=Jordan|first2=Hubert F.|title=A Method for the Determination of Surface and Interfacial Tension from the Maximum Pull on a Ring |date=1930-05-01|url=https://doi.org/10.1021/ja01368a004|journal=Journal of the American Chemical Society|volume=52|issue=5|pages=1751–1772|doi=10.1021/ja01368a004|issn=0002-7863|url-access=subscription}}{{Cite journal|last1=Harkins|first1=William D.|last2=Jordan|first2=Hubert F.|title=Surface Tension by the Ring Method |date=1930-07-18|url=https://www.science.org/doi/10.1126/science.72.1855.73|journal=Science|language=en|volume=72|issue=1855|pages=73–75|doi=10.1126/science.72.1855.73|issn=0036-8075|pmid=17819453|url-access=subscription}} tabulated the correction factors as a function of $R/r$ and $R^3/V$.

• Sessile drop technique
• Wilhelmy plate

{{reflist}}

{{Commons category|Du Noüy ring method}}

• [https://www.youtube.com/watch?v=Yy6dvChYtJg Video showing a classical torsion wire du Noüy tensiometer]
• [http://history.nih.gov/exhibits/galleries/instrument/big/tensiometer.jpg Picture of a classical torsion wire du Noüy tensiometer] (National Institutes of Health)

{{DEFAULTSORT:Du Nouy ring method}}

Category:Scientific techniques