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| {{more footnotes|date=February 2012}}
| | Emilia Shryock is my title but you can call me something you like. To do aerobics is a thing that I'm completely addicted to. I am a meter reader but I plan on altering it. California is where I've usually been living and I love each day residing right here.<br><br>Feel free to surf to my homepage - std testing at home ([http://ironptstudio.com/rev/239375 This Web page]) |
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| In [[fluid dynamics]] the '''Eötvös number''' ('''Eo''') is a [[dimensionless number]] named after Hungarian physicist [[Loránd Eötvös]] (1848–1919).<ref name="Clift1978">
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| {{cite book|last=Clift|first=R.|last2=Grace|first2=J. R.|last3=Weber|first3=M. E.|title=Bubbles Drops and Particles|publisher=Academic Press|location=New York|year=1978|isbn=0-12-176950-X|page=26}}
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| </ref><ref name="Tryggvason2011">
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| {{cite book|last1=Tryggvason|first1=Grétar|last2=Scardovelli|first2=Ruben|last3=Zaleski|first3=Stéphane|title=Direct Numerical Simulations of Gas–Liquid Multiphase Flows|year=2011|publisher=Cambridge University Press|location=Cambridge, UK|isbn=9781139153195|url=http://www.cambridge.org/fr/knowledge/isbn/item6796659|page=43}}</ref>
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| It is also known in a slightly different form as the '''Bond number''' ('''Bo'''),<ref name="Tryggvason2011" /><ref name="Hager2012">
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| {{cite journal|last=Hager|first=Willi H.|title=Wilfrid Noel Bond and the Bond number|journal=Journal of Hydraulic Research|year=2012|volume=50|issue=1|pages=3–9|doi=10.1080/00221686.2011.649839|url=http://www.tandfonline.com/doi/abs/10.1080/00221686.2011.649839}}
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| </ref><ref name=deGennes2004> | |
| {{cite book|last1=de Gennes|first1=Pierre-Gilles|last2=Brochard-Wyart|first2=Françoise|last3=Quéré|first3=David|title=Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves|year=2004|publisher=Springer|location=New York|isbn=978-0-387-00592-8|url=http://www.springer.com/materials/surfaces+interfaces/book/978-0-387-00592-8|page=119}}</ref>
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| named after the English physicist Wilfrid Noel Bond (1897–1937).<ref name="Hager2012" /><ref>
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| {{cite journal|title=Dr. W. N. Bond|journal=Nature|year=1937|volume=140|issue=3547|pages=716-716|doi=10.1038/140716a0|url=http://www.nature.com/nature/journal/v140/n3547/abs/140716a0.html|bibcode = 1937Natur.140Q.716. }}</ref>
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| The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.{{Citation needed|date=July 2012}}
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| Together with [[Morton number]] it can be used to characterize the shape of [[Liquid bubble|bubbles]] or [[drop (liquid)|drops]] moving in a surrounding fluid.
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| Eötvös number may be regarded as proportional to [[buoyancy]] force divided by [[surface tension]] force.
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| :<math>\mathrm{Eo}=\frac{\Delta\rho \,g \,L^2}{\sigma}</math>
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| * Eo is the Eötvös number
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| * <math>\Delta\rho</math>: difference in [[density]] of the two phases, ([[SI]] units: [[kilogram|kg]]/[[meter|m]]<sup>3</sup>)
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| * ''g'': [[gravitational acceleration]], ([[SI]] units : m/[[second|s]]<sup>2</sup>)
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| * ''L'': characteristic length, ([[SI]] units : m)
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| * <math>\sigma</math>: [[surface tension]], ([[SI]] units : [[Newton (unit)|N]]/m)
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| A different statement of the equation is as follows:
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| :<math>\mathrm{Bo} = \frac{\rho a L^2}{\gamma}</math>
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| where
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| * Bo is the Bond Number
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| * <math>\rho</math> is the [[density]], or the density difference between fluids.
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| * ''a'' the acceleration associated with the [[body force]], almost always [[gravity]].
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| * ''L'' the 'characteristic length scale', e.g. [[radius]] of a drop or the radius of a [[capillary]] tube.
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| * <math>\gamma</math> is the surface tension of the interface.
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| The Bond number is a measure of the importance of surface tension forces compared to body forces. A high Bond number indicates that the system is relatively unaffected by surface tension effects; a low number (typically less than one is the requirement) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects.
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| The Bond number is the most common comparison of gravity and surface tension effects and it may be derived in a number of ways, such as [[scale analysis (mathematics)|scaling]] the pressure of a drop of liquid on a solid surface. It is usually important, however, to find the right length scale specific to a problem by doing a ground-up [[scale analysis (mathematics)|scale analysis]]. Other dimensionless numbers are related to the Bond number:
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| :<math>\mathrm{Bo} = \mathrm{Eo} = 2\, \mathrm{Go}^2 = 2\, \mathrm{De}^2\,</math>
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| Where Eo, Go, and De are respectively the Eötvös, Goucher, and Deryagin numbers. The "difference" between the Goucher and Deryagin numbers is that the Goucher number (which arises in wire coating problems) uses the letter ''R'' to represent length scales while the Deryagin number (which arises in plate film thickness problems) uses ''L''.
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| ==References==
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| {{Reflist}}
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| {{NonDimFluMech}}
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| {{DEFAULTSORT:Eotvos Number}}
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| [[Category:Dimensionless numbers of fluid mechanics]]
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| [[Category:Fluid dynamics]]
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| [[ru:Число Этвёша]]
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Emilia Shryock is my title but you can call me something you like. To do aerobics is a thing that I'm completely addicted to. I am a meter reader but I plan on altering it. California is where I've usually been living and I love each day residing right here.
Feel free to surf to my homepage - std testing at home (This Web page)