Washburn's equation
In physics, the Washburn's equation describes capillary flow in a bundle of parallel cylindrical tubes; it is extended with some issues also to imbibition into porous materials. The equation is named after Edward Wight Washburn; also known as Lucas–Washburn equation, considering that Richard Lucas wrote a similar paper three years earlier, or the Bell-Cameron-Lucas-Washburn equation, considering J.M. Bell and F.K. Cameron's discovery of the form of the equation fifteen years earlier.
In case of a fully wettable capillary, it is
L^2=\frac{\gamma Dt}{4\eta}
where t is the time for a liquid of dynamic viscosity \eta and surface tension \gamma to penetrate a distance L into the capillary whose pore diameter is D. In case of a porous materials many issues have been raised both about the physical meaning of the calculated pore diameter D and the real possibility to use this equation for the calculation of the contact angle of the solid.
The equation is derived for capillary flow in a cylindrical tube in the absence of a gravitational field, but according to physicist Len Fisher can be extremely accurate for more complex materials including biscuits (see dunk (biscuit)). Following National biscuit dunking day, some newspaper articles quoted the equation as Fisher's equation.[citation needed]
In his paper from 1921 Washburn applies Poiseuille's law for fluid motion in a circular tube. Inserting the expression for the differential volume in terms of the length l of fluid in the tube dV=\pi r^2 dl, one obtains
\frac{\delta l}{\delta t}=\frac{\sum P}{8 r^2 \eta l}(r^4 +4 \epsilon r^3)
where \sum P is the sum over the participating pressures, such as the atmospheric pressure P_A, the hydrostatic pressure P_h and the equivalent pressure due to capillary forces P_c. \eta is the viscosity of the liquid, and \epsilon is the coefficient of slip, which is assumed to be 0 for wetting materials. r is the radius of the capillary. The pressures in turn can be written as
P_h=h g \rho - l g \rho\sin\psi
P_c=\frac{2\gamma}{r}\cos\phi
where \rho is the density of the liquid and \gamma its surface tension. \psi is the angle of the tube with respect to the horizontal axis. \phi is the contact angle of the liquid on the capillary material. Substituting these expressions leads to the first-order differential equation for the distance the fluid penetrates into the tube l:
\frac{\delta l}{\delta t}=\frac{[P_A+g \rho (h-l\sin\psi)+\frac{2\gamma}{r}\cos\phi](r^4 +4 \epsilon r^3)}{8 r^2 \eta l}

This is an excerpt from the article Washburn's equation from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Washburn's equation at en.wikipedia.org was accessed 1,005 times in the last 30 days. (as of: 06/07/2013)
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Washburn's equation - Wikipedia, the free encyclopedia
In physics, the Washburn's equation describes capillary flow in a bundle of parallel cylindrical tubes; it is extended with some issues also to imbibition into ...
en.wikipedia.org/wiki/Washburn's_equation
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Talk:Washburn's equation - Wikipedia, the free encyclopedia
Talk:Washburn's equation. From Wikipedia, the ... Retrieved from "http://en. wikipedia.org/w/index.php?title=Talk:Washburn%27s_equation&oldid= 275040412" ...
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Comparison of the Use of Washburn's Equation in the Distance ...
J Colloid Interface Sci. 2001 Jan 15;233(2):356-360. Comparison of the Use of Washburn's equation in the Distance-Time and Weight-Time Imbibition ...
www.ncbi.nlm.nih.gov/pubmed/11121287
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Washburn's equation facing Galileo's transformation: some remarks.
J Colloid Interface Sci. 2002 Sep 15;253(2):472-4. Washburn's equation facing Galileo's transformation: some remarks. Labajos-Broncano L, González-Martín ...
www.ncbi.nlm.nih.gov/pubmed/16290880
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characterization of porous materials by capillary rise method
Mar 15, 2005 ... Key words: capillary rise, penetration kinetics, Washburn's equation, ... The Washburn's equation is obtained after the integration of Eq. (7) with ...
www.ig.pwr.wroc.pl/minproc/journal/pdf/2005/s47-65.pdf
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Eat a Lion's Heart: Cookies and Milk? Just Use Washburn's Equation!
Nov 29, 2011 ... According to researchers (I'm not making this up), we should rely on Washburn's equation, L2=γDt/4η, which relates capillary flow in porous ...
english119fall2011.blogspot.com/2011/11/cookies-and-milk-just-use-washburns.html
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Lucas-Washburn equation - Soft-Matter
Dec 10, 2011 ... Entry by Meredith Duffy, AP225, Fall 2011. The Lucas-Washburn equation, also known simply as Washburn's equation, describes the rate dl/dt ...
soft-matter.seas.harvard.edu/index.php/Lucas-Washburn_equation
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Washburn's Equation - E-Cigarette Forum
I was looking around at some of the mods and I noticed that you guys use the wicking effect but no one mentioned Washburn's equation.
www.e-cigarette-forum.com/forum/cartridge-mods/80110-washburns-equation.html
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On the use of Washburn's equation for contact angle determination
Apr 2, 2012 ... A systematic study on the possibility of Young's contact angle determination from Washburn's equation was performed using the so-called ...
www.tandfonline.com/doi/abs/10.1163/156856197X00147
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Washburn equation - physicsworld.com
Washburn equation. The Washburn equation explains how quickly biscuits absorb fluids. Back to article · Copyright · Privacy and Cookies Policy · Disclaimer ...
physicsworld.com/cws/article/news/3094/1/news-3-6-3-1
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Washburn's equation in science
Analytical approach for the Lucas-Washburn equation - Lund ...
Title, Analytical approach for the Lucas-Washburn equation. Author/s, A Hamraoui, Tommy Nylander. Department/s, Physical Chemistry 1 (S). Full-text, Full text ...
Comparison of the Use of Washburn's Equation in the Distance ...
Comparison of the Use of Washburn's equation in the Distance-Time and Weight -Time ... Department of Physics, Extremadura University, Badajoz, 06071, Spain ...
Hydrophilicity of 3-D biomaterials: the Washburn equation.
Department of Clinical Engineering UKCTE, The University of Liverpool, UK. ... This paper describes the application of the Washburn equation to measure the ...
Washburn's equation facing Galileo's transformation: some remarks.
Washburn's equation facing Galileo's transformation: some remarks. Labajos- Broncano L, González-Martín ML, Bruque JM. Department of Physic, University of ...
Capillary Rise in Nanopores: Molecular Dynamics Evidence for the ...
Mar 30, 2007 ... ... Molecular Dynamics Evidence for the Lucas-Washburn Equation ... upon modification of the Lucas-Washburn law which takes explicitly into ...
[PDF]Analytical Approach for the Lucas–Washburn Equation
... Chemistry 1, Center for Chemistry and Chemical Engineering, Lund University, P.O. Box 124, ... force is zero, we obtain the Lucas–Washburn equation (LWE): ...
[PDF]On the use of Washburn's equation for contact angle determination ...
that the contact angle calculated from Washburn's equation was not equal to Young's .... ber (Chromdes, Medical University, Lublin, Poland) used for thin-layer ...
Use of the Washburn equation for surface free energy determination ...
Publication » Use of the Washburn equation for surface free energy determination. ... Emil Chibowski. Maria Curie-Sklodowska University in Lublin ...
[PDF]Hydrophilicity of 3-D biomaterials: The Washburn equation - Springer
Department of Clinical Engineering UKCTE, The University of Liverpool, UK ... describes the application of the Washburn equation to measure the surface ...
Books on the term Washburn's equation
Physico-Chemical Analysis of Industrial Catalysts: A Practical ...
Physico-Chemical Analysis of Industrial Catalysts: A Practical ...
John Lynch, 2003
The liquid penetrates a pore with a radius rp under a pressure P given by Washburn's equation: -2ycos9 (1.7) where y is the surface tension (N-nr1 ) at the liquid-gas interface 9 is the wetting angle of the liquid with the material. The values ...
Washburn's Equation
Washburn's Equation
Lambert M Surhone, Mariam T Tennoe, Susan F Henssonow, 2011
In physics, Washburn's equation describes capillary flow in porous materials.It is L^2=frac{gamma Dt}{4eta} where t is the time for a liquid of viscosity and surface tension to penetrate a distance L into a fully wettable, porous material ...
Handbook of sol-gel science and technology. 2. Characterization ...
Handbook of sol-gel science and technology. 2. Characterization ...
Sumio Sakka, 2005
They note very important differences and conclude that Washburn's equation is not appropriate for mercury porosimetry data analysis ... Vittoratos rightly points out that the inadequate use of Washburn's analysis leads to an interpretation of the ...
Free Surface Flows Under Compensated Gravity Conditions
Free Surface Flows Under Compensated Gravity Conditions
Michael Dreyer, 2007
[116] found that their equation reduces to the Lucas-Washburn equation (4.31). Levine et al. [117] presented the most detailed theory for the capillary rise in tubes up to now. They applied the Navier-Stokes equations on the liquid volume ...
Powder Surface Area and Porosity
Powder Surface Area and Porosity
S. Lowell, Joan E. Shields, 1991
When 0 = 0°, equation (10.23) reduces to equation (10.4) where AP is identical to the pressure within a bubble in excess of ambient. According to the Washburn equation (10.23) a capillary of sufficiently small radius will require more than one ...
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Washburn's equation
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Photo Credit: evergraphics. comWe’ve all experienced it.
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Some of us, butter-toothed blokes, dunk our biscuits in tea or coffee before chewing on them. Dunked biscuits are tasty, but have their fender-bender moments.
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Washburn: Paul Pierce’s family is preparing for relocation | Celtics Town | Boston Celtics blog | Celtics news
Paul Pierce seems to be preparing himself to leave. small http://cash2advance3.
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Students to solve 250,000 algebra equations in one week with iOS app - GeekWire
Video games are making their way into Washington schools early next month and for all the right reasons. Using an iteration of a learning app called DragonBox, the Washington State Algebra Challenge is a one-of-a-kind campaign to get students across the state to solve 250,000 equations in just one week.
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National Tea Dunking Day | Tea Dunking
It may come as a surprise, but there is no official UK National Biscuit Dunking Day. We want this to change, and need your help! Apparently, back in 1999, the
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Historical Badass: Mountaineer and Photographer Bradford Washburn
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