Title, Analytical approach for the Lucas-Washburn equation. Author/s, A Hamraoui, Tommy Nylander. Department/s, Physical Chemistry 1 (S). Full-text, Full text ...

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

where is the time for a liquid of dynamic viscosity and surface tension to penetrate a distance into the capillary whose pore diameter is . In case of a porous materials many issues have been raised both about the physical meaning of the calculated pore diameter 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 of fluid in the tube , one obtains

where is the sum over the participating pressures, such as the atmospheric pressure , the hydrostatic pressure and the equivalent pressure due to capillary forces . is the viscosity of the liquid, and is the coefficient of slip, which is assumed to be 0 for wetting materials. is the radius of the capillary. The pressures in turn can be written as

where is the density of the liquid and its surface tension. is the angle of the tube with respect to the horizontal axis. 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 :

This is an excerpt from the article Washburn's equation from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.

In case of a fully wettable capillary, it is

where is the time for a liquid of dynamic viscosity and surface tension to penetrate a distance into the capillary whose pore diameter is . In case of a porous materials many issues have been raised both about the physical meaning of the calculated pore diameter 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 of fluid in the tube , one obtains

where is the sum over the participating pressures, such as the atmospheric pressure , the hydrostatic pressure and the equivalent pressure due to capillary forces . is the viscosity of the liquid, and is the coefficient of slip, which is assumed to be 0 for wetting materials. is the radius of the capillary. The pressures in turn can be written as

where is the density of the liquid and its surface tension. is the angle of the tube with respect to the horizontal axis. 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 :

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 919 times in the last 30 days. (as of: 11/03/2013)

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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" ...

en.wikipedia.org/wiki/Talk%3AWashburn's_equation

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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

Search results for "Washburn's equation"

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Washburn's equation in science

Analytical approach for the Lucas-Washburn equation - Lund ...

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 ...

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

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 ...

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

[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

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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Blog posts on the term

Washburn's equation

Washburn's equation

Eat a Lion's Heart: Cookies and Milk? Just Use Washburn's Equation!

Photo Credit: evergraphics. comWe’ve all experienced it.

english119fall2011.blogspot.com/2011/11/cookies-and-milk-just-use-washburns.html
Why A Boston Globe Writer Didn't Vote LeBron James For MVP

Mystery solved. The lone writer who listed Carmelo Anthony first, denying LeBron James the first-ever unanimous MVP, was Gary Washburn of the Boston Globe. And he sounds almost...apologetic?

deadspin.com/why-a-boston-globe-writer-didnt-vote-lebron-james-for-493102035
MAKE | Capillary action colors calendar in real time
blog.makezine.com/2009/07/25/capillary-action-colors-calendar-in/

10 Places President Obama Should Visit to See Climate Change In Action - The Equation

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blog.ucsusa.org/10-places-president-obama-should-visit-to-see-climate-change-in-action-127
nanopolitan: How to Dunk your Biscuits

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.

nanopolitan.blogspot.com/2012/10/how-to-dunk-your-biscuits.html
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.

www.celticstown.com/2013/05/17/washburn-paul-pierces-family-is-preparing-for-relocation/
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.

www.geekwire.com/2013/algebra-challenge/
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

www.teadunking.co.uk/national-tea-dunking-day.html
Historical Badass: Mountaineer and Photographer Bradford Washburn

Bradford Washburn suffered from terrible hay fever as a child and long told friends that he became a mountain climber because the mountains were the only place he could breathe. Others might say he became a mountain climber because he

www.adventure-journal.com/2013/02/historical-badass-mountaineer-and-photographer-bradford-washburn/
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