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 ...

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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Theory Note 5 — Washburn Method - Biolin Scientific

Thus equation (1) can be written. ATTENSION SIGMA. Figure 1. Schematic of the Washburn method. Capillary rise method is based on the Poiseuille law related ...

www.biolinscientific.com/zafepress.php?url=%2Fpdf%2FAttension%2FTheory%20Notes%2FAT_TN_5_washburn.pdf

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Analytical Approach for the Lucas–Washburn Equation

Journal of Colloid and Interface Science 250, 415–421 (2002) doi:10.1006/jcis.
2002.8288. Analytical Approach for the Lucas–Washburn Equation.

218.4.189.15:8090/download/1b9e5c0d-b39e-4f7c-a14c-e9de386d201d.pdf

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CAPILLARITY - University of Connecticut

Note that this equation reduces to Eq. 4 for spherical geometry with R1=R2, and
.... order terms) yields the so-called Lucas-Washburn-Rideal (LWR) equation:.

www.engr.uconn.edu/environ/envphys/pdf/vadose_pdf/Capillarity_revised01.pdf

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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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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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An experimental study of the washburn equation for liquid flow in ...

The Washburn equation describes the flow of a liquid under its own capillary
force in a horizontal tube. The equation has been tested and shown to be
adequate ...

www.sciencedirect.com/science/article/pii/0021979779901383

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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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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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Use of the Washburn Equation for Surface Free Energy Determination

thin-layer chromatography silica (Merck) by the Washburn equation. It has been
found that wick-wetting is a reproducible process and the results of the wetting ...

pubs.acs.org/doi/pdf/10.1021/la00038a066

Search results for "Washburn's equation"

Google: approx. 8.400

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Washburn's equation in science

Washburn's equation - Wikipedia, the free encyclopedia

[PDF]CAPILLARITY - University of Connecticut

University of Connecticut, Storrs, Connecticut, USA. Markus Tuller ..... order terms
) yields the so-called Lucas-Washburn-Rideal (LWR) equation: t. 2. )(Cos. R.

[PDF]Use of the Washburn Equation for Surface Free Energy Determination

University, 20-031 Lublin, Poland. Received July 1, 1991. ... thin-layer
chromatography silica (Merck) by the Washburn equation. It has been found that
wick- ...

[PDF]Analytical Approach for the Lucas–Washburn Equation

ahmed.hamraoui@crmc2.univ-mrs.fr. vity (5). In this paper, we ... force is zero, we
obtain the Lucas–Washburn equation (LWE): ρπr2 ∂. ∂t. ( h(t). ∂h(t). ∂t. ).

On the use of Washburn's equation for contact angle determination

Apr 2, 2012 ... On the use of Washburn's equation for contact angle determination ... Faculty of
Chemistry, Maria Curie-Skłodowska University, 20-031 Lublin, ...

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

Lund University 350th Ann.. ... Analytical approach for the Lucas-Washburn equation ... we circumvent these obstacies by exploring another approach and
suggest an analytical approach of the classical Lucas-Washburn equation (LWE).

Hydrophilicity of 3-D biomaterials: the Washburn equation.

(1)Department of Clinical Engineering UKCTE, The University of Liverpool, UK. ...
This paper describes the application of the Washburn equation to measure the ...

The rate of capillary penetration and the applicability ... - ScienceDirect

The computed results explain an apparent anomaly posed by the Washburn equation. It is shown that the Washburn equation would be appropriate for the ...

Capillary Rise in Nanopores: Molecular Dynamics Evidence for the ...

Mar 30, 2007 ... Title: Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation. Authors: D. I. Dimitrov, A. Milchev, ...

Books on the term Washburn's equation

Physico-chemical Analysis of Industrial Catalysts: A ...

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 ...

Handbook of sol-gel science and technology. 2. ...

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 ...

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 ...

Technologies for Smart Sensors and Sensor Fusion

... and the wettability of the solid–liquid–fluid system, cos θ0, which is given by
Equation 2.8 for a cylindrical capillary98: 0 θ ... (2.10) Equation 2.10, known as Washburn's equation, has become a reliable basis for any study of liquid
penetration ...

Pharmaceutical Emulsions and Suspensions: Second Edition, ...

According to the original Washburn equation (20, p. 496), the square of the
penetrated distance, x1, should be a linear function of time t for a particular liquid
of viscosity T| and surface tension TC, at a constant temperature: •5 A/ , *2 = — YL
[16] ...

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Blog posts on the term

Washburn's equation

Washburn's equation

An experimental study of the washburn equation for liquid flow in very fine capillaries
www.sciencedirect.com/science/article/pii/0021979779901383

Use of the Washburn equation for surface free energy determination - ResearchGate

Publication » Use of the Washburn equation for surface free energy determination.

www.researchgate.net/publication/231670008_Use_of_the_Washburn_equation_for_surface_free_energy_determination
Eat a Lion's Heart: Cookies and Milk? Just Use Washburn's Equation!

Photo Credit: evergraphics.comWe’ve all experienced it. The failed cookie dunk.

english119fall2011.blogspot.com/2011/11/cookies-and-milk-just-use-washburns.html
Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation - CERN Document Server
cds.cern.ch/record/1028347/linkbacks?ln=en

How to make a cup of tea for an academic | Higher Education Network | The Guardian

Ever wondered where all the bloody teaspoons are? Or how to avoid that pesky dribble down the underside of the teapot spout? Thankfully researchers have tackled these pressing issues

www.theguardian.com/higher-education-network/blog/2014/oct/17/-sp-how-to-make-a-cup-of-tea-for-an-academic
Analytical approach for the Lucas-Washburn equation. - Abstract - Europe PubMed Central

Abstract: Porous media can be characterized by studying the kinetics of liquid rise within the pore spaces. Although porous media generally have a complex...

europepmc.org/abstract/MED/16290679
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