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 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
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Washburn's equation in science
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 ...
[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 ...
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 ...
Handbook of sol-gel science and technology. 2. ...
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 ...
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 ...
Technologies for Smart Sensors and Sensor Fusion
Kevin Yallup, Krzysztof Iniewski, 2014
... 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, ...
Françoise Nielloud, 2000
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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Washburn's equation
Washburn's equation - Wikipedia, the free encyclopedia
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An experimental study of the washburn equation for liquid flow in very fine capillaries
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Washburn equation - physicsworld.com
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Use of the Washburn equation for surface free energy determination - ResearchGate
Publication » Use of the Washburn equation for surface free energy determination.
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Photo Credit: evergraphics.comWe’ve all experienced it. The failed cookie dunk.
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Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation - CERN Document Server
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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
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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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