Washburn's equation

In physics, 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.

For wet-out flow, it is

where ${\displaystyle t}$ is the time for a liquid of dynamic viscosity ${\displaystyle \eta }$ and surface tension ${\displaystyle \gamma }$ to penetrate a distance ${\displaystyle L}$ into the capillary whose pore diameter is ${\displaystyle D}$. In case of a porous materials many issues have been raised both about the physical meaning of the calculated pore diameter ${\displaystyle D}$ 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 is sufficiently accurate in many cases when the capillary force is still significantly greater than the gravitational force.

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