Washburn's equation

In physics, the Washburn equation for describing the capillary flow in porous materials is used.

This is defined as follows:

Is the time it takes for a liquid having the viscosity and surface tension of the penetration into a fully wettable, porous material having an average pore diameter over a certain penetration depth.

The equation is derived from the equation for capillary flow in a cylindrical tube without action of an external gravitational field. Gained popularity on the Washburn equation in England by the physicist Len Fisher of the University of Bristol. He demonstrated the application of the Washburn equation based on a Kekstauchexperiments to make accessible the science of physics by describing everyday problems.

The equation goes back to an article by Edward W. Washburn of 1921. Washburn there applies the law of Hagen-Poiseuille on the movement of a liquid in a circular pipe. After insertion of the expression for a differential volume which is defined by the differential length of a fluid in a tube, one obtains the following equation:

Is the sum of all pressures acting, including from atmospheric pressure of a hydrostatic pressure and from the pressure equivalent due to capillary forces. is the viscosity of the fluid and the coefficient of sliding friction, which for wettable materials is 0. is the radius of the capillary. The pressure can also be expressed as follows:

Is the density of the liquid and the surface tension thereof. is the angle of orientation of the tube relative to a horizontal axis. means the wetting angle of the liquid in contact with the pipe material.

Substituting these equations into the above leads to a first order differential equation which describes the penetration depth of the liquid in the pipe: