On the use of Zisman’s function for the determination of the velocity of spontaneous capillary microflows

J. Berthier, Jing Lee, D. Gosselin, F. Navarro, E. Berthier, A. Theberge

Keywords: Zisman's plot, capillary flow, capillary velocity


Capillary-based microfluidic systems are increasingly used in the fields of biotechnology, medicine, thermics, energy and space. In such systems the energy source responsible for the flow is the surface energy of the walls. Extending the Lucas-Washburn-Rideal (LWR) law, a general expression for the velocity and marching distance of an open capillary flow, valid for any channel geometry, has been reported in the literature. This expression stems from the balance between the capillary force and the wall friction. It makes use of the cosine of the contact angle. In the case of non-polar liquids and some polar fluids, the introduction of the Zisman’s relation between the cosine of the contact angle and the surface tension of the liquid brings a new perspective on the general expression of the capillary velocity.