Abstract
Frenkel's method is used to obtain a relation between the edge velocity and the dynamic contact angle for the spreading of small spherical droplets of viscous and non-volatile fluids. The change in surface free energy is equated to the viscous dissipation caused by Poiseuille flow, first in a wedge and then in a cone inscribed within the spherical cap and this introduces a cut-off integral. An equation relating the edge velocity to the dynamic contact angle for both complete and partial wetting is obtained. In the small angle limit this formula corresponds to a generalized Tanner's law and, in the case of the cone model, also predicts the variation of the edge velocity over a wide angular range. A form for the angular dependence in the cut-off integral is suggested and estimates of a related vertical cut-off length are obtained from existing data. Good agreement of the edge velocity angular dependence with literature values covering the range up to 165 degrees for complete spreading is found. In addition, for high-energy surfaces a closed form for the time dependence of the contact angle can be obtained.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
