scholarly journals Re-derivation of Young’s Equation, Wenzel Equation, and Cassie-Baxter Equation Based on Energy Minimization

10.5772/61066 ◽  
2015 ◽  
Author(s):  
Kwangseok Seo ◽  
Minyoung Kim ◽  
Do Hyun Kim
Keyword(s):  
Energy Minimization ◽  
Baxter Equation ◽  
Young's Equation

A singular minimization problem for droplet profiles

1993 ◽  
Vol 4 (4) ◽  
pp. 399-418 ◽  
Author(s):  
Amy Novick-Cohen
Keyword(s):  
Free Energy ◽  
Minimization Problem ◽  
Energy Minimization ◽  
Disjoining Pressure ◽  
Laplace's Equation ◽  
Absolute Minimizer ◽  
Contact Points ◽  
Absolute Minimizers ◽  
Definition Of ◽  
Young's Equation

A minimization problem for partially wetting droplet profiles is considered, in which Van der Waal's forces have been taken into account via a singular ‘disjoining pressure’. When the singular disjoining pressure is neglected, energy minimization leads to Laplace's equation and Young's equation; once the singular disjoining pressure is included, this is no longer the case. Indeed, the free energy is no longer bounded from below. Introducing the notion of overtaking to compare the energies of configurations whose energies are arbitrarily large and negative, we demonstrate that if a configuration is not convex then it cannot be an absolute minimizer. If profiles are allowed to ‘double-over’ then there does not exist an absolute minimizer. Within the class of profiles which do not double-over, absolute minimizers are shown to exist; these minimizing profiles are not single-valued. The singular minimization problem is shown to be discontinuously dependent on the definition of the wetting profile in the neighbourhood of the contact points; the implications of this discontinuity are discussed.

Comments on the Antonow and interfacial interaction rules

1990 ◽  
Vol 55 (5) ◽  
pp. 1143-1148 ◽  
Author(s):  
Jan Kloubek
Keyword(s):  
Free Energy ◽  
Energy Minimization ◽  
Interfacial Interaction ◽  
Aliphatic Hydrocarbon ◽  
Theoretical Base ◽  
Water Interface ◽  
Free Energy Minimization ◽  
Interaction Rule

Results presented for the aliphatic hydrocarbon-water interface show that the recent hypothesis of the free energy minimization called interfacial interaction rule, which was suggested as a theoretical base of the Antonow rule, cannot be generally valid.

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