Search Results (2)

The Shuttleworth and Lippman equations are well-known equations used to link surface tension and stress (Shuttleworth) and surface tension and electric surface potentials (Lippmann). We show that the Shuttleworth and Lippman equations have a common thermodynamic basis, common to systems that possess a relatively large interfacial energy. This is relevant for problems of droplet stability, colloidal suspensions, electrode surfaces and more. Both equations are derived for systems that are not Euler homogeneous in the manner classical systems are. Hill’s thermodynamics for small systems is used to address this problem. Small in this context refers to systems with interfacial energies that are size- or shape-dependent. The resulting Hill–Gibbs–Duhem equation, an extension of the classical Gibbs–Duhem’s equation, gives the common basis for the Shuttleworth and Lippman equations. Hill’s thermodynamics enables us to rigorously define two types of surface tension, the differential surface tension and the integral surface tension. These surface tensions are linked by the system’s subdivision potential. From Helfrich’s equation we obtain a scaling law for the subdivision potential as function of the interfacial curvature. The dependence of the resulting subdivision potential on the system curvature is predicted. A critical analysis of the literature about the Shuttleworth and Lippman equations is given. Full article

A new approach is proposed to derive evapotranspiration (E) and irrigation requirements by implementing the combination equation models of Penman–Monteith and Shuttleworth and Wallace with surface parameters and resistances derived from Sentinel-2 data. Surface parameters are derived from Sentinel-2 and used as an input in these models; namely: the hemispherical shortwave albedo, leaf area index and water status of the soil and canopy ensemble evaluated by using a shortwave infrared-based index. The proposed approach has been validated with data acquired during the GRAPEX (Grape Remote-sensing Atmospheric Profile and Evapotranspiration eXperiment) in California irrigated vineyards. The E products obtained with the combination equation models are evaluated by using eddy covariance flux tower measurements and are additionally compared with surface energy balance models with Landsat-7 and -8 thermal infrared data. The Shuttleworth and Wallace (S-W S-2) model provides an accuracy comparable to thermal-based methods when using local meteorological data, with daily E errors < 1 mm/day, which increased from 1 to 1.5 mm/day using meteorological forcing data from atmospheric models. The advantage of using the S-W S-2 modeling approach for monitoring ET is the high temporal revisit time of the Sentinel-2 satellites and the finer pixel resolution. These results suggest that, by integrating the thermal-based data fusion approach with the S-W S-2 modeling scheme, there is the potential to increase the frequency and reliability of satellite-based daily evapotranspiration products. Full article