Theoretical Model of Droplet Wettability on a Low-Surface-Energy Solid under the Influence of Gravity

The wettability of droplets on a low surface energy solid is evaluated experimentally and theoretically. Water-ethanol binary mixture drops of several volumes are used. In the experiment, the droplet radius, height, and contact angle are measured. Analytical equations are derived that incorporate the effect of gravity for the relationships between the droplet radius and height, radius and contact angle, and radius and liquid surface energy. All the analytical equations display good agreement with the experimental data. It is found that the fundamental wetting behavior of the droplet on the low surface energy solid can be predicted by our model which gives geometrical information of the droplet such as the contact angle, droplet radius, and height from physical values of liquid and solid

Macroscopic wettability based on an interfacial jump condition

Young's equation, describing an interfacial equilibrium condition of a liquid droplet on a smooth solid surface, raises issues concerning the existence of a sine term which has not yet been resolved theoretically and continues to be discussed to the present day. From a thermodynamics viewpoint, the equilibrium condition arises by minimizing the total free energy of the system while intensive parameters are kept constant. In the derivation, variations in the virtual work in both horizontal and vertical directions of the droplet on the smooth solid are considered. From a hydrodynamics viewpoint, there is a momentum jump condition at the gas-liquid interface that is derived based on a mechanical balance. Using standard mathematical procedures such as Stokes' theorem and differential geometry, a test volume is considered across the interface between two continuous phases from which the jump condition is derived. In the present paper, Young's equation is revisited from the point of view of the momentum jump condition at the two-phase interface and a modified Young's equation is derived. The analytical solution derived from the modified Young's equation is then used to compare theory with experimental data. The line tension and contact angle for a lens droplet are also discussed on the basis of this model

Analytical consideration of liquid droplet impingement on solid surfaces

平板に衝突した滴の濡れ面積が新理論で予測可能に！. 京都大学プレスリリース. 2017-05-25.In industrial applications involving spray-cooling, combustion, and so on, prediction of the maximum spreading diameter of a droplet impinging on a solid surface permits a quantitative estimation of heat removal and energy consumption. However, although there are many experimental studies regarding droplet impingement behaviour, theoretical models have an applicability limit for predicting the maximum spreading diameter. In the present study, we have developed an analytical model for droplet impingement based on energy conservation that considers adhesion energy in both horizontal and vertical directions at the contact line. The theory is validated by our experiment and existing experimental data possessing a wide range of Weber numbers. We demonstrate that our model can predict βm (i.e., the maximum spreading diameter normalised in terms of initial droplet diameter) for various Newtonian liquids ranging from micro- to millimetre-sized droplets on different solid surfaces and can determine the transition between capillary and viscous regimes. Furthermore, theoretical relations for scaling laws observed by many researchers are derived

Universality of Droplet Impingement: Low-to-High Viscosities and Surface Tensions

When a droplet impinges on a solid surface, its kinetic energy is mainly converted to capillary energy and viscous dissipation energy, the ratio of which depends on the wettability of the target surface and the liquid properties. Currently, there is no experimental or theoretical evidence that suggests which types of liquids exhibit the capillary energy-dominated impingement behavior. In this paper, we reported the droplet impingement behavior for a wide range of liquid viscosities, surface tensions and target surface wettabilities. Then, we showed that a recently developed energy balance equation for the droplet impingement behavior can be universally employed for predicting the maximum spreading contact area diameter of a droplet for Newtonian liquids in deposition process by modelling the droplet surface deformation. Subsequently, applicability limitations of recent existing models are discussed. The newly developed model demonstrated that the capillary energy-dominated impingement behavior can be observed at considerably low viscosities of liquid droplets such as that of the superfluid of liquid helium