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

Estimation of Completion of Dormancy in Grapevine Bud Based on Cumulative Temperature

　This study was conducted to investigate the relationship between completion of dormancy of grapevine bud and temperature. Canes of ‘Kyoho’ and ‘Pione’ grapevines (Vitis labrusca×V. vinifera) grown in 7 vineyards with different temperature conditions, in Nagano, Northern Okayama, Yamanashi, Okayama, Okayama University, Fukuoka and Miyazaki, were collected at three different chilling exposures, December, January and February. These were then sent to Okayama University all at the same time. Cuttings with one bud were put into growth chambers kept at 25 or 30°C with 14 hours daylength, and budbreak in each cutting was surveyed at two day intervals for 60 days. Cumulative chilling hours (CCH) of exposure to below 7.2°C in each treatment time was largest in Nagano, followed in order by Northern Okayama, Yamanashi, Okayama, Okayama University, Fukuoka and Miyazaki. The CCH in Nagano was 2.5 to 4.8 times larger than in Miyazaki depending on the treatment time. The later the treatment time and the higher the temperature, the fewer were the number of days to first budbreak (NDFB) after treatment, irrespective of cultivar. A similar trend was observed in the number of days to 60% budbreak. In ‘Kyoho’ the NDFB was short in Nagano, Okayama University and Miyazaki, and longer in Okayama, Yamanashi and Fukuoka. In ‘Pione’ the NDFB was short in Fukuoka and Okayama University, and longer in Yamanashi and Okayama. The result was a weak negative correlation observed between CCH and NDFB in 4 of 7 vineyards. However, there was a strong positive correlation between NDFB and cumulative temperature (CT), a summation of temperature and hours of exposure to above 0°C from November 1 to treatment time and hours of exposure to 25 or 30°C from start of treatment to budbreak in each plot, in 6 vineyards excluding Miyazaki. The importance of estimating the completion of dormancy in grapevine bud based on CT is discussed.ブドウの芽の休眠完了と温度との関係を調査するため，温度条件の異なる７園（中信農試，山梨果試，岡山農試，岡山農試北部支場，岡山大学，福岡農試および宮崎）で栽培されている‘巨峰’と‘ピオーネ’から低温遭遇量の異なる３時期（12月，１月，２月）に結果母枝を採取した．直ちに岡山大学に送り，１芽を持つ挿し穂に調整した後，25または30℃のインキュベーター（14時間日長）に入れ，２日間隔で60日間発芽を調査した．処理開始時の7.2℃以下の遭遇量は中信農試で最も多く，次いで岡山農試北部支場，山梨果試，岡山農試，岡山大学，福岡農試，宮崎の順で，中信農試と宮崎では処理時期により2.5～4.8倍の差があった．発芽所要日数は，両品種とも処理時期が遅いほど，また温度が高いほど少なく，60％発芽所要日数もほぼ同様の傾向であった．‘巨峰’の発芽所用日数は中信農試，岡山大学および宮崎で少ない一方，岡山農試，山梨果試および福岡農試で多く，また‘ピオーネ’では福岡農試と岡山大学で少なく，山梨果試と岡山農試で多かった．７園のうち４園で低温遭遇量と発芽所要日数との間に負の相関がみられたが，相関係数は低かった．一方，11月以降処理開始までの０℃以上の温度の積算値と処理開始から発芽までの25または30℃での積算値を合計した積算温度と発芽所要日数との間には１園を除き極めて高い正の相関が認められた．これらの結果を基に，積算温度によるブドウの休眠完了予測の可能性を考察した

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

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

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