4857:
triple line. The triple line, which is in contact with the heterogeneous surface, cannot rest on the heterogeneous surface like the rest of the drop. In theory, it should follow the surface imperfection. This bending in the triple line is unfavorable and is not seen in real-world situations. A theory that preserves the CassieâBaxter equation while at the same time explaining the presence of the minimized energy state of the triple line hinges on the idea of a precursor film. This film of submicrometer thickness advances ahead of the motion of the droplet and is found around the triple line. Furthermore, this precursor film allows the triple line to bend and take different conformations that were originally considered unfavorable. This precursor fluid has been observed using
6186:
52:
4848:). Therefore, the Cassie equation can be easily derived from the CassieâBaxter equation. Experimental results regarding the surface properties of Wenzel versus CassieâBaxter systems showed the effect of pinning for a Young angle of 180 to 90°, a region classified under the CassieâBaxter model. This liquid/air composite system is largely hydrophobic. After that point, a sharp transition to the Wenzel regime was found where the drop wets the surface, but no further than the edges of the drop. Actually, the Young, Wenzel and Cassie-Baxter equations represent the transversality conditions of the variational problem of wetting.
4189:
wetting regime, though, is where the surface is a composite of two types of patches. An important example of such a composite surface is one composed of patches of both air and solid. Such surfaces have varied effects on the contact angles of wetting liquids. CassieâBaxter and Wenzel are the two main models that attempt to describe the wetting of textured surfaces. However, these equations only apply when the drop size is sufficiently large compared with the surface roughness scale. When the droplet size is comparable to that of the underlying pillars, the effect of line tension should be considered.
801:
4153:. When these values are exceeded, the displacement of the contact line, such as the one in Figure 3, will take place by either expansion or retraction of the droplet. Figure 6 depicts the advancing and receding contact angles. The advancing contact angle is the maximum stable angle, whereas the receding contact angle is the minimum stable angle. Contact angle hysteresis occurs because many different thermodynamically stable contact angles are found on a nonideal solid. These varying thermodynamically stable contact angles are known as metastable states.
2652:
4185:, When a contact line advances, covering more of the surface with liquid, the contact angle is increased and is generally related to the velocity of the contact line. If the velocity of a contact line is increased without bound, the contact angle increases, and as it approaches 180°, the gas phase will become entrained in a thin layer between the liquid and solid. This is a kinetic nonequilibrium effect which results from the contact line moving at such a high speed that complete wetting cannot occur.
506:
135:
3616:
2334:
477:
485:
4930:
265:
796:{\displaystyle {\begin{aligned}\gamma _{\alpha \theta }+\gamma _{\theta \beta }\cos \left(\theta \right)+\gamma _{\alpha \beta }\cos \left(\alpha \right)&=0\\\gamma _{\alpha \theta }\cos \left(\theta \right)+\gamma _{\theta \beta }+\gamma _{\alpha \beta }\cos \left(\beta \right)&=0\\\gamma _{\alpha \theta }\cos \left(\alpha \right)+\gamma _{\theta \beta }\cos \left(\beta \right)+\gamma _{\alpha \beta }&=0\end{aligned}}}
4074:
881:
4320:
3607:
8405:
5051:
4870:
2647:{\displaystyle r_{\mathrm {A} }=\left({\frac {\sin ^{3}\left(\theta _{\mathrm {A} }\right)}{2-3\cos \left(\theta _{\mathrm {A} }\right)+\cos ^{3}\left(\theta _{\mathrm {A} }\right)}}\right)^{\frac {1}{3}}~;~~r_{\mathrm {R} }=\left({\frac {\sin ^{3}\left(\theta _{\mathrm {R} }\right)}{2-3\cos \left(\theta _{\mathrm {R} }\right)+\cos ^{3}\left(\theta _{\mathrm {R} }\right)}}\right)^{\frac {1}{3}}}
4921:
impregnating wetting regime. Since the liquid can wet the larger-scale grooves, the adhesive force between the water and solid is very high. This explains why the water droplet will not fall off even if the petal is tilted at an angle or turned upside down. This effect will fail if the droplet has a volume larger than 10 ÎŒL because the balance between weight and surface tension is surpassed.
4198:
296:(Ξ), as seen in Figure 1, is the angle at which the liquidâvapor interface meets the solidâliquid interface. The contact angle is determined by the balance between adhesive and cohesive forces. As the tendency of a drop to spread out over a flat, solid surface increases, the contact angle decreases. Thus, the contact angle provides an inverse measure of wettability.
4894:" describes the fact that a water droplet on the surface of a rose petal is spherical in shape, but cannot roll off even if the petal is turned upside down. The water drops maintain their spherical shape due to the superhydrophobicity of the petal (contact angle of about 152.4°), but do not roll off because the petal surface has a high adhesive force with water.
2323:
4033:
6142:
3292:
3269:
2017:. In many cases, surfaces are far from this ideal situation, and two are considered here: the case of rough surfaces and the case of smooth surfaces that are still real (finitely rigid). Even in a perfectly smooth surface, a drop will assume a wide spectrum of contact angles ranging from the so-called advancing contact angle,
5072:, the penetration front spreads beyond the drop and a liquid film forms over the surface. Figure 11 depicts the transition from the Wenzel state to the surface film state. The film smoothes the surface roughness and the Wenzel model no longer applies. In this state, the equilibrium condition and Young's relation yields:
315:". The table describes varying contact angles and their corresponding solid/liquid and liquid/liquid interactions. For nonwater liquids, the term lyophilic is used for low contact angle conditions and lyophobic is used when higher contact angles result. Similarly, the terms omniphobic and omniphilic apply to both
6247:
are oxidised to produce positively charged groups, as illustrated at right. The contact angle with water on the PFcMA-coated wafers was 70° smaller following oxidation, while in the case of PVFc the decrease was 30°, and the switching of wettability has been shown to be reversible. In the PFcMA case,
4912:
hysteresis, which means the water droplet is not able to wet the microstructure spaces between the spikes. This allows air to remain inside the texture, causing a heterogeneous surface composed of both air and solid. As a result, the adhesive force between the water and the solid surface is extremely
4188:
A well-known departure from ideal conditions is when the surface of interest has a rough texture. The rough texture of a surface can fall into one of two categories: homogeneous or heterogeneous. A homogeneous wetting regime is where the liquid fills in the grooves of a rough surface. A heterogeneous
446:
Knowing the critical surface tension of a solid, it is possible to predict the wettability of the surface. The wettability of a surface is determined by the outermost chemical groups of the solid. Differences in wettability between surfaces that are similar in structure are due to differences in the
5175:
If a drop is placed on a smooth, horizontal surface, it is generally not in the equilibrium state. Hence, it spreads until an equilibrium contact radius is reached (partial wetting). While taking into account capillary, gravitational, and viscous contributions, the drop radius as a function of time
4920:
The rose petal's micro- and nanostructures are larger in scale than those of the lotus leaf, which allows the liquid film to impregnate the texture. However, as seen in Figure 9, the liquid can enter the larger-scale grooves, but it cannot enter into the smaller grooves. This is known as the Cassie
4843:
Here the key difference to notice is that there is no surface tension between the solid and the vapor for the second surface tension component. This is because of the assumption that the surface of air that is exposed is under the droplet and is the only other substrate in the system. Subsequently,
4298:
is the apparent contact angle which corresponds to the stable equilibrium state (i.e. minimum free energy state for the system). The roughness ratio, r, is a measure of how surface roughness affects a homogeneous surface. The roughness ratio is defined as the ratio of true area of the solid surface
467:
implies the advancing and receding contact angles are equal. In other words, only one thermodynamically stable contact angle exists. When a drop of liquid is placed on such a surface, the characteristic contact angle is formed as depicted in Figure 1. Furthermore, on an ideal surface, the drop will
299:
A contact angle less than 90° (low contact angle) usually indicates that wetting of the surface is very favorable, and the fluid will spread over a large area of the surface. Contact angles greater than 90° (high contact angle) generally mean that wetting of the surface is unfavorable, so the fluid
5974:
increases. Surfactants are absorbed onto the liquidâvapor, solidâliquid, and solidâvapor interfaces, which modify the wetting behavior of hydrophobic materials to reduce the free energy. When surfactants are absorbed onto a hydrophobic surface, the polar head groups face into the solution with the
4327:
When dealing with a heterogeneous surface, the Wenzel model is not sufficient. A more complex model is needed to measure how the apparent contact angle changes when various materials are involved. This heterogeneous surface, like that seen in Figure 8, is explained using the CassieâBaxter equation
5058:
The penetration front propagates to minimize the surface energy until it reaches the edges of the drop, thus arriving at the Wenzel state. Since the solid can be considered an absorptive material due to its surface roughness, this phenomenon of spreading and imbibition is called hemiwicking. The
4856:
With the advent of high resolution imaging, researchers have started to obtain experimental data which have led them to question the assumptions of the CassieâBaxter equation when calculating the apparent contact angle. These groups believe the apparent contact angle is largely dependent on the
2883:
With improvements in measuring techniques such as AFM, confocal microscopy and SEM, researchers were able to produce and image droplets at ever smaller scales. With the reduction in droplet size came new experimental observations of wetting. These observations confirm that the modified Young's
4047:
For many surface/adsorbate configurations, surface energy data and experimental observations are unavailable. As wetting interactions are of great importance in various applications, it is often desired to predict and compare the wetting behavior of various material surfaces with particular
355:) are very strong. Thus, it takes a large amount of energy to break these solids (alternatively, a large amount of energy is required to cut the bulk and make two separate surfaces), so they are termed "high-energy". Most molecular liquids achieve complete wetting with high-energy surfaces.
2168:
4838:
4889:
takes advantage of this by using a hierarchy of micro- and nanostructures on each petal to provide sufficient roughness for superhydrophobicity. More specifically, each rose petal has a collection of micropapillae on the surface and each papilla, in turn, has many nanofolds. The term
3814:
5981:
5975:
tail pointing outward. In more hydrophobic surfaces, surfactants may form a bilayer on the solid, causing it to become more hydrophilic. The dynamic drop radius can be characterized as the drop begins to spread. Thus, the contact angle changes based on the following equation:
4619:
3602:{\displaystyle \cos(\theta \mp \alpha )=A+B{\frac {\cos(\alpha )}{a}}\pm C\sin(\theta \mp \alpha )(\cos(\theta )+1)^{2}{\biggl (}{\frac {\sin(\alpha )(\cos(\alpha )+2)}{(\cos(\alpha )+1)^{2}}}\mp {\frac {\sin(\theta )(\cos(\theta )+2)}{(\cos(\theta )+1)^{2}}}{\biggr )}}
4038:
The first two terms are the modified Young's equation, while the third term is due to the
Laplace pressure. This nonlinear equation correctly predicts the sign and magnitude of Îș, the flattening of the contact angle at very small scales, and contact angle hysteresis.
1532:
3054:
1244:
1785:
374:). Since these solids are held together by weak forces, a very low amount of energy is required to break them, thus they are termed "low-energy". Depending on the type of liquid chosen, low-energy surfaces can permit either complete or partial wetting.
6841:
Chen, Kuang-Yen; Ivashenko, Oleksii; Carroll, Gregory T.; Robertus, Jort; Kistemaker, Jos C. M.; London, GĂĄbor; Browne, Wesley R.; Rudolf, Petra; Feringa, Ben L. (2014). "Control of
Surface Wettability Using Tripodal Light-Activated Molecular Motors".
871:
meaning that not one of the surface tensions can exceed the sum of the other two. If three fluids with surface energies that do not follow these inequalities are brought into contact, no equilibrium configuration consistent with Figure 3 will exist.
5162:
4945:
from the Cassie state to the Wenzel state, the air pockets are no longer thermodynamically stable and liquid begins to nucleate from the middle of the drop, creating a "mushroom state" as seen in Figure 10. The penetration condition is given by:
3043:
4424:
5917:
4306:
for a system in thermodynamic equilibrium, defined for a perfectly flat surface. Although Wenzel's equation demonstrates the contact angle of a rough surface is different from the intrinsic contact angle, it does not describe contact angle
810:
is the surface energy between the two indicated phases. These relations can also be expressed by an analog to a triangle known as
Neumann's triangle, shown in Figure 4. Neumann's triangle is consistent with the geometrical restriction that
4716:
is the solid liquid surface tension of every component. A case that is worth mentioning is when the liquid drop is placed on the substrate and creates small air pockets underneath it. This case for a two-component system is denoted by:
468:
return to its original shape if it is disturbed. The following derivations apply only to ideal solid surfaces; they are only valid for the state in which the interfaces are not moving and the phase boundary line exists in equilibrium.
4060:
approaches such as DFT, ice is commonly substituted for water. This is because DFT calculations are generally conducted assuming conditions of zero thermal movement of atoms, essentially meaning the simulation is conducted at
5015:
3808:, a geometric property of a sessile droplet to the bulk thermodynamics, the energy at the three phase contact boundary, and the curvature of the surface α. For the special case of a sessile droplet on a flat surface (α=0),
4861:(ESEM) in surfaces with pores formed in the bulk. With the introduction of the precursor film concept, the triple line can follow energetically feasible conformations, thereby correctly explaining the CassieâBaxter model.
968:
5823:
Many technological processes require control of liquid spreading over solid surfaces. When a drop is placed on a surface, it can completely wet, partially wet, or not wet the surface. By reducing the surface tension with
4266:
2318:{\displaystyle \theta _{\mathrm {c} }=\arccos \left({\frac {r_{\mathrm {A} }\cos \left(\theta _{\mathrm {A} }\right)+r_{\mathrm {R} }\cos \left(\theta _{\mathrm {R} }\right)}{r_{\mathrm {A} }+r_{\mathrm {R} }}}\right)}
4723:
4028:{\displaystyle \cos(\theta )={\frac {\gamma _{SG}-\gamma _{SL}}{\gamma _{LG}}}+{\frac {\kappa }{\gamma _{LG}}}{\frac {1}{a}}-{\frac {\gamma }{3\gamma _{LG}}}(2+\cos(\theta )-2\cos ^{2}(\theta )-\cos ^{3}(\theta ))}
1891:
2870:
2784:
6137:{\displaystyle \cos \,\left(\theta (t)\right)=\cos \,\left(\theta _{0}\right)+\left(\cos \,\left(\theta _{\infty }\right)-\cos \,\left(\theta _{0}\right)\right)\left(1-\mathrm {e} ^{-{\frac {t}{\tau }}}\right)}
3692:
447:
packing of the atoms. For instance, if a surface has branched chains, it will have poorer packing than a surface with straight chains. Lower critical surface tension means a less wettable material surface.
5167:
By fine-tuning the surface roughness, it is possible to achieve a transition between both superhydrophobic and superhydrophilic regions. Generally, the rougher the surface, the more hydrophobic it is.
4515:
4065:. This simplification nevertheless yields results that are relevant for the adsorption of water under realistic conditions and the use of ice for the theoretical simulation of wetting is commonplace.
7651:
de Gennes, Pierre-Gilles; Brochard-Wyart, Françoise; Quéré, David (2004). Capillarity and
Wetting Phenomena. Springer New York. doi:10.1007/978-0-387-21656-0. ISBN 978-1-4419-1833-8. S2CID 137894832
6264:
and other applications involving high-temperature hydrophobicity. The presence of oxygen vacancies at surfaces of ceria or other rare earth oxides is instrumental in governing surface wettability.
4144:
4452:, the CassieâBaxter equations becomes the Wenzel equation. On the other hand, when there are many different fractions of surface roughness, each fraction of the total surface area is denoted by
3264:{\displaystyle 0={\frac {dA_{LG}}{dA_{SL}}}+{\frac {\gamma _{SL}-\gamma _{SG}}{\gamma _{LG}}}-{\frac {\kappa }{\gamma _{LG}}}{\frac {dL}{dA_{SL}}}-{\frac {V}{\gamma _{LG}}}{\frac {dP}{dA_{SL}}}}
2003:
511:
3783:
8298:
Saini, C. P.; Barman, A.; Das, D.; Satpati, B.; Bhattacharyya, S. R.; Kanjilal, D.; Ponomaryov, A.; Zvyagin, S.; Kanjilal, A. (2017). "Role of Oxygen
Vacancy on the Hydrophobic Behavior of TiO
3735:
4156:
Such motion of a phase boundary, involving advancing and receding contact angles, is known as dynamic wetting. The difference between dynamic and static wetting angles is proportional to the
5414:
1607:
1655:
850:
5723:
4905:", it is important to note some striking differences. The surface structure of the lotus leaf and the rose petal, as seen in Figure 9, can be used to explain the two different effects.
7851:
Muzammil, I.; Li, Y.P.; Li, X.Y.; Lei, M.K. (2018). "Duty cycle dependent chemical structure and wettability of RF pulsed plasma copolymers of acrylic acid and octafluorocyclobutane".
1397:
1100:
6276:, in which OH and H are adsorbed separately at solid surfaces. The presence of oxygen vacancies is generally found to enhance hydrophobicity while promoting dissociative adsorption.
2160:
2131:
2102:
2073:
2044:
1663:
1344:
5078:
2698:. The lack of a solution to the YoungâDuprĂ© equation is an indicator that there is no equilibrium configuration with a contact angle between 0 and 180° for those situations.
500:
per unit length acting along the boundary line between the three phases must be zero. The components of net force in the direction along each of the interfaces are given by:
4714:
4678:
1386:
2893:
311:. Superhydrophobic surfaces have contact angles greater than 150°, showing almost no contact between the liquid drop and the surface. This is sometimes referred to as the "
1562:
4338:
4296:
1297:
6677:
Sharfrin, E.; Zisman, William A. (1960). "Constitutive relations in the wetting of low energy surfaces and the theory of the retraction method of preparing monolayers".
5834:
436:
4642:
3806:
1072:
1929:
8241:
Fronzi, Marco; Assadi, M. Hussein N.; Hanaor, Dorian A.H.; Hanaor, Dorian A. H.; Gan, Yixiang (2019). "Theoretical insights into the hydrophobicity of low index CeO
4507:
4477:
4205:
The Wenzel model describes the homogeneous wetting regime, as seen in Figure 7, and is defined by the following equation for the contact angle on a rough surface:
1028:
8116:
4081:
Unlike ideal surfaces, real surfaces do not have perfect smoothness, rigidity, or chemical homogeneity. Such deviations from ideality result in phenomenon called
488:
Figure 4: Neumann's triangle relating the surface energies and contact angles of three fluid phases coexisting in static equilibrium, as depicted in Figure 3
4182:
4149:
When the contact angle is between the advancing and receding cases, the contact line is considered to be pinned and hysteretic behaviour can be observed, namely
1828:
1808:
1092:
6793:
852:, and applying the law of sines and law of cosines to it produce relations that describe how the interfacial angles depend on the ratios of surface energies.
7576:
888:
If the ÎČ phase is replaced by a flat rigid surface, as shown in Figure 5, then ÎČ = Ï, and the second net force equation simplifies to the Young equation,
8191:
Elbert, J.; Gallei, M.; RĂŒttiger, C.; Brunsen, A.; Didzoleit, H.; StĂŒhn, B.; Rehahn, M. (2013). "Ferrocene
Polymers for Switchable Surface Wettability".
114:
Wetting is a focus of research attention in nanotechnology and nanoscience studies due to the advent of many nanomaterials in the past two decades (e.g.
6177:
As the surfactants are absorbed, the solidâvapor surface tension increases and the edges of the drop become hydrophilic. As a result, the drop spreads.
4952:
3286:, which is proportional to the mean curvature of the droplet, and is non zero. Solving the above equation for both convex and concave surfaces yields:
894:
6553:
2884:
equation does not hold at the micro-nano scales. In addition the sign of the line tension is not maintained through the modified Young's equation.
4211:
7890:
4833:{\displaystyle \gamma \cos \,\left(\theta ^{*}\right)=f_{1}\left(\gamma _{\text{1,sv}}-\gamma _{\text{1,sl}}\right)-\left(1-f_{1}\right)\gamma }
4048:
crystallographic orientations, with relation to water or other adsorbates. This can be done from an atomistic perspective with tools including
2674:
can be larger than the sum of the other two surface energies. The consequence of this restriction is the prediction of complete wetting when Îł
1836:
8032:
Lee, K. S.; Ivanova, N.; Starov, V. M.; Hilal, N.; Dutschk, V. (2008). "Kinetics of wetting and spreading by aqueous surfactant solutions".
2806:
8164:
Liu, W.-Y.; Xu, Q.-H.; Ma, Y.-X.; Liang, Y.-M.; Dong, N.-L.; Guan, D.-P. (2001). "Solvent-free synthesis of ferrocenylethene derivatives".
5828:, a nonwetting material can be made to become partially or completely wetting. The excess free energy (Ï) of a drop on a solid surface is:
2711:
989:
on a solid surface from knowledge of the three surface energies involved. This equation also applies if the "gas" phase is another liquid,
3626:
17:
7816:
Lin, F.; Zhang, Y; Xi, J; Zhu, Y; Wang, N; Xia, F; Jiang, L (2008). "Petal Effect: A Superhydrophobic State with High
Adhesive Force".
4858:
3282:
work becomes significant at small scales. The variation in pressure at constant volume at the free liquid-vapor boundary is due to the
7705:"Young, BoruvkaâNeumann, Wenzel and CassieâBaxter equations as the transversality conditions for the variational problem of wetting"
4614:{\displaystyle \gamma \cos \,\left(\theta ^{*}\right)=\sum _{n=1}^{N}f_{i}\left(\gamma _{\text{i,sv}}-\gamma _{\text{i,sl}}\right)}
7666:"The rigorous derivation of Young, CassieâBaxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon"
7639:
Wenzel, Robert N. "Resistance of solid surfaces to wetting by water." Industrial & engineering chemistry 28.8 (1936): 988-994.
480:
Figure 3: Coexistence of three fluid phases in mutual contact; here, α, ÎČ, and Ξ each indicate both a phase and its contact angle.
7575:
Chen, Xuemei; Ma, Ruiyuan; Li, Jintao; Hao, Chonglei; Guo, Wei; Luk, B. L.; Li, Shuai Cheng; Yao, Shuhuai; Wang, Zuankai (2012).
6609:
Mertens, Stijn F. L.; Hemmi, Adrian; Muff, Stefan; Gröning, Oliver; De Feyter, Steven; Osterwalder, JĂŒrg; Greber, Thomas (2016).
331:
and low-energy solids. The relative energy of a solid has to do with the bulk nature of the solid itself. Solids such as metals,
103:
of two materials. Wetting and the surface forces that control wetting are also responsible for other related effects, including
7303:"Relationship between contact angle and contact line radius for micro to atto [10â6 to 10â18] liter size oil droplets"
8382:
8349:
7529:
6919:
6776:
6751:
6610:
6185:
443:) of that surface. This critical surface tension is an important parameter because it is a characteristic of only the solid.
7339:"A generalized variational approach for predicting contact angles of sessile nano-droplets on both flat and curved surfaces"
4099:
7405:
Costa, D (2017). "Edge wetting effects of Îł-Al2O3 and anatase-TiO2 supports by MoS2 and CoMoS active phases: A DFT study".
6979:
6936:
7955:
7742:
Bormashenko, Edward (2020-01-17). "Variational framework for defining contact angles: a general thermodynamic approach".
3740:
77:
interactions when the two are brought together. This happens in presence of a gaseous phase or another liquid phase not
8147:
3697:
327:
Liquids can interact with two main types of solid surfaces. Traditionally, solid surfaces have been divided into high-
6898:
6536:
5182:
6824:
6252:) has been investigated, and it was found that longer chains produce significantly larger contact angle reductions.
1934:
8219:
7152:"Evaluation of three methods of static contact angle measurements for TiO 2 nanofluid droplets during evaporation"
6421:
1527:{\displaystyle {\cal {L}}=\gamma _{LG}{\sqrt {1+y'^{2}}}+(\gamma _{SL}-\gamma _{SG})-\lambda _{1}y'-\lambda _{2}y}
814:
7623:
1239:{\displaystyle {\cal {F}}=\int _{0}^{L}\left(\gamma _{LG}{\sqrt {1+y'^{2}}}+(\gamma _{SL}-\gamma _{SG})\right)dx}
5425:
1567:
6552:
Rafiee, J.; Mi, X.; Gullapalli, H.; Thomas, A. V.; Yavari, F.; Shi, Y.; Ajayan, P. M.; Koratkar, N. A. (2012).
6471:
1780:{\displaystyle {\cal {H}}=-\gamma _{LG}{\frac {1}{\sqrt {1+y'^{2}}}}-(\gamma _{SL}-\gamma _{SG})+\lambda _{2}y}
1612:
7378:
7022:
Tadmor, Rafael (2004). "Line energy and the relation between advancing, receding and Young contact angles".
2136:
2107:
2078:
2049:
2020:
996:
6528:
Bio-aggregates Based
Building Materials: State-of-the-Art Report of the RILEM Technical Committee 236-BBM
5419:
For the complete wetting situation, the drop radius at any time during the spreading process is given by
5157:{\displaystyle \cos \,\left(\theta ^{*}\right)=\phi \cos \,\left(\theta _{C}\right)+\left(1-\phi \right)}
8002:
HĂ€rth, Michael; Schubert, Dirk W. (2012). "Simple
Approach for Spreading Dynamics of Polymeric Fluids".
7577:"Evaporation of Droplets on Superhydrophobic Surfaces: Surface Roughness and Small Droplet Size Effects"
6592:
4303:
7786:
4150:
4082:
3038:{\displaystyle \delta w=\gamma _{LV}dA_{LV}+\gamma _{SL}dA_{SL}+\gamma _{SV}dA_{SV}-\kappa dL-PdV-VdP}
2800:
Combining the spreading parameter definition with the Young relation yields the YoungâDuprĂ© equation:
460:
7937:
7704:
4053:
1302:
493:
4683:
4647:
4419:{\displaystyle \cos \,\left(\theta ^{*}\right)=r_{f}\,f\,\cos \,\left(\theta _{\text{Y}}\right)+f-1}
2878:
1349:
8432:
8427:
8409:
6383:"Photochemical Immobilization of Polymers on a Surface: Controlling Film Thickness and Wettability"
5912:{\displaystyle \sigma =\gamma S+PV+\pi \,R^{2}\left(\gamma _{\text{SL}}-\gamma _{\text{SV}}\right)}
2663:
38:
8368:
7548:
Abraham Marmur (2003). "Wetting of
Hydrophobic Rough Surfaces: To be heterogeneous or not to be".
1540:
7432:
7338:
7302:
7208:
6273:
6243:
wafers and the wettability measured when the polymer chains are uncharged and when the ferrocene
4274:
1252:
81:
with the first one. The degree of wetting (wettability) is determined by a force balance between
4308:
381:
upon the application of an appropriate stimuli. For example, a surface presenting photon-driven
6361:
6350: â Minimum electric current through a contact to break through the surface film resistance
6344: â Minimum electric current through a contact to break through the surface film resistance
6323:
5777:
4914:
7376:
Sun, Xuegui (2017). "Molecular dynamics simulation of wetting behaviors of Li on W surfaces".
6260:
Rare earth oxides exhibit intrinsic hydrophobicity, and hence can be used in thermally stable
6526:
6356:
6200:
surface due to electrostatic attractions between the resulting charges and the polar solvent.
4627:
3791:
1033:
1899:
51:
8264:
7905:
7860:
7677:
7591:
7220:
7163:
6988:
6808:
6625:
6568:
6483:
6436:
6314:
4509:
equals 1 or the total surface. CassieâBaxter can also be recast in the following equation:
4485:
4455:
154:
86:
45:
31:
1004:
8:
8437:
6381:
Carroll, Gregory T.; Turro, Nicholas J.; Mammana, Angela; Koberstein, Jeffrey T. (2017).
398:
367:
8398:
8268:
7909:
7864:
7681:
7595:
7224:
7167:
7085:
6992:
6812:
6629:
6572:
6487:
6440:
6382:
4164:
997:
Simplification to planar geometry, Young's relation derived from variational computation
8355:
8280:
8254:
7929:
7767:
7615:
7502:
7484:
7358:
7189:
7102:
7004:
6959:
6867:
6649:
6507:
6452:
6300: â Chemicals that prevent the condensation of water as small droplets on a surface
6244:
4942:
4941:, the drop sits on top of the textured surface with trapped air underneath. During the
4049:
1813:
1793:
1077:
386:
157:
forces within the liquid cause the drop to ball up and avoid contact with the surface.
8177:
7974:
7000:
2887:
For a sessile droplet, the free energy of the three phase system can be expressed as:
2013:
The Young equation assumes a perfectly flat and rigid surface often referred to as an
8378:
8359:
8345:
8284:
8139:
8097:
8049:
7921:
7833:
7771:
7759:
7724:
7665:
7607:
7525:
7362:
7283:
7275:
7236:
7193:
7181:
7039:
7008:
6963:
6915:
6894:
6871:
6859:
6772:
6747:
6721:
6653:
6641:
6584:
6532:
6511:
6499:
6402:
6228:
316:
7933:
7619:
7506:
7391:
7256:"Line Energy and the Relation between Advancing, Receding, and Young Contact Angles"
366:, etc.) where the molecules are held together essentially by physical forces (e.g.,
8337:
8311:
8272:
8200:
8173:
8131:
8087:
8041:
8011:
7970:
7913:
7868:
7825:
7802:
7798:
7751:
7720:
7716:
7685:
7603:
7599:
7557:
7498:
7494:
7475:
Shi, Z.; et al. (2018). "Dynamic contact angle hysteresis in liquid bridges".
7454:
7414:
7387:
7350:
7314:
7267:
7228:
7171:
7066:
7031:
6996:
6951:
6851:
6816:
6713:
6686:
6633:
6576:
6491:
6456:
6444:
6394:
4157:
3283:
425:
352:
119:
104:
7755:
7445:
Robert J. Good (1992). "Contact angle, wetting, and adhesion: a critical review".
6657:
8372:
8366:
8276:
7917:
7872:
7689:
7354:
7318:
6347:
6341:
6261:
6224:
5741:
5010:{\displaystyle \cos \,\left(\theta _{\text{C}}\right)={\frac {\phi -1}{r-\phi }}}
4938:
4329:
2879:
A generalized model for the contact angle of droplets on flat and curved surfaces
417:
409:
382:
70:
7132:
6474:(2013). "The effect of oxygen vacancies on water wettability of a ZnO surface".
7978:
7418:
6309:
6220:
5966:
Based on this equation, the excess free energy is minimized when Îł decreases, Îł
5038:
is the fraction of solid/liquid interface where drop is in contact with surface
4881:
of a surface can be enhanced by being textured with different length scales of
3619:
Schematic Diagrams for droplets on flat (a) concave (b) and convex (c) surfaces
963:{\displaystyle \gamma _{SG}=\gamma _{SL}+\gamma _{LG}\cos \left(\theta \right)}
435:
and Ξ is low. Zisman termed the intercept of these lines when cos Ξ = 1 as the
402:
378:
74:
8341:
8045:
6820:
6448:
8421:
8315:
7763:
7728:
7279:
7255:
7185:
6725:
6406:
4909:
4062:
2014:
456:
371:
348:
344:
340:
293:
96:
92:. There are two types of wetting: non-reactive wetting and reactive wetting.
7458:
7209:"Line Tension and the Intrinsic Contact Angle in SolidâLiquidâFluid Systems"
4261:{\displaystyle \cos \,\left(\theta ^{*}\right)=r\cos \,\left(\theta \right)}
55:
Water bead on a fabric that has been made non-wetting by chemical treatment.
8143:
8101:
8053:
8015:
7925:
7837:
7611:
7287:
7232:
7043:
6955:
6863:
6645:
6588:
6503:
6335:
6317: â Upward force that opposes the weight of an object immersed in fluid
5059:
contact angles at which spreading/imbibition occurs are between 0 and Ï/2.
4902:
4898:
4891:
884:
Figure 5: Contact angle of a liquid droplet wetted to a rigid solid surface
359:
312:
8332:
de Gennes, Pierre-Gilles; Brochard-Wyart, Françoise; Quéré, David (2004).
7240:
6239:
ferrocenecarboxylate), PFcMA. Both PVFc and PFcMA have been tethered onto
1391:
The modified Lagrangian, taking into account the constraints is therefore
385:
was shown to undergo changes in water contact angle when switched between
300:
will minimize contact with the surface and form a compact liquid droplet.
134:
6329:
6248:
the effect of longer chains with more ferrocene groups (and also greater
6232:
6197:
6190:
5825:
363:
308:
304:
7070:
6690:
6637:
6268:
of water at oxide surfaces can occur as molecular adsorption, in which H
6189:
Strands of an uncharged ferrocene-substituted polymer are tethered to a
4864:
2793:> 0, the liquid wets the surface completely (complete wetting). When
2008:
397:
Low-energy surfaces primarily interact with liquids through dispersive (
8092:
8075:
6717:
6495:
6292:
6286:
6265:
6249:
6211:-active organometallic compound which can be incorporated into various
4878:
1886:{\displaystyle {\frac {\partial {\cal {F}}}{\partial L}}=-{\cal {H}}=0}
990:
464:
459:
is flat, rigid, perfectly smooth, chemically homogeneous, and has zero
108:
8204:
8135:
7829:
7561:
7271:
7176:
7151:
7035:
6855:
6398:
2865:{\displaystyle S=\gamma _{LG}\left(\cos \left(\theta \right)-1\right)}
875:
6741:
6580:
6303:
6204:
5757:
4073:
2779:{\displaystyle S=\gamma _{SG}-\left(\gamma _{SL}+\gamma _{LG}\right)}
2657:
4929:
476:
8259:
7489:
6306: â Retraction of a fluid from a surface it was forced to cover
6297:
4882:
3687:{\displaystyle A={\frac {\gamma _{SG}-\gamma _{SL}}{\gamma _{LG}}}}
3615:
856:
142:
123:
115:
100:
82:
78:
3048:
At constant volume in thermodynamic equilibrium, this reduces to:
2666:
1805; Anthanase Dupré and Paul Dupré 1869) dictates that neither γ
484:
264:
111:
can be used to increase the wetting power of a liquid like water.
6216:
6212:
5767:
986:
336:
7709:
Colloids and Surfaces A: Physicochemical and Engineering Aspects
4319:
880:
8404:
6240:
6193:
4644:
is the CassieâBaxter surface tension between liquid and vapor,
978:
492:
Figure 3 shows the line of contact where three phases meet. In
328:
146:
138:
Figure 1: Contact angle for a liquid droplet on a solid surface
63:
5050:
4869:
4440:
is the fraction of solid surface area wet by the liquid. When
6380:
6208:
4085:, which is defined as the difference between the advancing (Ξ
974:
973:
which relates the surface tensions between the three phases:
497:
332:
273:
150:
89:
67:
8331:
6840:
4077:
Figure 6: Schematic of advancing and receding contact angles
985:. Subsequently, this predicts the contact angle of a liquid
416:) of the liquid decreased. Thus, he was able to establish a
377:
Dynamic surfaces have been reported that undergo changes in
30:"Wetness" redirects here. For the biological secretion, see
27:
Ability of a liquid to maintain contact with a solid surface
8190:
6326: â Method of determining the surface energy of a solid
6272:
O molecules remain intact at the terminated surface, or as
6227:
and then polymerized to form polyvinylferrocene (PVFc), an
4886:
4680:
is the solid vapor surface tension of every component, and
7301:
Jasper, Warren J.; Rasipuram, Srinivasan (December 2017).
3612:
Where the constant parameters A, B, and C are defined as:
358:
The other type of solid is weak molecular crystals (e.g.,
6944:
Philosophical Transactions of the Royal Society of London
6769:
Modern Approaches to Wettability. Theory and Applications
6704:
Mantanis, G. I.; Young, R. A. (1997). "Wetting of wood".
6422:"Fundamental issues of reactive wetting by liquid metals"
4197:
982:
855:
Because these three surface energies form the sides of a
8240:
6611:"Switching stiction and adhesion of a liquid on a solid"
6551:
1094:
is a free parameter. The free energy to be minimized is
7433:
Applied Surface Science, Elsevier, 2019, 478, pp.68-74.
6608:
6352:
Pages displaying short descriptions of redirect targets
6319:
Pages displaying short descriptions of redirect targets
6196:
surface. Oxidation of the ferrocenyl groups produces a
2875:
which only has physical solutions for Ξ when S < 0.
471:
7891:"Wetting transitions on textured hydrophilic surfaces"
7664:
Whyman, G.; Bormashenko, Edward; Stein, Tamir (2008).
7663:
7057:
Schrader, Malcolm E. (1995). "Young-Dupre Revisited".
6742:
Eustathopoulos, N.; Nicholas, M.G.; Drevet B. (1999).
6419:
4139:{\displaystyle {\text{H}}=\,\theta _{a}-\,\theta _{r}}
4042:
1564:
are Lagrange multipliers. By definition, the momentum
859:, they are constrained by the triangle inequalities, Îł
322:
8297:
8031:
6893:
Ed. Berg, John. C. New York, NY: Marcel Dekker, Inc.
5984:
5837:
5428:
5185:
5081:
4955:
4924:
4726:
4686:
4650:
4630:
4518:
4488:
4458:
4341:
4277:
4214:
4167:
4102:
3817:
3794:
3743:
3700:
3629:
3295:
3278:
term has been neglected for large droplets, however,
3057:
2896:
2809:
2714:
2337:
2171:
2139:
2110:
2081:
2052:
2023:
2009:
Non-ideal smooth surfaces and the Young contact angle
1937:
1902:
1839:
1816:
1796:
1666:
1615:
1570:
1543:
1400:
1352:
1305:
1255:
1103:
1080:
1036:
1007:
897:
817:
509:
408:
Zisman observed that cos Ξ increases linearly as the
8117:"Chemical Redox Agents for Organometallic Chemistry"
4908:
The lotus leaf has a randomly rough surface and low
4436:is the roughness ratio of the wet surface area and
876:
Simplification to planar geometry, Young's relation
7150:WciĆlik, Sylwia; Mukherjee, Sayantan (June 2022).
6909:
6766:
6136:
5911:
5717:
5408:
5156:
5009:
4913:low, allowing the water to roll off easily (i.e. "
4832:
4708:
4672:
4636:
4613:
4501:
4471:
4418:
4290:
4260:
4176:
4138:
4027:
3800:
3778:{\displaystyle C={\frac {\gamma }{3\gamma _{LG}}}}
3777:
3729:
3686:
3601:
3263:
3037:
2864:
2778:
2658:The YoungâDuprĂ© equation and spreading coefficient
2646:
2317:
2154:
2125:
2096:
2067:
2038:
1997:
1923:
1885:
1822:
1802:
1779:
1649:
1601:
1556:
1526:
1380:
1338:
1291:
1238:
1086:
1066:
1022:
962:
844:
795:
153:cause a liquid drop to spread across the surface.
7083:
6525:Amziane, Sofiane; Collet, Florence (2017-03-05).
4068:
3730:{\displaystyle B={\frac {\kappa }{\gamma _{LG}}}}
3594:
3416:
392:
303:For water, a wettable surface may also be termed
8419:
8217:
7953:
7149:
6977:T. S. Chow (1998). "Wetting of rough surfaces".
5054:Figure 11: Penetration front spreads beyond drop
1790:Now, we recall that the boundary is free in the
7850:
7647:
7645:
7300:
5813:
5409:{\displaystyle r(t)=r_{e}\left^{\frac {1}{6}}.}
8114:
7547:
7444:
7131:Gibbs, Josiah Willard Auteur du texte (1928).
6697:
6676:
6332: â Thin film of soapy water enclosing air
6235:. Another polymer which can be formed is poly(
4056:. In the theoretical prediction of wetting by
2701:A useful parameter for gauging wetting is the
1998:{\displaystyle (1+y'^{2})^{-1/2}=\cos \theta }
1830:is a free parameter. Therefore, we must have:
993:with the droplet of the first "liquid" phase.
8220:"Rare-Earth Oxides Are Naturally Hydrophobic"
8069:
8067:
8065:
8063:
8001:
7954:Quere, D.; Thiele, Uwe; Quéré, David (2008).
7888:
7815:
7524:. Cambridge, UK: Cambridge University Press.
7337:Jasper, Warren J.; Anand, Nadish (May 2019).
6703:
6524:
389:conformations of differing surface energies.
8302:Nanorods on Chemically Etched Si Pyramids".
8163:
7787:"Why does the CassieâBaxter equation apply?"
7642:
7084:Athanase M. Dupré, Paul Dupré (1869-01-01).
5066:and Ï/2. If the contact angle is less than Î
5044:is solid roughness (for flat surface, r = 1)
845:{\displaystyle \alpha +\beta +\theta =2\pi }
806:where α, ÎČ, and Ξ are the angles shown and Îł
7784:
7778:
7741:
7702:
7574:
7336:
4873:Figure 9: "Petal effect" vs. "lotus effect"
2046:, to the so-called receding contact angle,
2005:, therefore we recover the Young equation.
66:to displace gas to maintain contact with a
8073:
8060:
7744:Journal of Adhesion Science and Technology
7543:
7541:
7447:Journal of Adhesion Science and Technology
6976:
6885:
6883:
6881:
5718:{\displaystyle r(t)=\left^{\frac {1}{6}},}
4859:environmental scanning electron microscopy
1602:{\displaystyle p=\partial _{y'}{\cal {L}}}
8258:
8091:
8034:Advances in Colloid and Interface Science
7884:
7882:
7659:
7657:
7519:
7488:
7431:Hydrophobicity of low index CeO2 planes,
7175:
6791:
6785:
6672:
6670:
6420:Dezellus, O.; Eustathopoulos, N. (2010).
6223:(ferroceneylethene) can be prepared by a
6072:
6047:
6017:
5988:
5865:
5113:
5085:
4959:
4733:
4525:
4385:
4381:
4377:
4345:
4246:
4218:
4125:
4111:
1650:{\displaystyle {\cal {H}}=py'-{\cal {L}}}
7213:Journal of Colloid and Interface Science
7134:The collected works / of J. W. Gibbs,...
7056:
6844:Journal of the American Chemical Society
6737:
6735:
6184:
5049:
4928:
4868:
4318:
4196:
4072:
3788:This equation relates the contact angle
3614:
879:
483:
475:
420:between cos Ξ and the surface tension (γ
263:
133:
50:
8115:Connelly, N. G.; Geiger, W. E. (1996).
7538:
6878:
6469:
5935:is the solidâliquid interfacial tension
5928:is the liquidâvapor interfacial tension
4844:the equation is then expressed as (1 â
450:
339:are known as 'hard solids' because the
268:Figure 2: Wetting of different fluids:
14:
8420:
8027:
8025:
7879:
7654:
7470:
7468:
7253:
7206:
7021:
6667:
6289: â Phenomenon of surface adhesion
6219:which can be tethered onto a surface.
5942:is the solidâvapor interfacial tension
4314:
2155:{\displaystyle \theta _{\mathrm {R} }}
2126:{\displaystyle \theta _{\mathrm {A} }}
2097:{\displaystyle \theta _{\mathrm {c} }}
2068:{\displaystyle \theta _{\mathrm {R} }}
2039:{\displaystyle \theta _{\mathrm {A} }}
7404:
7332:
7330:
7328:
7145:
7143:
7130:
7126:
7124:
7103:"Contact Angle Spreading Coefficient"
7100:
6934:
6732:
6171:is the surfactant transfer time scale
5948:is the area of liquidâvapor interface
5170:
8218:Kemsley, Jyllian (28 January 2013).
8004:Macromolecular Chemistry and Physics
7015:
6980:Journal of Physics: Condensed Matter
6937:"An Essay on the Cohesion of Fluids"
5954:is the excess pressure inside liquid
472:Minimization of energy, three phases
8371:; Clayton J. Radke (2 April 2007).
8304:The Journal of Physical Chemistry C
8166:Journal of Organometallic Chemistry
8022:
7474:
7465:
7375:
6910:Rowlinson, J.S.; Widom, B. (1982).
6476:Physical Chemistry Chemical Physics
6255:
5062:The Wenzel model is valid between Ξ
4043:Computational prediction of wetting
323:High-energy vs. low-energy surfaces
24:
8325:
8076:"Polymers with pendant ferrocenes"
7703:Bormashenko, Edward (2009-08-05).
7325:
7140:
7121:
6767:Schrader, M.E; Loeb, G.I. (1992).
6554:"Wetting transparency of graphene"
6180:
6109:
6057:
4925:CassieâBaxter to Wenzel transition
2616:
2580:
2543:
2503:
2457:
2421:
2384:
2344:
2302:
2287:
2269:
2247:
2228:
2206:
2178:
2146:
2117:
2088:
2059:
2030:
1872:
1855:
1848:
1843:
1669:
1642:
1618:
1594:
1578:
1403:
1106:
1001:Consider the interface as a curve
25:
8449:
8392:
8334:Capillarity and Wetting Phenomena
7207:Marmur, Abraham (February 1997).
6679:The Journal of Physical Chemistry
4865:"Petal effect" vs. "lotus effect"
4851:
4192:
2075:. The equilibrium contact angle (
431:A surface is more wettable when Îł
280:shows a fluid with more wetting.
8403:
6744:Wettability at high temperatures
2797:< 0, partial wetting occurs.
276:with very little wetting, while
8291:
8234:
8224:Chemical & Engineering News
8211:
8184:
8157:
8108:
7995:
7947:
7889:Ishino, C.; Okumura, K (2008).
7844:
7809:
7735:
7696:
7633:
7568:
7513:
7438:
7425:
7398:
7392:10.1016/j.fusengdes.2016.06.037
7369:
7294:
7247:
7200:
7094:
7087:Théorie mécanique de la chaleur
7077:
7050:
6970:
6928:
6914:. Oxford, UK: Clarendon Press.
6912:Molecular Theory of Capillarity
6903:
6834:
6794:"Wetting: statics and dynamics"
6760:
6387:Photochemistry and Photobiology
1339:{\displaystyle \int _{I}y'dx=0}
405:produced several key findings:
343:that hold them together (e.g.,
284:has a large contact angle, and
8374:Wetting and Spreading Dynamics
7956:"Wetting of Textured Surfaces"
7803:10.1016/j.colsurfa.2008.03.025
7721:10.1016/j.colsurfa.2009.04.054
7604:10.1103/PhysRevLett.109.116101
7499:10.1016/j.colsurfa.2018.07.004
7090:(in French). Gauthier-Villars.
6602:
6545:
6518:
6463:
6413:
6374:
6003:
5997:
5818:
5581:
5562:
5438:
5432:
5195:
5189:
4709:{\displaystyle \gamma _{i,sl}}
4673:{\displaystyle \gamma _{i,sv}}
4069:Non-ideal rough solid surfaces
4022:
4019:
4013:
3994:
3988:
3966:
3960:
3945:
3830:
3824:
3580:
3570:
3564:
3555:
3550:
3541:
3535:
3526:
3523:
3517:
3493:
3483:
3477:
3468:
3463:
3454:
3448:
3439:
3436:
3430:
3405:
3395:
3389:
3380:
3377:
3365:
3344:
3338:
3314:
3302:
1963:
1938:
1912:
1906:
1758:
1726:
1484:
1452:
1381:{\displaystyle \int _{I}ydx=A}
1280:
1274:
1265:
1259:
1222:
1190:
1123:
1111:
1061:
1049:
1017:
1011:
393:Wetting of low-energy surfaces
129:
13:
1:
8178:10.1016/S0022-328X(00)00927-X
7975:10.1016/S0927-7757(02)00061-4
7756:10.1080/01694243.2019.1663030
7379:Fusion Engineering and Design
7254:Tadmor, Rafael (2004-08-01).
6368:
5960:is the radius of droplet base
5807:is drop radius in equilibrium
5032:is the critical contact angle
4323:Figure 8: CassieâBaxter model
44:For other uses of "Wet", see
8277:10.1016/j.apsusc.2019.01.208
7873:10.1016/j.apsusc.2017.11.261
7690:10.1016/j.cplett.2007.11.033
7355:10.1016/j.molliq.2019.02.039
7343:Journal of Molecular Liquids
7319:10.1016/j.molliq.2017.10.134
7307:Journal of Molecular Liquids
6889:Johnson, Rulon E. (1993) in
6429:Journal of Materials Science
5814:Modifying wetting properties
1557:{\displaystyle \lambda _{i}}
95:Wetting is important in the
7:
7001:10.1088/0953-8984/10/27/001
6706:Wood Science and Technology
6279:
4291:{\displaystyle \theta ^{*}}
2162:as was shown by Tadmor as,
1292:{\displaystyle y(0)=y(L)=0}
10:
8454:
7918:10.1140/epje/i2007-10308-y
7419:10.1016/j.jcat.2006.12.007
6771:. New York: Plenum Press.
5798:is experimental delay time
2662:The YoungâDuprĂ© equation (
307:and a nonwettable surface
288:has a small contact angle.
43:
36:
29:
8342:10.1007/978-0-387-21656-0
8046:10.1016/j.cis.2008.08.005
7898:European Physical Journal
7520:De Gennes, P. G. (1994).
6821:10.1103/RevModPhys.57.827
6801:Reviews of Modern Physics
6449:10.1007/s10853-009-4128-x
4933:Figure 10: Mushroom state
4054:density functional theory
2104:) can be calculated from
1657:which is computed to be:
209:
206:
203:
173:
168:
165:
162:
8316:10.1021/acs.jpcc.6b08991
8080:Chemical Society Reviews
7785:Bormashenko, E. (2008).
7670:Chemical Physics Letters
7435:in HAL archives ouvertes
6792:de Gennes, P.G. (1985).
6746:. Oxford, UK: Pergamon.
6237:2-(methacryloyloxy)ethyl
6156:is initial contact angle
4151:contact angle hysteresis
4083:contact angle hysteresis
461:contact angle hysteresis
437:critical surface tension
39:Wetting (disambiguation)
8247:Applied Surface Science
8074:Pietschnig, R. (2016).
7963:Colloids and Surfaces A
7853:Applied Surface Science
7791:Colloids and Surfaces A
7584:Physical Review Letters
7477:Colloids and Surfaces A
7459:10.1163/156856192X00629
6470:Hu, Han; Ji, Hai-Feng;
6274:dissociative adsorption
4637:{\displaystyle \gamma }
3801:{\displaystyle \theta }
2686:and zero wetting when Îł
1067:{\displaystyle x\in I=}
8016:10.1002/macp.201100631
7233:10.1006/jcis.1996.4666
6956:10.1098/rstl.1805.0005
6362:USBM wettability index
6324:Sessile drop technique
6201:
6165:is final contact angle
6138:
5913:
5778:gravitational constant
5719:
5410:
5158:
5055:
5011:
4934:
4874:
4834:
4710:
4674:
4638:
4615:
4567:
4503:
4473:
4420:
4324:
4299:to the apparent area.
4292:
4262:
4202:
4201:Figure 7: Wenzel model
4178:
4140:
4078:
4029:
3802:
3779:
3731:
3688:
3620:
3603:
3265:
3039:
2866:
2780:
2648:
2319:
2156:
2127:
2098:
2069:
2040:
1999:
1925:
1924:{\displaystyle y(L)=0}
1887:
1824:
1804:
1781:
1651:
1603:
1558:
1528:
1382:
1340:
1299:which we can write as
1293:
1240:
1088:
1068:
1024:
964:
885:
846:
797:
489:
481:
289:
139:
56:
8336:. Springer New York.
6357:Lak wettability index
6338: â Lab technique
6188:
6139:
5914:
5785:is shape factor, 37.1
5720:
5411:
5159:
5053:
5012:
4932:
4872:
4835:
4711:
4675:
4639:
4616:
4547:
4504:
4502:{\displaystyle f_{i}}
4474:
4472:{\displaystyle f_{i}}
4421:
4322:
4293:
4263:
4200:
4179:
4141:
4076:
4030:
3803:
3780:
3732:
3689:
3618:
3604:
3266:
3040:
2867:
2781:
2703:spreading parameter S
2649:
2320:
2157:
2128:
2099:
2070:
2041:
2000:
1926:
1888:
1825:
1805:
1782:
1652:
1604:
1559:
1529:
1383:
1341:
1294:
1249:with the constraints
1241:
1089:
1069:
1025:
965:
883:
847:
798:
487:
479:
267:
174:Interaction strength
137:
54:
8412:at Wikimedia Commons
8399:What is wettability?
7407:Journal of Catalysis
7101:Clegg, Carl (2016).
5982:
5835:
5426:
5183:
5176:can be expressed as
5079:
4953:
4897:When comparing the "
4724:
4684:
4648:
4628:
4516:
4486:
4456:
4339:
4275:
4212:
4165:
4100:
3815:
3792:
3741:
3698:
3627:
3293:
3055:
2894:
2807:
2712:
2335:
2169:
2137:
2108:
2079:
2050:
2021:
1935:
1900:
1837:
1814:
1794:
1664:
1613:
1609:and the Hamiltonian
1568:
1541:
1398:
1350:
1303:
1253:
1101:
1078:
1034:
1023:{\displaystyle y(x)}
1005:
895:
815:
507:
451:Ideal solid surfaces
368:van der Waals forces
319:and apolar liquids.
62:is the ability of a
46:Wet (disambiguation)
37:For other uses, see
32:subpreputial wetness
18:YoungâDuprĂ© equation
8269:2019ApSS..478...68F
7910:2008EPJE...25..415I
7865:2018ApSS..436..411M
7682:2008CPL...450..355W
7596:2012PhRvL.109k6101C
7590:(11): 116101(1â6).
7225:1997JCIS..186..462M
7168:2022PhFl...34f2006W
7071:10.1021/la00009a049
6993:1998JPCM...10L.445C
6813:1985RvMP...57..827D
6691:10.1021/j100834a002
6638:10.1038/nature18275
6630:2016Natur.534..676M
6573:2012NatMa..11..217R
6488:2013PCCP...1516557H
6441:2010JMatS..45.4256D
5692:
5310:
5276:
4939:CassieâBaxter model
4482:A summation of all
4315:CassieâBaxter model
1143:
8367:Victor M. Starov;
8093:10.1039/C6CS00196C
6935:Young, T. (1805).
6718:10.1007/BF01159153
6496:10.1039/C3CP51848E
6202:
6134:
5909:
5715:
5670:
5406:
5296:
5262:
5171:Spreading dynamics
5154:
5056:
5007:
4943:wetting transition
4935:
4875:
4830:
4706:
4670:
4634:
4611:
4499:
4469:
4416:
4325:
4288:
4258:
4203:
4177:{\displaystyle Ca}
4174:
4136:
4079:
4050:molecular dynamics
4025:
3798:
3775:
3727:
3684:
3621:
3599:
3261:
3035:
2862:
2776:
2644:
2315:
2152:
2123:
2094:
2065:
2036:
1995:
1921:
1883:
1820:
1800:
1777:
1647:
1599:
1554:
1524:
1378:
1336:
1289:
1236:
1129:
1084:
1064:
1020:
960:
886:
842:
793:
791:
490:
482:
290:
232:90° †Ξ < 180°
207:0 < Ξ < 90°
140:
57:
8408:Media related to
8384:978-1-4200-1617-8
8369:Manuel G. Velarde
8351:978-1-4419-1833-8
8205:10.1021/om400468p
8199:(20): 5873â5878.
8136:10.1021/cr940053x
8086:(19): 5216â5231.
7830:10.1021/la703821h
7562:10.1021/la0344682
7556:(20): 8343â8348.
7531:978-0-521-56417-5
7453:(12): 1269â1302.
7272:10.1021/la049410h
7266:(18): 7659â7664.
7177:10.1063/5.0096644
7156:Physics of Fluids
7036:10.1021/la049410h
6987:(27): L445âL451.
6921:978-0-19-855642-8
6856:10.1021/ja412110t
6778:978-0-306-43985-8
6753:978-0-08-042146-9
6624:(7609): 676â679.
6435:(16): 4256â4264.
6399:10.1111/php.12751
6215:and used to make
6125:
5901:
5888:
5709:
5694:
5690:
5667:
5652:
5629:
5602:
5588:
5545:
5504:
5400:
5380:
5312:
5277:
5005:
4971:
4790:
4777:
4603:
4590:
4397:
4106:
4093:) contact angles
4089:) and receding (Ξ
3943:
3915:
3905:
3882:
3773:
3725:
3682:
3590:
3503:
3351:
3259:
3229:
3206:
3176:
3153:
3102:
2641:
2627:
2496:
2493:
2487:
2482:
2468:
2309:
1862:
1823:{\displaystyle L}
1803:{\displaystyle x}
1721:
1720:
1447:
1346:and fixed volume
1185:
1087:{\displaystyle L}
262:
261:
210:High wettability
145:forces between a
73:, resulting from
16:(Redirected from
8445:
8407:
8388:
8363:
8320:
8319:
8295:
8289:
8288:
8262:
8238:
8232:
8231:
8215:
8209:
8208:
8188:
8182:
8181:
8161:
8155:
8154:
8152:
8146:. Archived from
8124:Chemical Reviews
8121:
8112:
8106:
8105:
8095:
8071:
8058:
8057:
8029:
8020:
8019:
7999:
7993:
7992:
7990:
7989:
7983:
7977:. Archived from
7960:
7951:
7945:
7944:
7942:
7936:. Archived from
7895:
7886:
7877:
7876:
7848:
7842:
7841:
7824:(8): 4114â4119.
7813:
7807:
7806:
7782:
7776:
7775:
7739:
7733:
7732:
7700:
7694:
7693:
7676:(4â6): 355â359.
7661:
7652:
7649:
7640:
7637:
7631:
7630:
7628:
7622:. Archived from
7581:
7572:
7566:
7565:
7545:
7536:
7535:
7517:
7511:
7510:
7492:
7472:
7463:
7462:
7442:
7436:
7429:
7423:
7422:
7402:
7396:
7395:
7373:
7367:
7366:
7334:
7323:
7322:
7298:
7292:
7291:
7251:
7245:
7244:
7204:
7198:
7197:
7179:
7147:
7138:
7137:
7128:
7119:
7118:
7116:
7114:
7107:www.ramehart.com
7098:
7092:
7091:
7081:
7075:
7074:
7065:(9): 3585â3589.
7054:
7048:
7047:
7019:
7013:
7012:
6974:
6968:
6967:
6941:
6932:
6926:
6925:
6907:
6901:
6887:
6876:
6875:
6850:(8): 3219â3224.
6838:
6832:
6831:
6829:
6823:. Archived from
6798:
6789:
6783:
6782:
6764:
6758:
6757:
6739:
6730:
6729:
6701:
6695:
6694:
6674:
6665:
6664:
6662:
6656:. Archived from
6615:
6606:
6600:
6599:
6597:
6591:. Archived from
6581:10.1038/nmat3228
6561:Nature Materials
6558:
6549:
6543:
6542:
6522:
6516:
6515:
6482:(39): 16557â65.
6467:
6461:
6460:
6426:
6417:
6411:
6410:
6393:(5): 1165â1169.
6378:
6353:
6320:
6256:Oxygen vacancies
6238:
6143:
6141:
6140:
6135:
6133:
6129:
6128:
6127:
6126:
6118:
6112:
6095:
6091:
6090:
6086:
6085:
6065:
6061:
6060:
6035:
6031:
6030:
6010:
6006:
5918:
5916:
5915:
5910:
5908:
5904:
5903:
5902:
5899:
5890:
5889:
5886:
5875:
5874:
5788:
5724:
5722:
5721:
5716:
5711:
5710:
5702:
5700:
5696:
5695:
5693:
5691:
5683:
5681:
5669:
5668:
5660:
5654:
5653:
5645:
5632:
5631:
5630:
5622:
5606:
5604:
5603:
5595:
5593:
5589:
5584:
5580:
5579:
5557:
5547:
5546:
5538:
5536:
5532:
5531:
5527:
5526:
5525:
5505:
5503:
5499:
5498:
5488:
5487:
5486:
5470:
5468:
5467:
5415:
5413:
5412:
5407:
5402:
5401:
5393:
5391:
5387:
5386:
5382:
5381:
5379:
5375:
5374:
5364:
5363:
5359:
5358:
5357:
5337:
5336:
5320:
5318:
5314:
5313:
5311:
5309:
5304:
5291:
5283:
5278:
5275:
5270:
5261:
5260:
5259:
5243:
5210:
5209:
5163:
5161:
5160:
5155:
5153:
5149:
5131:
5127:
5126:
5103:
5099:
5098:
5016:
5014:
5013:
5008:
5006:
5004:
4993:
4982:
4977:
4973:
4972:
4969:
4839:
4837:
4836:
4831:
4826:
4822:
4821:
4820:
4797:
4793:
4792:
4791:
4788:
4779:
4778:
4775:
4764:
4763:
4751:
4747:
4746:
4715:
4713:
4712:
4707:
4705:
4704:
4679:
4677:
4676:
4671:
4669:
4668:
4643:
4641:
4640:
4635:
4620:
4618:
4617:
4612:
4610:
4606:
4605:
4604:
4601:
4592:
4591:
4588:
4577:
4576:
4566:
4561:
4543:
4539:
4538:
4508:
4506:
4505:
4500:
4498:
4497:
4478:
4476:
4475:
4470:
4468:
4467:
4425:
4423:
4422:
4417:
4403:
4399:
4398:
4395:
4376:
4375:
4363:
4359:
4358:
4297:
4295:
4294:
4289:
4287:
4286:
4267:
4265:
4264:
4259:
4257:
4236:
4232:
4231:
4183:
4181:
4180:
4175:
4158:capillary number
4145:
4143:
4142:
4137:
4135:
4134:
4121:
4120:
4107:
4104:
4034:
4032:
4031:
4026:
4009:
4008:
3984:
3983:
3944:
3942:
3941:
3940:
3921:
3916:
3908:
3906:
3904:
3903:
3888:
3883:
3881:
3880:
3868:
3867:
3866:
3851:
3850:
3837:
3807:
3805:
3804:
3799:
3784:
3782:
3781:
3776:
3774:
3772:
3771:
3770:
3751:
3736:
3734:
3733:
3728:
3726:
3724:
3723:
3708:
3693:
3691:
3690:
3685:
3683:
3681:
3680:
3668:
3667:
3666:
3651:
3650:
3637:
3608:
3606:
3605:
3600:
3598:
3597:
3591:
3589:
3588:
3587:
3553:
3509:
3504:
3502:
3501:
3500:
3466:
3422:
3420:
3419:
3413:
3412:
3352:
3347:
3330:
3284:Laplace pressure
3270:
3268:
3267:
3262:
3260:
3258:
3257:
3256:
3240:
3232:
3230:
3228:
3227:
3212:
3207:
3205:
3204:
3203:
3187:
3179:
3177:
3175:
3174:
3159:
3154:
3152:
3151:
3139:
3138:
3137:
3122:
3121:
3108:
3103:
3101:
3100:
3099:
3083:
3082:
3081:
3065:
3044:
3042:
3041:
3036:
2998:
2997:
2982:
2981:
2966:
2965:
2950:
2949:
2934:
2933:
2918:
2917:
2871:
2869:
2868:
2863:
2861:
2857:
2850:
2828:
2827:
2785:
2783:
2782:
2777:
2775:
2771:
2770:
2769:
2754:
2753:
2733:
2732:
2653:
2651:
2650:
2645:
2643:
2642:
2634:
2632:
2628:
2626:
2625:
2621:
2620:
2619:
2602:
2601:
2589:
2585:
2584:
2583:
2553:
2552:
2548:
2547:
2546:
2529:
2528:
2518:
2508:
2507:
2506:
2494:
2491:
2485:
2484:
2483:
2475:
2473:
2469:
2467:
2466:
2462:
2461:
2460:
2443:
2442:
2430:
2426:
2425:
2424:
2394:
2393:
2389:
2388:
2387:
2370:
2369:
2359:
2349:
2348:
2347:
2324:
2322:
2321:
2316:
2314:
2310:
2308:
2307:
2306:
2305:
2292:
2291:
2290:
2279:
2278:
2274:
2273:
2272:
2252:
2251:
2250:
2237:
2233:
2232:
2231:
2211:
2210:
2209:
2198:
2183:
2182:
2181:
2161:
2159:
2158:
2153:
2151:
2150:
2149:
2132:
2130:
2129:
2124:
2122:
2121:
2120:
2103:
2101:
2100:
2095:
2093:
2092:
2091:
2074:
2072:
2071:
2066:
2064:
2063:
2062:
2045:
2043:
2042:
2037:
2035:
2034:
2033:
2004:
2002:
2001:
1996:
1982:
1981:
1977:
1961:
1960:
1959:
1930:
1928:
1927:
1922:
1896:At the boundary
1892:
1890:
1889:
1884:
1876:
1875:
1863:
1861:
1853:
1852:
1851:
1841:
1829:
1827:
1826:
1821:
1809:
1807:
1806:
1801:
1786:
1784:
1783:
1778:
1773:
1772:
1757:
1756:
1741:
1740:
1722:
1719:
1718:
1717:
1698:
1694:
1692:
1691:
1673:
1672:
1656:
1654:
1653:
1648:
1646:
1645:
1636:
1622:
1621:
1608:
1606:
1605:
1600:
1598:
1597:
1591:
1590:
1589:
1563:
1561:
1560:
1555:
1553:
1552:
1533:
1531:
1530:
1525:
1520:
1519:
1507:
1499:
1498:
1483:
1482:
1467:
1466:
1448:
1446:
1445:
1444:
1425:
1423:
1422:
1407:
1406:
1387:
1385:
1384:
1379:
1362:
1361:
1345:
1343:
1342:
1337:
1323:
1315:
1314:
1298:
1296:
1295:
1290:
1245:
1243:
1242:
1237:
1229:
1225:
1221:
1220:
1205:
1204:
1186:
1184:
1183:
1182:
1163:
1161:
1160:
1142:
1137:
1110:
1109:
1093:
1091:
1090:
1085:
1073:
1071:
1070:
1065:
1029:
1027:
1026:
1021:
969:
967:
966:
961:
959:
942:
941:
926:
925:
910:
909:
851:
849:
848:
843:
802:
800:
799:
794:
792:
778:
777:
762:
745:
744:
729:
712:
711:
685:
668:
667:
652:
651:
636:
619:
618:
592:
575:
574:
559:
542:
541:
526:
525:
383:molecular motors
235:Low wettability
160:
159:
122:, boron nitride
21:
8453:
8452:
8448:
8447:
8446:
8444:
8443:
8442:
8433:Surface science
8428:Fluid mechanics
8418:
8417:
8395:
8385:
8352:
8328:
8326:Further reading
8323:
8301:
8296:
8292:
8244:
8239:
8235:
8216:
8212:
8193:Organometallics
8189:
8185:
8162:
8158:
8150:
8119:
8113:
8109:
8072:
8061:
8030:
8023:
8000:
7996:
7987:
7985:
7981:
7958:
7952:
7948:
7940:
7893:
7887:
7880:
7849:
7845:
7814:
7810:
7783:
7779:
7740:
7736:
7701:
7697:
7662:
7655:
7650:
7643:
7638:
7634:
7626:
7579:
7573:
7569:
7546:
7539:
7532:
7522:Soft Interfaces
7518:
7514:
7473:
7466:
7443:
7439:
7430:
7426:
7403:
7399:
7374:
7370:
7335:
7326:
7299:
7295:
7252:
7248:
7205:
7201:
7148:
7141:
7129:
7122:
7112:
7110:
7099:
7095:
7082:
7078:
7055:
7051:
7030:(18): 7659â64.
7020:
7016:
6975:
6971:
6939:
6933:
6929:
6922:
6908:
6904:
6888:
6879:
6839:
6835:
6827:
6796:
6790:
6786:
6779:
6765:
6761:
6754:
6740:
6733:
6702:
6698:
6675:
6668:
6660:
6613:
6607:
6603:
6595:
6556:
6550:
6546:
6539:
6523:
6519:
6468:
6464:
6424:
6418:
6414:
6379:
6375:
6371:
6366:
6351:
6348:Wetting voltage
6342:Wetting current
6318:
6282:
6271:
6262:heat exchangers
6258:
6236:
6225:Wittig reaction
6183:
6181:Surface changes
6164:
6155:
6117:
6113:
6108:
6107:
6100:
6096:
6081:
6077:
6073:
6056:
6052:
6048:
6043:
6039:
6026:
6022:
6018:
5993:
5989:
5983:
5980:
5979:
5973:
5970:decreases, or Îł
5969:
5941:
5934:
5898:
5894:
5885:
5881:
5880:
5876:
5870:
5866:
5836:
5833:
5832:
5821:
5816:
5806:
5797:
5786:
5742:surface tension
5739:
5701:
5682:
5674:
5659:
5655:
5644:
5640:
5633:
5621:
5617:
5607:
5605:
5594:
5575:
5571:
5558:
5556:
5552:
5551:
5537:
5521:
5517:
5510:
5506:
5494:
5490:
5489:
5482:
5478:
5471:
5469:
5460:
5456:
5455:
5451:
5450:
5449:
5445:
5444:
5427:
5424:
5423:
5392:
5370:
5366:
5365:
5353:
5349:
5342:
5338:
5332:
5328:
5321:
5319:
5305:
5300:
5292:
5284:
5282:
5271:
5266:
5252:
5248:
5244:
5242:
5241:
5237:
5233:
5229:
5216:
5212:
5211:
5205:
5201:
5184:
5181:
5180:
5173:
5139:
5135:
5122:
5118:
5114:
5094:
5090:
5086:
5080:
5077:
5076:
5071:
5065:
5030:
4994:
4983:
4981:
4968:
4964:
4960:
4954:
4951:
4950:
4927:
4917:" phenomenon).
4867:
4854:
4816:
4812:
4805:
4801:
4787:
4783:
4774:
4770:
4769:
4765:
4759:
4755:
4742:
4738:
4734:
4725:
4722:
4721:
4691:
4687:
4685:
4682:
4681:
4655:
4651:
4649:
4646:
4645:
4629:
4626:
4625:
4600:
4596:
4587:
4583:
4582:
4578:
4572:
4568:
4562:
4551:
4534:
4530:
4526:
4517:
4514:
4513:
4493:
4489:
4487:
4484:
4483:
4463:
4459:
4457:
4454:
4453:
4449:
4434:
4394:
4390:
4386:
4371:
4367:
4354:
4350:
4346:
4340:
4337:
4336:
4317:
4282:
4278:
4276:
4273:
4272:
4247:
4227:
4223:
4219:
4213:
4210:
4209:
4195:
4166:
4163:
4162:
4130:
4126:
4116:
4112:
4103:
4101:
4098:
4097:
4092:
4088:
4071:
4045:
4004:
4000:
3979:
3975:
3933:
3929:
3925:
3920:
3907:
3896:
3892:
3887:
3873:
3869:
3859:
3855:
3843:
3839:
3838:
3836:
3816:
3813:
3812:
3793:
3790:
3789:
3763:
3759:
3755:
3750:
3742:
3739:
3738:
3716:
3712:
3707:
3699:
3696:
3695:
3673:
3669:
3659:
3655:
3643:
3639:
3638:
3636:
3628:
3625:
3624:
3593:
3592:
3583:
3579:
3554:
3510:
3508:
3496:
3492:
3467:
3423:
3421:
3415:
3414:
3408:
3404:
3331:
3329:
3294:
3291:
3290:
3249:
3245:
3241:
3233:
3231:
3220:
3216:
3211:
3196:
3192:
3188:
3180:
3178:
3167:
3163:
3158:
3144:
3140:
3130:
3126:
3114:
3110:
3109:
3107:
3092:
3088:
3084:
3074:
3070:
3066:
3064:
3056:
3053:
3052:
2990:
2986:
2974:
2970:
2958:
2954:
2942:
2938:
2926:
2922:
2910:
2906:
2895:
2892:
2891:
2881:
2840:
2833:
2829:
2820:
2816:
2808:
2805:
2804:
2762:
2758:
2746:
2742:
2741:
2737:
2725:
2721:
2713:
2710:
2709:
2697:
2693:
2689:
2685:
2681:
2677:
2673:
2669:
2660:
2633:
2615:
2614:
2610:
2606:
2597:
2593:
2579:
2578:
2574:
2570:
2554:
2542:
2541:
2537:
2533:
2524:
2520:
2519:
2517:
2513:
2512:
2502:
2501:
2497:
2474:
2456:
2455:
2451:
2447:
2438:
2434:
2420:
2419:
2415:
2411:
2395:
2383:
2382:
2378:
2374:
2365:
2361:
2360:
2358:
2354:
2353:
2343:
2342:
2338:
2336:
2333:
2332:
2301:
2300:
2296:
2286:
2285:
2281:
2280:
2268:
2267:
2263:
2259:
2246:
2245:
2241:
2227:
2226:
2222:
2218:
2205:
2204:
2200:
2199:
2197:
2193:
2177:
2176:
2172:
2170:
2167:
2166:
2145:
2144:
2140:
2138:
2135:
2134:
2116:
2115:
2111:
2109:
2106:
2105:
2087:
2086:
2082:
2080:
2077:
2076:
2058:
2057:
2053:
2051:
2048:
2047:
2029:
2028:
2024:
2022:
2019:
2018:
2011:
1973:
1966:
1962:
1955:
1951:
1947:
1936:
1933:
1932:
1901:
1898:
1897:
1871:
1870:
1854:
1847:
1846:
1842:
1840:
1838:
1835:
1834:
1815:
1812:
1811:
1795:
1792:
1791:
1768:
1764:
1749:
1745:
1733:
1729:
1713:
1709:
1705:
1693:
1684:
1680:
1668:
1667:
1665:
1662:
1661:
1641:
1640:
1629:
1617:
1616:
1614:
1611:
1610:
1593:
1592:
1582:
1581:
1577:
1569:
1566:
1565:
1548:
1544:
1542:
1539:
1538:
1515:
1511:
1500:
1494:
1490:
1475:
1471:
1459:
1455:
1440:
1436:
1432:
1424:
1415:
1411:
1402:
1401:
1399:
1396:
1395:
1357:
1353:
1351:
1348:
1347:
1316:
1310:
1306:
1304:
1301:
1300:
1254:
1251:
1250:
1213:
1209:
1197:
1193:
1178:
1174:
1170:
1162:
1153:
1149:
1148:
1144:
1138:
1133:
1105:
1104:
1102:
1099:
1098:
1079:
1076:
1075:
1035:
1032:
1031:
1006:
1003:
1002:
999:
949:
934:
930:
918:
914:
902:
898:
896:
893:
892:
878:
870:
866:
862:
816:
813:
812:
809:
790:
789:
779:
770:
766:
752:
737:
733:
719:
704:
700:
697:
696:
686:
675:
660:
656:
644:
640:
626:
611:
607:
604:
603:
593:
582:
567:
563:
549:
534:
530:
518:
514:
510:
508:
505:
504:
474:
453:
442:
434:
423:
418:linear function
415:
410:surface tension
395:
325:
193:Perfect wetting
170:
132:
120:carbon nanotube
49:
42:
35:
28:
23:
22:
15:
12:
11:
5:
8451:
8441:
8440:
8435:
8430:
8414:
8413:
8401:
8394:
8393:External links
8391:
8390:
8389:
8383:
8364:
8350:
8327:
8324:
8322:
8321:
8299:
8290:
8242:
8233:
8210:
8183:
8156:
8153:on 2016-01-22.
8130:(2): 877â910.
8107:
8059:
8040:(1â2): 54â65.
8021:
8010:(6): 654â665.
7994:
7969:(1â3): 41â46.
7946:
7943:on 2019-04-11.
7904:(4): 415â424.
7878:
7843:
7808:
7797:(1â3): 47â50.
7777:
7750:(2): 219â230.
7734:
7715:(1): 163â165.
7695:
7653:
7641:
7632:
7629:on 2019-04-11.
7567:
7537:
7530:
7512:
7464:
7437:
7424:
7413:(2): 325â334.
7397:
7368:
7324:
7293:
7246:
7219:(2): 462â466.
7199:
7139:
7120:
7093:
7076:
7049:
7014:
6969:
6927:
6920:
6902:
6877:
6833:
6830:on 2016-09-10.
6807:(3): 827â863.
6784:
6777:
6759:
6752:
6731:
6712:(5): 339â353.
6696:
6685:(5): 519â524.
6666:
6663:on 2019-04-11.
6601:
6598:on 2017-11-15.
6544:
6537:
6517:
6462:
6412:
6372:
6370:
6367:
6365:
6364:
6359:
6354:
6345:
6339:
6333:
6327:
6321:
6312:
6310:Electrowetting
6307:
6301:
6295:
6290:
6283:
6281:
6278:
6269:
6257:
6254:
6221:Vinylferrocene
6182:
6179:
6175:
6174:
6173:
6172:
6166:
6162:
6157:
6153:
6145:
6144:
6132:
6124:
6121:
6116:
6111:
6106:
6103:
6099:
6094:
6089:
6084:
6080:
6076:
6071:
6068:
6064:
6059:
6055:
6051:
6046:
6042:
6038:
6034:
6029:
6025:
6021:
6016:
6013:
6009:
6005:
6002:
5999:
5996:
5992:
5987:
5971:
5967:
5964:
5963:
5962:
5961:
5955:
5949:
5943:
5939:
5936:
5932:
5929:
5920:
5919:
5907:
5897:
5893:
5884:
5879:
5873:
5869:
5864:
5861:
5858:
5855:
5852:
5849:
5846:
5843:
5840:
5820:
5817:
5815:
5812:
5811:
5810:
5809:
5808:
5804:
5799:
5795:
5790:
5780:
5771:
5761:
5751:
5750:is drop volume
5745:
5737:
5726:
5725:
5714:
5708:
5705:
5699:
5689:
5686:
5680:
5677:
5673:
5666:
5663:
5658:
5651:
5648:
5643:
5639:
5636:
5628:
5625:
5620:
5616:
5613:
5610:
5601:
5598:
5592:
5587:
5583:
5578:
5574:
5570:
5567:
5564:
5561:
5555:
5550:
5544:
5541:
5535:
5530:
5524:
5520:
5516:
5513:
5509:
5502:
5497:
5493:
5485:
5481:
5477:
5474:
5466:
5463:
5459:
5454:
5448:
5443:
5440:
5437:
5434:
5431:
5417:
5416:
5405:
5399:
5396:
5390:
5385:
5378:
5373:
5369:
5362:
5356:
5352:
5348:
5345:
5341:
5335:
5331:
5327:
5324:
5317:
5308:
5303:
5299:
5295:
5290:
5287:
5281:
5274:
5269:
5265:
5258:
5255:
5251:
5247:
5240:
5236:
5232:
5228:
5225:
5222:
5219:
5215:
5208:
5204:
5200:
5197:
5194:
5191:
5188:
5172:
5169:
5165:
5164:
5152:
5148:
5145:
5142:
5138:
5134:
5130:
5125:
5121:
5117:
5112:
5109:
5106:
5102:
5097:
5093:
5089:
5084:
5067:
5063:
5048:
5047:
5046:
5045:
5039:
5033:
5028:
5018:
5017:
5003:
5000:
4997:
4992:
4989:
4986:
4980:
4976:
4967:
4963:
4958:
4926:
4923:
4879:hydrophobicity
4877:The intrinsic
4866:
4863:
4853:
4852:Precursor film
4850:
4841:
4840:
4829:
4825:
4819:
4815:
4811:
4808:
4804:
4800:
4796:
4786:
4782:
4773:
4768:
4762:
4758:
4754:
4750:
4745:
4741:
4737:
4732:
4729:
4703:
4700:
4697:
4694:
4690:
4667:
4664:
4661:
4658:
4654:
4633:
4622:
4621:
4609:
4599:
4595:
4586:
4581:
4575:
4571:
4565:
4560:
4557:
4554:
4550:
4546:
4542:
4537:
4533:
4529:
4524:
4521:
4496:
4492:
4466:
4462:
4447:
4432:
4427:
4426:
4415:
4412:
4409:
4406:
4402:
4393:
4389:
4384:
4380:
4374:
4370:
4366:
4362:
4357:
4353:
4349:
4344:
4316:
4313:
4285:
4281:
4269:
4268:
4256:
4253:
4250:
4245:
4242:
4239:
4235:
4230:
4226:
4222:
4217:
4194:
4193:Wenzel's model
4191:
4173:
4170:
4147:
4146:
4133:
4129:
4124:
4119:
4115:
4110:
4090:
4086:
4070:
4067:
4044:
4041:
4036:
4035:
4024:
4021:
4018:
4015:
4012:
4007:
4003:
3999:
3996:
3993:
3990:
3987:
3982:
3978:
3974:
3971:
3968:
3965:
3962:
3959:
3956:
3953:
3950:
3947:
3939:
3936:
3932:
3928:
3924:
3919:
3914:
3911:
3902:
3899:
3895:
3891:
3886:
3879:
3876:
3872:
3865:
3862:
3858:
3854:
3849:
3846:
3842:
3835:
3832:
3829:
3826:
3823:
3820:
3797:
3786:
3785:
3769:
3766:
3762:
3758:
3754:
3749:
3746:
3722:
3719:
3715:
3711:
3706:
3703:
3679:
3676:
3672:
3665:
3662:
3658:
3654:
3649:
3646:
3642:
3635:
3632:
3610:
3609:
3596:
3586:
3582:
3578:
3575:
3572:
3569:
3566:
3563:
3560:
3557:
3552:
3549:
3546:
3543:
3540:
3537:
3534:
3531:
3528:
3525:
3522:
3519:
3516:
3513:
3507:
3499:
3495:
3491:
3488:
3485:
3482:
3479:
3476:
3473:
3470:
3465:
3462:
3459:
3456:
3453:
3450:
3447:
3444:
3441:
3438:
3435:
3432:
3429:
3426:
3418:
3411:
3407:
3403:
3400:
3397:
3394:
3391:
3388:
3385:
3382:
3379:
3376:
3373:
3370:
3367:
3364:
3361:
3358:
3355:
3350:
3346:
3343:
3340:
3337:
3334:
3328:
3325:
3322:
3319:
3316:
3313:
3310:
3307:
3304:
3301:
3298:
3272:
3271:
3255:
3252:
3248:
3244:
3239:
3236:
3226:
3223:
3219:
3215:
3210:
3202:
3199:
3195:
3191:
3186:
3183:
3173:
3170:
3166:
3162:
3157:
3150:
3147:
3143:
3136:
3133:
3129:
3125:
3120:
3117:
3113:
3106:
3098:
3095:
3091:
3087:
3080:
3077:
3073:
3069:
3063:
3060:
3046:
3045:
3034:
3031:
3028:
3025:
3022:
3019:
3016:
3013:
3010:
3007:
3004:
3001:
2996:
2993:
2989:
2985:
2980:
2977:
2973:
2969:
2964:
2961:
2957:
2953:
2948:
2945:
2941:
2937:
2932:
2929:
2925:
2921:
2916:
2913:
2909:
2905:
2902:
2899:
2880:
2877:
2873:
2872:
2860:
2856:
2853:
2849:
2846:
2843:
2839:
2836:
2832:
2826:
2823:
2819:
2815:
2812:
2787:
2786:
2774:
2768:
2765:
2761:
2757:
2752:
2749:
2745:
2740:
2736:
2731:
2728:
2724:
2720:
2717:
2695:
2691:
2687:
2683:
2679:
2675:
2671:
2667:
2659:
2656:
2655:
2654:
2640:
2637:
2631:
2624:
2618:
2613:
2609:
2605:
2600:
2596:
2592:
2588:
2582:
2577:
2573:
2569:
2566:
2563:
2560:
2557:
2551:
2545:
2540:
2536:
2532:
2527:
2523:
2516:
2511:
2505:
2500:
2490:
2481:
2478:
2472:
2465:
2459:
2454:
2450:
2446:
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2180:
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2148:
2143:
2119:
2114:
2090:
2085:
2061:
2056:
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2027:
2010:
2007:
1994:
1991:
1988:
1985:
1980:
1976:
1972:
1969:
1965:
1958:
1954:
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1946:
1943:
1940:
1920:
1917:
1914:
1911:
1908:
1905:
1894:
1893:
1882:
1879:
1874:
1869:
1866:
1860:
1857:
1850:
1845:
1819:
1810:direction and
1799:
1788:
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1776:
1771:
1767:
1763:
1760:
1755:
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1748:
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1128:
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1122:
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1060:
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1054:
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1013:
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971:
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958:
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948:
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829:
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773:
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524:
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512:
473:
470:
452:
449:
440:
432:
424:) for various
421:
413:
403:William Zisman
394:
391:
379:surface energy
372:hydrogen bonds
341:chemical bonds
324:
321:
260:
259:
256:
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250:
247:
243:
242:
239:
236:
233:
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214:
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201:
200:
197:
194:
191:
188:
184:
183:
182:Liquidâliquid
180:
176:
175:
172:
167:
166:Contact angle
164:
131:
128:
75:intermolecular
26:
9:
6:
4:
3:
2:
8450:
8439:
8436:
8434:
8431:
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8386:
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8377:. CRC Press.
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7984:on 2012-05-27
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6574:
6570:
6567:(3): 217â22.
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6534:
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4947:
4944:
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4922:
4918:
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4915:self-cleaning
4911:
4910:contact angle
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4312:
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4305:
4304:contact angle
4300:
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4224:
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4899:petal effect
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313:Lotus effect
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252:Non-wetting
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8245:surfaces".
8172:: 128â132.
7859:: 411â418.
7483:: 365â371.
7386:: 188â193.
7349:: 196â203.
7313:: 920â926.
7109:. ramé-hart
6891:Wettability
6330:Soap bubble
6233:polystyrene
6198:hydrophilic
6191:hydrophobic
5826:surfactants
5819:Surfactants
494:equilibrium
309:hydrophobic
305:hydrophilic
130:Explanation
109:Surfactants
8438:Hysteresis
8422:Categories
8260:1902.02662
7988:2011-12-17
7490:1712.04703
6369:References
6293:Amott test
6287:Adsorption
6266:Adsorption
6250:molar mass
4901:" to the "
4885:. The red
4309:hysteresis
991:immiscible
496:, the net
465:hysteresis
401:) forces.
169:Degree of
8360:137894832
8285:118895100
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7764:0169-4243
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6726:0043-7719
6654:205249367
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6472:Sun, Ying
6407:0031-8655
6315:Flotation
6304:Dewetting
6205:Ferrocene
6123:τ
6115:−
6105:−
6079:θ
6067:−
6058:∞
6054:θ
6024:θ
5995:θ
5896:γ
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5863:π
5845:γ
5839:σ
5758:viscosity
5672:γ
5657:π
5638:⋅
5612:ρ
5586:η
5560:λ
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1993:θ
1990:
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539:β
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516:γ
428:liquids.
249:Ξ = 180°
107:effects.
105:capillary
101:adherence
8144:11848774
8102:27156979
8054:18834966
7934:35973585
7926:18431542
7838:18312016
7818:Langmuir
7620:29794436
7612:23005650
7550:Langmuir
7507:51916594
7288:15323516
7260:Langmuir
7059:Langmuir
7044:15323516
7024:Langmuir
6864:24490770
6646:27357755
6589:22266468
6504:23949186
6298:Anti-fog
6280:See also
6245:moieties
6217:polymers
6213:monomers
4444:= 1 and
1953:′
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1634:′
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1438:′
1321:′
1176:′
857:triangle
387:bistable
353:metallic
345:covalent
337:ceramics
272:shows a
171:wetting
155:Cohesive
143:Adhesive
124:nanomesh
116:graphene
87:cohesive
83:adhesive
79:miscible
8410:Wetting
8265:Bibcode
7906:Bibcode
7861:Bibcode
7678:Bibcode
7592:Bibcode
7241:9056376
7221:Bibcode
7164:Bibcode
6989:Bibcode
6809:Bibcode
6626:Bibcode
6569:Bibcode
6484:Bibcode
6457:4512480
6437:Bibcode
5768:density
4937:In the
987:droplet
463:. Zero
426:organic
333:glasses
258:Strong
241:Strong
216:Strong
163:Fig. 2
97:bonding
71:surface
60:Wetting
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4271:where
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2328:where
2188:arccos
1537:where
1074:where
979:liquid
863:< Îł
335:, and
329:energy
213:Strong
196:Strong
190:Ξ = 0
147:liquid
90:forces
64:liquid
8356:S2CID
8281:S2CID
8255:arXiv
8151:(PDF)
8120:(PDF)
7982:(PDF)
7959:(PDF)
7941:(PDF)
7930:S2CID
7894:(PDF)
7768:S2CID
7627:(PDF)
7616:S2CID
7580:(PDF)
7503:S2CID
7485:arXiv
7359:S2CID
7190:S2CID
7005:S2CID
6960:S2CID
6940:(PDF)
6868:S2CID
6828:(PDF)
6797:(PDF)
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6508:S2CID
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6209:redox
6207:is a
4624:Here
2789:When
2670:nor Îł
975:solid
498:force
351:, or
349:ionic
317:polar
274:fluid
224:Weak
199:Weak
151:solid
68:solid
8379:ISBN
8346:ISBN
8230:(4).
8140:PMID
8098:PMID
8050:PMID
7922:PMID
7834:PMID
7760:ISSN
7725:ISSN
7608:PMID
7526:ISBN
7284:PMID
7276:ISSN
7237:PMID
7182:ISSN
7115:2016
7040:PMID
6916:ISBN
6895:ISBN
6860:PMID
6773:ISBN
6748:ISBN
6722:ISSN
6642:PMID
6585:PMID
6533:ISBN
6500:PMID
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4887:rose
4789:1,sl
4776:1,sv
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4052:and
3737:and
2133:and
1931:and
1030:for
981:and
370:and
292:The
255:Weak
238:Weak
221:Weak
149:and
85:and
8338:doi
8312:doi
8308:121
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8170:625
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8088:doi
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8038:144
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