1545:
the drop and surface remains constant. The "downhill" side of the drop will adopt a higher contact angle while the "uphill" side of the drop will adopt a lower contact angle. As the tilt angle increases the contact angles will continue to change but the contact area between the drop and surface will remain constant. At a given surface tilt angle, the advancing and receding contact angles will be met and the drop will move on the surface. In practice, the measurement can be influenced by shear forces and momentum if the tilt velocity is high. The measurement method can also be challenging in practice for systems with high (>30 degrees) or low (<10 degrees) contact angle hysteresis.
105:
2704:
2728:
2640:
2440:
565:
2513:
selection of the organic molecules with varying molecular structures and amounts of hydrocarbon and/or perfluorinated terminations, the contact angle of the surface can tune. The deposition of these specialty silanes can be achieved in the gas phase through the use of a specialized vacuum ovens or liquid-phase process. Molecules that can bind more perfluorinated terminations to the surface can results in lowering the surface energy (high water contact angle).
2628:
1496:
measured from dynamic experiments where droplets or liquid bridges are in movement. In contrast, the equilibrium contact angle described by the Young-Laplace equation is measured from a static state. Static measurements yield values in-between the advancing and receding contact angle depending on deposition parameters (e.g. velocity, angle, and drop size) and drop history (e.g. evaporation from time of deposition). Contact angle hysteresis is defined as
2452:
20:
1985:
1106:
826:
1479:
1733:
836:
593:
1274:
1257:
2755:
In case of a porous materials many issues have been raised both about the physical meaning of the calculated pore diameter and the real possibility to use this equation for the calculation of the contact angle of the solid, even if this method is often offered by much software as consolidated. Change
1544:
Advancing and receding contact angles can be measured directly from the same measurement if drops are moved linearly on a surface. For example, a drop of liquid will adopt a given contact angle when static, but when the surface is tilted the drop will initially deform so that the contact area between
2512:
Control of the wetting contact angle can often be achieved through the deposition or incorporation of various organic and inorganic molecules onto the surface. This is often achieved through the use of specialty silane chemicals which can form a SAM (self-assembled monolayers) layer. With the proper
2459:
Contact angles are extremely sensitive to contamination; values reproducible to better than a few degrees are generally only obtained under laboratory conditions with purified liquids and very clean solid surfaces. If the liquid molecules are strongly attracted to the solid molecules then the liquid
1548:
Advancing and receding contact angle measurements can be carried out by adding and removing liquid from a drop deposited on a surface. If a sufficiently small volume of liquid is added to a drop, the contact line will still be pinned, and the contact angle will increase. Similarly, if a small amount
2690:
The dynamic sessile drop is similar to the static sessile drop but requires the drop to be modified. A common type of dynamic sessile drop study determines the largest contact angle possible without increasing its solid–liquid interfacial area by adding volume dynamically. This maximum angle is the
1989:
On a surface that is rough or contaminated, there will also be contact angle hysteresis, but now the local equilibrium contact angle (the Young equation is now only locally valid) may vary from place to place on the surface. According to the Young–Dupré equation, this means that the adhesion energy
1724:
1495:
A given substrate-liquid-vapor combination yields a continuous range of contact angle values in practice. The maximum contact angle is referred to as the advancing contact angle and the minimum contact angle is referred to as the receding contact angle. The advancing and receding contact angles are
2740:
An optical variation of the single-fiber
Wilhelmy method. Instead of measuring with a balance, the shape of the meniscus on the fiber is directly imaged using a high resolution camera. Automated meniscus shape fitting can then directly measure the static, advancing or receding contact angle on the
2711:
The dynamic
Wilhelmy method is a method for calculating average advancing and receding contact angles on solids of uniform geometry. Both sides of the solid must have the same properties. Wetting force on the solid is measured as the solid is immersed in or withdrawn from a liquid of known surface
2671:
Measuring contact angles for pendant drops is much more complicated than for sessile drops due to the inherent unstable nature of inverted drops. This complexity is further amplified when one attempts to incline the surface. Experimental apparatus to measure pendant drop contact angles on inclined
2662:
using an optical subsystem to capture the profile of a pure liquid on a solid substrate. The angle formed between the liquid–solid interface and the liquid–vapor interface is the contact angle. Older systems used a microscope optical system with a back light. Current-generation systems employ high
2430:
that governs the shape of a three-dimensional drop, in conjunction with appropriate boundary conditions, is complicated, and an alternate energy minimization approach to this is generally adopted. The shapes of three-dimensional sessile and pendant drops have been successfully predicted using this
2087:
If the surface is wetted heterogeneously, the droplet is in Cassie-Baxter state. The most stable contact angle can be connected to the Young contact angle. The contact angles calculated from the Wenzel and Cassie-Baxter equations have been found to be good approximations of the most stable contact
1997:
Because liquid advances over previously dry surface but recedes from previously wet surface, contact angle hysteresis can also arise if the solid has been altered due to its previous contact with the liquid (e.g., by a chemical reaction, or absorption). Such alterations, if slow, can also produce
584:, 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 confirmed that the modified Young's equation does not hold at the micro-nano scales. Jasper proposed that including a
1536:
The advancing contact angle can be described as a measure of the liquid-solid cohesion while the receding contact angle is a measure of liquid-solid adhesion. The advancing and receding contact angles can be measured directly using different methods and can also be calculated from other wetting
416:
The earliest study on the relationship between contact angle and surface tensions for sessile droplets on flat surfaces was reported by Thomas Young in 1805. A century later Gibbs proposed a modification to Young's equation to account for the volumetric dependence of the contact angle. Gibbs
2422:
2096:
For liquid moving quickly over a surface, the contact angle can be altered from its value at rest. The advancing contact angle will increase with speed, and the receding contact angle will decrease. The discrepancies between static and dynamic contact angles are closely proportional to the
535:
83:
is often observed, ranging from the advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapour
2495:
If the contact angle is measured through the gas instead of through the liquid, then it should be replaced by 180° minus their given value. Contact angles are equally applicable to the interface of two liquids, though they are more commonly measured in solid products such as
1980:{\displaystyle {\begin{aligned}r_{\rm {A}}&={\sqrt{\frac {\sin ^{3}\theta _{\rm {A}}}{2-3\cos \theta _{\rm {A}}+\cos ^{3}\theta _{\rm {A}}}}}\\r_{\rm {R}}&={\sqrt{\frac {\sin ^{3}\theta _{\rm {R}}}{2-3\cos \theta _{\rm {R}}+\cos ^{3}\theta _{\rm {R}}}}}\end{aligned}}}
1552:
The Young's equation assumes a homogeneous surface and does not account for surface texture or outside forces such as gravity. Real surfaces are not atomically smooth or chemically homogeneous so a drop will assume contact angle hysteresis. The equilibrium contact angle
1101:{\displaystyle \cos(\theta \mp \alpha )=A+B\,{\frac {\cos \alpha }{a}}\pm C\sin(\theta \mp \alpha )(1+\cos \theta )^{2}{\biggl (}{\frac {\sin \alpha \,(2+\cos \alpha )}{(1+\cos \alpha )^{2}}}\mp {\frac {\sin \theta \,(2+\cos \theta )}{(1+\cos \theta )^{2}}}{\biggr )}}
1113:
1261:
This equation relates the contact angle, a geometric property of a sessile droplet to the bulk thermodynamics, the energy at the three phase contact boundary, and the mean curvature of the droplet. For the special case of a sessile droplet on a flat surface
91:
The contact angle depends upon the medium above the free surface of the liquid, and the nature of the liquid and solid in contact. It is independent of the inclination of solid to the liquid surface. It changes with surface tension and hence with the
2663:
resolution cameras and software to capture and analyze the contact angle. Angles measured in such a way are often quite close to advancing contact angles. Equilibrium contact angles can be obtained through the application of well defined vibrations.
821:{\displaystyle 0={\frac {dA_{\rm {LG}}}{dA_{\rm {SL}}}}+{\frac {\gamma _{\rm {SL}}-\gamma _{\rm {SG}}}{\gamma _{\rm {LG}}}}-{\frac {\kappa }{\gamma _{\rm {LG}}}}{\frac {dL}{dA_{\rm {SL}}}}-{\frac {V}{\gamma _{\rm {LG}}}}{\frac {dP}{dA_{\rm {SL}}}}}
1585:
269:
2488:) materials may have water contact angles as high as ≈ 120°. Some materials with highly rough surfaces may have a water contact angle even greater than 150°, due to the presence of air pockets under the liquid drop. These are called
1474:{\displaystyle \cos \theta ={\frac {\gamma _{\rm {SG}}-\gamma _{\rm {SL}}}{\gamma _{\rm {LG}}}}+{\frac {\kappa }{\gamma _{\rm {LG}}}}{\frac {1}{a}}-{\frac {\gamma }{3\gamma _{\rm {LG}}}}(2+\cos \theta -2\cos ^{2}\theta -\cos ^{3}\theta )}
2006:
Surface roughness has a strong effect on the contact angle and wettability of a surface. The effect of roughness depends on if the droplet will wet the surface grooves or if air pockets will be left between the droplet and the surface.
2178:
422:
366:
2010:
If the surface is wetted homogeneously, the droplet is in Wenzel state. In Wenzel state, adding surface roughness will enhance the wettability caused by the chemistry of the surface. The Wenzel correlation can be written as
830:
The variation in the pressure at the free liquid-vapor boundary is due to
Laplace pressure, which is proportional to the mean curvature. Solving the above equation for both convex and concave surfaces yields:
551:
is the droplet radius in meters. Although experimental data validates an affine relationship between the cosine of the contact angle and the inverse line radius, it does not account for the correct sign of
2712:
tension. Also in that case it is possible to measure the equilibrium contact angle by applying a very controlled vibration. That methodology, called VIECA, can be implemented in a quite simple way on every
1738:
1483:
In the above equation, 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
417:
postulated the existence of a line tension, which acts at the three-phase boundary and accounts for the excess energy at the confluence of the solid-liquid-gas phase interface, and is given as:
2064:
1529:. The static, advancing, or receding contact angle can be used in place of the equilibrium contact angle depending on the application. The overall effect can be seen as closely analogous to
3586:
Marco, Brugnara; Claudio, Della Volpe; Stefano, Siboni (2006). "Wettability of porous materials. II. Can we obtain the contact angle from the
Washburn equation?". In Mittal, K. L. (ed.).
2672:
substrates has been developed recently. This method allows for the deposition of multiple microdrops on the underside of a textured substrate, which can be imaged using a high resolution
181:
2472:
layer or contaminants on the solid surface can significantly increase the contact angle. Generally, if the water contact angle is smaller than 90°, the solid surface is considered
3523:
Bhutani, Gaurav; Muralidhar, K.; Khandekar, Sameer (2013). "Determination of apparent contact angle and shape of a static pendant drop on a physically textured inclined surface".
1252:{\displaystyle A={\frac {\gamma _{\rm {SG}}-\gamma _{\rm {SL}}}{\gamma _{\rm {LG}}}},\quad B={\frac {\kappa }{\gamma _{\rm {LG}}}},\quad C={\frac {\gamma }{3\gamma _{\rm {LG}}}}.}
588:
term in the variation of the free energy may be the key to solving the contact angle problem at such small scales. Given that the variation in free energy is zero at equilibrium:
406:
79:
A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice a dynamic phenomenon of contact angle
2691:
advancing angle. Volume is removed to produce the smallest possible angle, the receding angle. The difference between the advancing and receding angle is the contact angle
1994:: the extent of wetting, and therefore the observed contact angle (averaged along the contact line), depends on whether the liquid is advancing or receding on the surface.
2950:
Jasper, Warren J.; Anand, Nadish (May 2019). "A generalized variational approach for predicting contact angles of sessile nano-droplets on both flat and curved surfaces".
284:
3443:
2173:
3182:
2993:
Jasper, Warren J.; Rasipuram, Srinivasan (December 2017). "Relationship between contact angle and contact line radius for micro to atto liter size oil droplets".
132:
phase (G) (which could be a mixture of ambient atmosphere and an equilibrium concentration of the liquid vapor). (The "gaseous" phase could be replaced by another
2122:
1719:{\displaystyle \theta _{\rm {c}}=\arccos \left({\frac {r_{\rm {A}}\cos \theta _{\rm {A}}+r_{\rm {R}}\cos \theta _{\rm {R}}}{r_{\rm {A}}+r_{\rm {R}}}}\right)}
1990:
varies locally – thus, the liquid has to overcome local energy barriers in order to wet the surface. One consequence of these barriers is contact angle
2417:{\displaystyle \kappa _{m}={\frac {1}{2}}{\frac {(1+{f_{x}}^{2})f_{yy}-2f_{x}f_{y}f_{xy}+(1+{f_{y}}^{2})f_{xx}}{(1+{f_{x}}^{2}+{f_{y}}^{2})^{3/2}}}.}
2676:
camera. An automated system allows for tilting the substrate and analysing the images for the calculation of advancing and receding contact angles.
530:{\displaystyle \cos \theta ={\frac {\gamma _{\rm {SG}}-\gamma _{\rm {SL}}}{\gamma _{\rm {LG}}}}+{\frac {\kappa }{\gamma _{\rm {LG}}}}{\frac {1}{a}}}
3315:
2014:
2460:
drop will completely spread out on the solid surface, corresponding to a contact angle of 0°. This is often the case for water on bare
2132:
On the basis of interfacial energies, the profile of a surface droplet or a liquid bridge between two surfaces can be described by the
3104:
Chibowski, Emil (2008). "Surface free energy of sulfur—Revisited I. Yellow and orange samples solidified against glass surface".
3444:"About the possibility of experimentally measuring an equilibrium contact angle and its theoretical and practical consequences"
2427:
3724:
3688:
3407:
3271:
2136:. This equation is applicable for three-dimensional axisymmetric conditions and is highly non-linear. This is due to the
2084:
is the roughness ratio. The roughness ratio is defined as the ratio between the actual and projected solid surface area.
175:
2921:
3551:
3744:
3030:"Numerical simulation of droplet behavior on an inclined plate using the Moving Particle Semi-implicit method"
3069:
Tadmor, Rafael (2004). "Line energy and the relation between advancing, receding, and Young contact angles".
2543:
581:
373:
278:
73:
2133:
113:
3754:
3749:
2724:
Dynamic
Wilhelmy method applied to single fibers to measure advancing and receding contact angles.
2659:
2632:
3536:
559:
264:{\displaystyle \gamma _{\rm {SG}}-\gamma _{\rm {SL}}-\gamma _{\rm {LG}}\cos \theta _{\rm {C}}=0\,}
3643:
573:
3354:
3667:, 2nd revised edition, Elsevier Scientific Publishing Company, Amsterdam-Oxford-New York (1976)
2781:
2750:
2685:
2653:
2594:
2140:
term which includes products of first- and second-order derivatives of the drop shape function
3397:
2673:
63:
3552:"An experimental procedure to obtain the equilibrium contact angle from the Wilhelmy method"
3292:
2143:
104:
3614:
3330:
3280:
3156:
3113:
2484:
exhibit hydrophobic surfaces. Highly hydrophobic surfaces made of low surface energy (e.g.
85:
1487:, the flattening of the contact angle at very small scales, and contact angle hysteresis.
8:
3759:
3653:
2727:
1533:, i.e., a minimal amount of work per unit distance is required to move the contact line.
577:
3618:
3424:
3334:
3284:
3160:
3117:
2703:
2104:
3714:
3702:
3505:
2975:
2894:
2846:
2828:
66:
and the tangent on the solid–liquid interface at their intersection. It quantifies the
3720:
3706:
3694:
3684:
3497:
3489:
3403:
3346:
3296:
3251:
3216:
3129:
3086:
3051:
3010:
2979:
2967:
2927:
2917:
2898:
2886:
2771:
2501:
3509:
3199:
Wenzel, Robert N. (1936-08-01). "Resistance of Solid
Surfaces to Wetting by Water".
2850:
2639:
3676:
3622:
3602:
3566:
3532:
3481:
3469:
3338:
3288:
3243:
3208:
3164:
3121:
3078:
3041:
3002:
2959:
2876:
2842:
2838:
2819:
Shi, Z.; et al. (2018). "Dynamic contact angle hysteresis in liquid bridges".
2476:
and if the water contact angle is larger than 90°, the solid surface is considered
2098:
1580:
as was shown theoretically by Tadmor and confirmed experimentally by
Chibowski as,
361:{\displaystyle \gamma _{\rm {LG}}(1+\cos \theta _{\rm {C}})=\Delta W_{\rm {SLG}}\,}
2455:
A water drop on a lotus leaf surface showing contact angles of approximately 147°.
3006:
2963:
2786:
2489:
1530:
155:
56:
3395:
112:
The theoretical description of contact angle arises from the consideration of a
3739:
3342:
3125:
2713:
2137:
1538:
568:
Schematic
Diagrams for droplets on flat (a) concave (b) and convex (c) surfaces
560:
Contact angle prediction while accounting for line tension and
Laplace pressure
137:
117:
3680:
3671:
Yuan, Yuehua; Lee, T. Randall (2013). "Contact Angle and Wetting Properties".
3485:
3441:
3168:
3733:
3698:
3493:
3468:
Huhtamäki, Tommi; Tian, Xuelin; Korhonen, Juuso T.; Ras, Robin H. A. (2018).
3300:
3255:
3234:
Cassie, A. B. D.; Baxter, S. (1944-01-01). "Wettability of porous surfaces".
3220:
3055:
3014:
2971:
2890:
2497:
3626:
3571:
3549:
3501:
3350:
3269:
Marmur, Abraham (2009-07-06). "Solid-Surface Characterization by Wetting".
3133:
3090:
2881:
2864:
2485:
2931:
2578:
BIS(Tridecafluoro-1,1,2,2-tetrahydrooctyl)dimethylsiloxymethylchlorosilane
408:
is the solid – liquid adhesion energy per unit area when in the medium G.
3442:
Volpe, C. D.; Brugnara, M.; Maniglio, D.; Siboni, S.; Wangdu, T. (2006).
3247:
3046:
3029:
2776:
133:
93:
68:
3212:
2707:
Measuring dynamic contact angle of a rod/fiber with a force tensiometer.
55:
surface where they meet. More specifically, it is the angle between the
23:
Schematic of a liquid drop showing the quantities in the Young equation.
2766:
2692:
2627:
2477:
2473:
1991:
80:
3082:
2451:
2439:
2535:
Henicosyl-1,1,2,2-tetrahydrododecyldimethyltris(dimethylaminosilane)
3470:"Surface-wetting characterization using contact-angle measurements"
2833:
1549:
of liquid is removed from a drop, the contact angle will decrease.
564:
274:
3429:
209th Electrochemical Society meeting, May 7–12, 2006, Denver, CO
3183:"Influence of surface roughness on contact angle and wettability"
2791:
2481:
2465:
544:
48:
3648:
Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves
2821:
Colloids and Surfaces A: Physicochemical and Engineering Aspects
19:
121:
45:
3399:
Surface design: applications in bioscience and nanotechnology
3396:
Renate Förch; Holger Schönherr; A. Tobias A. Jenkins (2009).
2570:
Tridecafluoro-1,1,2,2-tetrahydrooctyltrichlorosilane – (FOTS)
2469:
2461:
2444:
129:
125:
108:
Cloth, treated to be hydrophobic, shows a high contact angle.
60:
52:
41:
2744:
556:
and overestimates its value by several orders of magnitude.
2554:
Nonafluoro-1,1,2,2-tetrahydrohexyltris(dimethylamino)silane
3550:
Volpe, C. D.; Maniglio, D.; Siboni, S.; Morra, M. (2001).
3522:
3425:"Choice of precursors in Vapor-phase Surface Modification"
1512:
although the term is also used to describe the expression
16:
Angle between a liquid–vapor interface and a solid surface
3147:
de Gennes, P.G. (1985). "Wetting: statics and dynamics".
2869:
Philosophical Transactions of the Royal Society of London
3467:
3422:
2001:
2443:
Image from a video contact angle device. Water drop on
2544:
Heptadecafluoro-1,1,2,2-tetrahydrodecyltrichlorosilane
3675:. Springer Series in Surface Sciences. Vol. 51.
2181:
2146:
2107:
2017:
1736:
1588:
1277:
1116:
839:
596:
425:
376:
287:
273:
The contact angle can also be related to the work of
184:
154:, and the liquid–vapor interfacial energy (i.e. the
3600:
3585:
3021:
2679:
2416:
2167:
2116:
2059:{\displaystyle \cos \theta _{m}=r\cos \theta _{Y}}
2058:
1979:
1718:
1473:
1251:
1100:
820:
572:With improvements in measuring techniques such as
529:
400:
360:
263:
3313:
2647:
1093:
949:
3731:
3027:
2945:
2943:
2941:
2731:Single-fiber meniscus contact angle measurement.
2658:The sessile drop contact angle is measured by a
2562:3,3,3,4,4,5,5,6,6-Nonafluorohexyltrichlorosilane
2992:
2735:
2719:
3028:Hattori, Tsuyoshi; Koshizuka, Seiichi (2019).
3537:10.1615/InterfacPhenomHeatTransfer.2013007038
3316:"Anisotropy in the wetting of rough surfaces"
2938:
2756:of weight as a function of time is measured.
3233:
2507:
1537:measurements such as force tensiometry (aka
411:
2949:
2912:Gibbs, J. Willard (Josiah Willard) (1961).
2519:Effect of surface fluorine on contact angle
1490:
174:is determined from these quantities by the
2698:
2666:
2127:
1998:measurably time-dependent contact angles.
3646:, Françoise Brochard-Wyart, David Quéré,
3570:
3376:
3374:
3314:Chen Y, He B, Lee J, Patankar NA (2005).
3146:
3103:
3045:
2880:
2865:"III. An essay on the cohesion of fluids"
2832:
2745:Washburn's equation capillary rise method
2434:
2091:
1036:
966:
873:
357:
260:
147:, the solid–liquid interfacial energy by
3594:
3579:
3383:Contact Angle, Wettability, and Adhesion
3323:Journal of Colloid and Interface Science
3106:Journal of Colloid and Interface Science
2726:
2702:
2638:
2626:
2450:
2438:
563:
103:
18:
3670:
3588:Contact Angle, Wettability and Adhesion
3525:Interfacial Phenomena and Heat Transfer
3516:
3448:Contact Angle, Wettability and Adhesion
3293:10.1146/annurev.matsci.38.060407.132425
3140:
72:of a solid surface by a liquid via the
3732:
3381:Zisman, W.A. (1964). F. Fowkes (ed.).
3380:
3371:
3268:
3201:Industrial & Engineering Chemistry
3198:
3068:
2613:Pentafluorophenylpropyltrichlorosilane
2468:surfaces, although the presence of an
2428:elliptic partial differential equation
3463:
3461:
2911:
2814:
2812:
2810:
2808:
2635:is used to measure the contact angle.
2002:Effect of roughness to contact angles
165:, then the equilibrium contact angle
3559:Oil & Gas Science and Technology
2622:
401:{\displaystyle \Delta W_{\rm {SLG}}}
3272:Annual Review of Materials Research
3236:Transactions of the Faraday Society
3097:
3062:
2818:
2605:10-Undecenyltrichlorosilane – (V11)
13:
3637:
3458:
2805:
1958:
1930:
1901:
1865:
1840:
1812:
1783:
1747:
1703:
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1201:
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136:liquid phase.) If the solid–vapor
14:
3771:
3658:Intermolecular and Surface Forces
3423:Kobrin, B.; Zhang, T.; Chinn, J.
99:
3603:"The Dynamics of Capillary Flow"
3543:
3435:
3416:
3389:
3307:
3262:
3227:
3192:
3175:
2680:The dynamic sessile drop method
2586:Dodecyltrichlorosilane – (DDTS)
2080:is the Young contact angle and
2073:is the measured contact angle,
1212:
1180:
3034:Mechanical Engineering Journal
2986:
2905:
2857:
2843:10.1016/j.colsurfa.2018.07.004
2648:The static sessile drop method
2391:
2340:
2322:
2294:
2236:
2208:
2162:
2150:
1468:
1409:
1079:
1060:
1055:
1037:
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990:
985:
967:
938:
919:
916:
904:
858:
846:
330:
303:
1:
2798:
3660:, Academic Press (1985–2004)
3601:Washburn, Edward W. (1921).
3007:10.1016/j.molliq.2017.10.134
2995:Journal of Molecular Liquids
2964:10.1016/j.molliq.2019.02.039
2952:Journal of Molecular Liquids
2736:Single-fiber meniscus method
2720:Single-fiber Wilhelmy method
2431:energy minimisation method.
582:scanning electron microscope
7:
2759:
2643:Dynamic sessile drop method
2530:on polished silicon (deg.)
2088:angles with real surfaces.
10:
3776:
3673:Surface Science Techniques
3402:. Wiley-VCH. p. 471.
3343:10.1016/j.jcis.2004.07.038
3126:10.1016/j.jcis.2007.10.059
2748:
2683:
2651:
128:phase (S), and the gas or
96:and purity of the liquid.
3681:10.1007/978-3-642-34243-1
3486:10.1038/s41596-018-0003-z
3169:10.1103/RevModPhys.57.827
3149:Reviews of Modern Physics
2508:Control of contact angles
1562:) can be calculated from
412:Modified Young’s equation
114:thermodynamic equilibrium
3745:Condensed matter physics
3040:(5): 19-00204–19-00204.
2660:contact angle goniometer
2633:contact angle goniometer
2447:, with reflection below.
1491:Contact angle hysteresis
3716:Contact Angle Made Easy
3644:Pierre-Gilles de Gennes
2875:: 65–87. January 1805.
2699:Dynamic Wilhelmy method
2667:The pendant drop method
2128:Contact angle curvature
574:atomic force microscopy
543:is the line tension in
3665:Properties of Polymers
3627:10.1103/PhysRev.17.273
2916:. Dover Publications.
2882:10.1098/rstl.1805.0005
2782:Sessile drop technique
2732:
2708:
2686:Sessile drop technique
2654:Sessile drop technique
2644:
2636:
2595:Dimethyldichlorosilane
2456:
2448:
2435:Typical contact angles
2418:
2169:
2168:{\displaystyle f(x,y)}
2134:Young–Laplace equation
2118:
2092:Dynamic contact angles
2060:
1981:
1720:
1475:
1253:
1102:
822:
569:
531:
402:
362:
265:
109:
24:
3385:. ACS. pp. 1–51.
2730:
2706:
2642:
2630:
2454:
2442:
2419:
2170:
2119:
2061:
1982:
1721:
1476:
1254:
1103:
823:
567:
532:
403:
363:
266:
107:
86:molecular interaction
22:
3719:, ramé-hart (2013),
3572:10.2516/ogst:2001002
3248:10.1039/tf9444000546
3047:10.1299/mej.19-00204
2522:Water contact angle
2179:
2144:
2105:
2015:
1734:
1586:
1275:
1114:
837:
594:
423:
374:
285:
279:Young–Dupré equation
182:
3663:D.W. Van Krevelen,
3654:Jacob Israelachvili
3619:1921PhRv...17..273W
3335:2005JCIS..281..458C
3285:2009AnRMS..39..473M
3213:10.1021/ie50320a024
3161:1985RvMP...57..827D
3118:2008JCIS..319..505C
2751:Washburn's equation
578:confocal microscopy
2733:
2709:
2645:
2637:
2502:waterproof fabrics
2457:
2449:
2414:
2165:
2117:{\displaystyle Ca}
2114:
2056:
1977:
1975:
1716:
1471:
1249:
1098:
818:
570:
527:
398:
358:
261:
138:interfacial energy
116:between the three
110:
25:
3725:978-1-300-66298-3
3690:978-3-642-34242-4
3650:, Springer (2004)
3409:978-3-527-40789-7
3083:10.1021/la049410h
2914:Scientific papers
2772:Meniscus (liquid)
2623:Measuring methods
2620:
2619:
2409:
2203:
1971:
1965:
1853:
1847:
1710:
1407:
1377:
1367:
1342:
1244:
1207:
1175:
1089:
1019:
890:
816:
784:
759:
727:
702:
645:
525:
515:
490:
3767:
3710:
3631:
3630:
3598:
3592:
3591:
3583:
3577:
3576:
3574:
3556:
3547:
3541:
3540:
3520:
3514:
3513:
3480:(7): 1521–1538.
3474:Nature Protocols
3465:
3456:
3455:
3439:
3433:
3432:
3420:
3414:
3413:
3393:
3387:
3386:
3378:
3369:
3368:
3366:
3365:
3359:
3353:. Archived from
3320:
3311:
3305:
3304:
3266:
3260:
3259:
3231:
3225:
3224:
3196:
3190:
3189:
3187:
3179:
3173:
3172:
3144:
3138:
3137:
3101:
3095:
3094:
3066:
3060:
3059:
3049:
3025:
3019:
3018:
2990:
2984:
2983:
2947:
2936:
2935:
2909:
2903:
2902:
2884:
2861:
2855:
2854:
2836:
2816:
2516:
2515:
2490:superhydrophobic
2423:
2421:
2420:
2415:
2410:
2408:
2407:
2406:
2402:
2389:
2388:
2383:
2382:
2381:
2367:
2366:
2361:
2360:
2359:
2338:
2337:
2336:
2321:
2320:
2315:
2314:
2313:
2290:
2289:
2277:
2276:
2267:
2266:
2251:
2250:
2235:
2234:
2229:
2228:
2227:
2206:
2204:
2196:
2191:
2190:
2174:
2172:
2171:
2166:
2123:
2121:
2120:
2115:
2099:capillary number
2083:
2079:
2072:
2065:
2063:
2062:
2057:
2055:
2054:
2033:
2032:
1986:
1984:
1983:
1978:
1976:
1972:
1970:
1964:
1963:
1962:
1961:
1948:
1947:
1935:
1934:
1933:
1907:
1906:
1905:
1904:
1891:
1890:
1880:
1879:
1870:
1869:
1868:
1854:
1852:
1846:
1845:
1844:
1843:
1830:
1829:
1817:
1816:
1815:
1789:
1788:
1787:
1786:
1773:
1772:
1762:
1761:
1752:
1751:
1750:
1725:
1723:
1722:
1717:
1715:
1711:
1709:
1708:
1707:
1706:
1693:
1692:
1691:
1680:
1679:
1678:
1677:
1661:
1660:
1659:
1646:
1645:
1644:
1628:
1627:
1626:
1615:
1600:
1599:
1598:
1579:
1570:
1561:
1528:
1511:
1486:
1480:
1478:
1477:
1472:
1461:
1460:
1442:
1441:
1408:
1406:
1405:
1404:
1403:
1383:
1378:
1370:
1368:
1366:
1365:
1364:
1348:
1343:
1341:
1340:
1339:
1326:
1325:
1324:
1323:
1307:
1306:
1305:
1291:
1268:
1258:
1256:
1255:
1250:
1245:
1243:
1242:
1241:
1240:
1220:
1208:
1206:
1205:
1204:
1188:
1176:
1174:
1173:
1172:
1159:
1158:
1157:
1156:
1140:
1139:
1138:
1124:
1107:
1105:
1104:
1099:
1097:
1096:
1090:
1088:
1087:
1086:
1058:
1025:
1020:
1018:
1017:
1016:
988:
955:
953:
952:
946:
945:
891:
886:
875:
827:
825:
824:
819:
817:
815:
814:
813:
812:
795:
787:
785:
783:
782:
781:
765:
760:
758:
757:
756:
755:
738:
730:
728:
726:
725:
724:
708:
703:
701:
700:
699:
686:
685:
684:
683:
667:
666:
665:
651:
646:
644:
643:
642:
641:
624:
623:
622:
621:
604:
587:
555:
550:
542:
536:
534:
533:
528:
526:
518:
516:
514:
513:
512:
496:
491:
489:
488:
487:
474:
473:
472:
471:
455:
454:
453:
439:
407:
405:
404:
399:
397:
396:
395:
367:
365:
364:
359:
356:
355:
354:
329:
328:
327:
302:
301:
300:
270:
268:
267:
262:
253:
252:
251:
235:
234:
233:
217:
216:
215:
199:
198:
197:
173:
164:
153:
146:
39:
3775:
3774:
3770:
3769:
3768:
3766:
3765:
3764:
3755:Surface science
3750:Fluid mechanics
3730:
3729:
3691:
3640:
3638:Further reading
3635:
3634:
3607:Physical Review
3599:
3595:
3584:
3580:
3554:
3548:
3544:
3521:
3517:
3466:
3459:
3440:
3436:
3421:
3417:
3410:
3394:
3390:
3379:
3372:
3363:
3361:
3357:
3318:
3312:
3308:
3267:
3263:
3232:
3228:
3197:
3193:
3185:
3181:
3180:
3176:
3145:
3141:
3102:
3098:
3077:(18): 7659–64.
3067:
3063:
3026:
3022:
2991:
2987:
2948:
2939:
2924:
2910:
2906:
2863:
2862:
2858:
2817:
2806:
2801:
2796:
2787:Surface tension
2762:
2753:
2747:
2738:
2722:
2701:
2688:
2682:
2669:
2656:
2650:
2625:
2510:
2437:
2398:
2394:
2390:
2384:
2377:
2373:
2372:
2371:
2362:
2355:
2351:
2350:
2349:
2339:
2329:
2325:
2316:
2309:
2305:
2304:
2303:
2282:
2278:
2272:
2268:
2262:
2258:
2243:
2239:
2230:
2223:
2219:
2218:
2217:
2207:
2205:
2195:
2186:
2182:
2180:
2177:
2176:
2145:
2142:
2141:
2130:
2106:
2103:
2102:
2094:
2081:
2078:
2074:
2071:
2067:
2050:
2046:
2028:
2024:
2016:
2013:
2012:
2004:
1974:
1973:
1966:
1957:
1956:
1952:
1943:
1939:
1929:
1928:
1924:
1908:
1900:
1899:
1895:
1886:
1882:
1881:
1878:
1871:
1864:
1863:
1859:
1856:
1855:
1848:
1839:
1838:
1834:
1825:
1821:
1811:
1810:
1806:
1790:
1782:
1781:
1777:
1768:
1764:
1763:
1760:
1753:
1746:
1745:
1741:
1737:
1735:
1732:
1731:
1702:
1701:
1697:
1687:
1686:
1682:
1681:
1673:
1672:
1668:
1655:
1654:
1650:
1640:
1639:
1635:
1622:
1621:
1617:
1616:
1614:
1610:
1594:
1593:
1589:
1587:
1584:
1583:
1578:
1572:
1569:
1563:
1560:
1554:
1531:static friction
1527:
1520:
1513:
1510:
1503:
1497:
1493:
1484:
1456:
1452:
1437:
1433:
1396:
1395:
1391:
1387:
1382:
1369:
1357:
1356:
1352:
1347:
1332:
1331:
1327:
1316:
1315:
1311:
1298:
1297:
1293:
1292:
1290:
1276:
1273:
1272:
1263:
1233:
1232:
1228:
1224:
1219:
1197:
1196:
1192:
1187:
1165:
1164:
1160:
1149:
1148:
1144:
1131:
1130:
1126:
1125:
1123:
1115:
1112:
1111:
1092:
1091:
1082:
1078:
1059:
1026:
1024:
1012:
1008:
989:
956:
954:
948:
947:
941:
937:
876:
874:
838:
835:
834:
805:
804:
800:
796:
788:
786:
774:
773:
769:
764:
748:
747:
743:
739:
731:
729:
717:
716:
712:
707:
692:
691:
687:
676:
675:
671:
658:
657:
653:
652:
650:
634:
633:
629:
625:
614:
613:
609:
605:
603:
595:
592:
591:
585:
562:
553:
548:
540:
517:
505:
504:
500:
495:
480:
479:
475:
464:
463:
459:
446:
445:
441:
440:
438:
424:
421:
420:
414:
385:
384:
380:
375:
372:
371:
344:
343:
339:
323:
322:
318:
293:
292:
288:
286:
283:
282:
247:
246:
242:
226:
225:
221:
208:
207:
203:
190:
189:
185:
183:
180:
179:
172:
166:
163:
159:
156:surface tension
152:
148:
145:
141:
124:phase (L), the
102:
57:surface tangent
38:
32:
17:
12:
11:
5:
3773:
3763:
3762:
3757:
3752:
3747:
3742:
3728:
3727:
3711:
3689:
3668:
3661:
3651:
3639:
3636:
3633:
3632:
3593:
3578:
3542:
3515:
3457:
3434:
3415:
3408:
3388:
3370:
3329:(2): 458–464.
3306:
3279:(1): 473–489.
3261:
3226:
3207:(8): 988–994.
3191:
3174:
3155:(3): 827–863.
3139:
3096:
3061:
3020:
2985:
2937:
2923:978-0486607214
2922:
2904:
2856:
2803:
2802:
2800:
2797:
2795:
2794:
2789:
2784:
2779:
2774:
2769:
2763:
2761:
2758:
2749:Main article:
2746:
2743:
2737:
2734:
2721:
2718:
2700:
2697:
2684:Main article:
2681:
2678:
2668:
2665:
2652:Main article:
2649:
2646:
2624:
2621:
2618:
2617:
2614:
2610:
2609:
2606:
2602:
2601:
2598:
2591:
2590:
2587:
2583:
2582:
2579:
2575:
2574:
2571:
2567:
2566:
2563:
2559:
2558:
2555:
2551:
2550:
2547:
2540:
2539:
2536:
2532:
2531:
2528:
2524:
2523:
2520:
2509:
2506:
2498:non-stick pans
2436:
2433:
2413:
2405:
2401:
2397:
2393:
2387:
2380:
2376:
2370:
2365:
2358:
2354:
2348:
2345:
2342:
2335:
2332:
2328:
2324:
2319:
2312:
2308:
2302:
2299:
2296:
2293:
2288:
2285:
2281:
2275:
2271:
2265:
2261:
2257:
2254:
2249:
2246:
2242:
2238:
2233:
2226:
2222:
2216:
2213:
2210:
2202:
2199:
2194:
2189:
2185:
2164:
2161:
2158:
2155:
2152:
2149:
2138:mean curvature
2129:
2126:
2113:
2110:
2093:
2090:
2076:
2069:
2053:
2049:
2045:
2042:
2039:
2036:
2031:
2027:
2023:
2020:
2003:
2000:
1969:
1960:
1955:
1951:
1946:
1942:
1938:
1932:
1927:
1923:
1920:
1917:
1914:
1911:
1903:
1898:
1894:
1889:
1885:
1877:
1874:
1872:
1867:
1862:
1858:
1857:
1851:
1842:
1837:
1833:
1828:
1824:
1820:
1814:
1809:
1805:
1802:
1799:
1796:
1793:
1785:
1780:
1776:
1771:
1767:
1759:
1756:
1754:
1749:
1744:
1740:
1739:
1714:
1705:
1700:
1696:
1690:
1685:
1676:
1671:
1667:
1664:
1658:
1653:
1649:
1643:
1638:
1634:
1631:
1625:
1620:
1613:
1609:
1606:
1603:
1597:
1592:
1576:
1567:
1558:
1525:
1518:
1508:
1501:
1492:
1489:
1470:
1467:
1464:
1459:
1455:
1451:
1448:
1445:
1440:
1436:
1432:
1429:
1426:
1423:
1420:
1417:
1414:
1411:
1402:
1399:
1394:
1390:
1386:
1381:
1376:
1373:
1363:
1360:
1355:
1351:
1346:
1338:
1335:
1330:
1322:
1319:
1314:
1310:
1304:
1301:
1296:
1289:
1286:
1283:
1280:
1248:
1239:
1236:
1231:
1227:
1223:
1218:
1215:
1211:
1203:
1200:
1195:
1191:
1186:
1183:
1179:
1171:
1168:
1163:
1155:
1152:
1147:
1143:
1137:
1134:
1129:
1122:
1119:
1095:
1085:
1081:
1077:
1074:
1071:
1068:
1065:
1062:
1057:
1054:
1051:
1048:
1045:
1042:
1039:
1035:
1032:
1029:
1023:
1015:
1011:
1007:
1004:
1001:
998:
995:
992:
987:
984:
981:
978:
975:
972:
969:
965:
962:
959:
951:
944:
940:
936:
933:
930:
927:
924:
921:
918:
915:
912:
909:
906:
903:
900:
897:
894:
889:
885:
882:
879:
872:
869:
866:
863:
860:
857:
854:
851:
848:
845:
842:
811:
808:
803:
799:
794:
791:
780:
777:
772:
768:
763:
754:
751:
746:
742:
737:
734:
723:
720:
715:
711:
706:
698:
695:
690:
682:
679:
674:
670:
664:
661:
656:
649:
640:
637:
632:
628:
620:
617:
612:
608:
602:
599:
561:
558:
524:
521:
511:
508:
503:
499:
494:
486:
483:
478:
470:
467:
462:
458:
452:
449:
444:
437:
434:
431:
428:
413:
410:
394:
391:
388:
383:
379:
353:
350:
347:
342:
338:
335:
332:
326:
321:
317:
314:
311:
308:
305:
299:
296:
291:
259:
256:
250:
245:
241:
238:
232:
229:
224:
220:
214:
211:
206:
202:
196:
193:
188:
176:Young equation
170:
161:
150:
143:
140:is denoted by
101:
100:Thermodynamics
98:
74:Young equation
59:on the liquid–
36:
15:
9:
6:
4:
3:
2:
3772:
3761:
3758:
3756:
3753:
3751:
3748:
3746:
3743:
3741:
3738:
3737:
3735:
3726:
3722:
3718:
3717:
3712:
3708:
3704:
3700:
3696:
3692:
3686:
3682:
3678:
3674:
3669:
3666:
3662:
3659:
3655:
3652:
3649:
3645:
3642:
3641:
3628:
3624:
3620:
3616:
3612:
3608:
3604:
3597:
3589:
3582:
3573:
3568:
3564:
3560:
3553:
3546:
3538:
3534:
3530:
3526:
3519:
3511:
3507:
3503:
3499:
3495:
3491:
3487:
3483:
3479:
3475:
3471:
3464:
3462:
3453:
3449:
3445:
3438:
3430:
3426:
3419:
3411:
3405:
3401:
3400:
3392:
3384:
3377:
3375:
3360:on 2017-08-10
3356:
3352:
3348:
3344:
3340:
3336:
3332:
3328:
3324:
3317:
3310:
3302:
3298:
3294:
3290:
3286:
3282:
3278:
3274:
3273:
3265:
3257:
3253:
3249:
3245:
3241:
3237:
3230:
3222:
3218:
3214:
3210:
3206:
3202:
3195:
3184:
3178:
3170:
3166:
3162:
3158:
3154:
3150:
3143:
3135:
3131:
3127:
3123:
3119:
3115:
3112:(2): 505–13.
3111:
3107:
3100:
3092:
3088:
3084:
3080:
3076:
3072:
3065:
3057:
3053:
3048:
3043:
3039:
3035:
3031:
3024:
3016:
3012:
3008:
3004:
3000:
2996:
2989:
2981:
2977:
2973:
2969:
2965:
2961:
2957:
2953:
2946:
2944:
2942:
2933:
2929:
2925:
2919:
2915:
2908:
2900:
2896:
2892:
2888:
2883:
2878:
2874:
2870:
2866:
2860:
2852:
2848:
2844:
2840:
2835:
2830:
2826:
2822:
2815:
2813:
2811:
2809:
2804:
2793:
2790:
2788:
2785:
2783:
2780:
2778:
2775:
2773:
2770:
2768:
2765:
2764:
2757:
2752:
2742:
2729:
2725:
2717:
2715:
2705:
2696:
2694:
2687:
2677:
2675:
2664:
2661:
2655:
2641:
2634:
2629:
2615:
2612:
2611:
2607:
2604:
2603:
2599:
2596:
2593:
2592:
2588:
2585:
2584:
2580:
2577:
2576:
2572:
2569:
2568:
2564:
2561:
2560:
2556:
2553:
2552:
2548:
2545:
2542:
2541:
2537:
2534:
2533:
2529:
2526:
2525:
2521:
2518:
2517:
2514:
2505:
2503:
2499:
2493:
2491:
2487:
2483:
2479:
2475:
2471:
2467:
2463:
2453:
2446:
2441:
2432:
2429:
2426:Solving this
2424:
2411:
2403:
2399:
2395:
2385:
2378:
2374:
2368:
2363:
2356:
2352:
2346:
2343:
2333:
2330:
2326:
2317:
2310:
2306:
2300:
2297:
2291:
2286:
2283:
2279:
2273:
2269:
2263:
2259:
2255:
2252:
2247:
2244:
2240:
2231:
2224:
2220:
2214:
2211:
2200:
2197:
2192:
2187:
2183:
2159:
2156:
2153:
2147:
2139:
2135:
2125:
2111:
2108:
2100:
2089:
2085:
2051:
2047:
2043:
2040:
2037:
2034:
2029:
2025:
2021:
2018:
2008:
1999:
1995:
1993:
1987:
1967:
1953:
1949:
1944:
1940:
1936:
1925:
1921:
1918:
1915:
1912:
1909:
1896:
1892:
1887:
1883:
1875:
1873:
1860:
1849:
1835:
1831:
1826:
1822:
1818:
1807:
1803:
1800:
1797:
1794:
1791:
1778:
1774:
1769:
1765:
1757:
1755:
1742:
1729:
1726:
1712:
1698:
1694:
1683:
1669:
1665:
1662:
1651:
1647:
1636:
1632:
1629:
1618:
1611:
1607:
1604:
1601:
1590:
1581:
1575:
1566:
1557:
1550:
1546:
1542:
1540:
1539:Wilhemy-Plate
1534:
1532:
1524:
1517:
1507:
1500:
1488:
1481:
1465:
1462:
1457:
1453:
1449:
1446:
1443:
1438:
1434:
1430:
1427:
1424:
1421:
1418:
1415:
1412:
1392:
1388:
1384:
1379:
1374:
1371:
1353:
1349:
1344:
1328:
1312:
1308:
1294:
1287:
1284:
1281:
1278:
1270:
1266:
1259:
1246:
1229:
1225:
1221:
1216:
1213:
1209:
1193:
1189:
1184:
1181:
1177:
1161:
1145:
1141:
1127:
1120:
1117:
1108:
1083:
1075:
1072:
1069:
1066:
1063:
1052:
1049:
1046:
1043:
1040:
1033:
1030:
1027:
1021:
1013:
1005:
1002:
999:
996:
993:
982:
979:
976:
973:
970:
963:
960:
957:
942:
934:
931:
928:
925:
922:
913:
910:
907:
901:
898:
895:
892:
887:
883:
880:
877:
870:
867:
864:
861:
855:
852:
849:
843:
840:
832:
828:
801:
797:
792:
789:
770:
766:
761:
744:
740:
735:
732:
713:
709:
704:
688:
672:
668:
654:
647:
630:
626:
610:
606:
600:
597:
589:
583:
579:
575:
566:
557:
546:
537:
522:
519:
501:
497:
492:
476:
460:
456:
442:
435:
432:
429:
426:
418:
409:
381:
368:
340:
333:
319:
315:
312:
309:
306:
289:
280:
276:
271:
257:
254:
243:
239:
236:
222:
218:
204:
200:
186:
177:
169:
157:
139:
135:
131:
127:
123:
119:
115:
106:
97:
95:
89:
87:
82:
77:
75:
71:
70:
65:
62:
58:
54:
50:
47:
43:
35:
30:
29:contact angle
21:
3715:
3713:Clegg, Carl
3672:
3664:
3657:
3647:
3610:
3606:
3596:
3590:. Mass. VSP.
3587:
3581:
3562:
3558:
3545:
3528:
3524:
3518:
3477:
3473:
3451:
3447:
3437:
3428:
3418:
3398:
3391:
3382:
3362:. Retrieved
3355:the original
3326:
3322:
3309:
3276:
3270:
3264:
3239:
3235:
3229:
3204:
3200:
3194:
3177:
3152:
3148:
3142:
3109:
3105:
3099:
3074:
3070:
3064:
3037:
3033:
3023:
2998:
2994:
2988:
2955:
2951:
2913:
2907:
2872:
2868:
2859:
2824:
2820:
2754:
2739:
2723:
2710:
2689:
2670:
2657:
2511:
2494:
2458:
2425:
2131:
2095:
2086:
2009:
2005:
1996:
1988:
1730:
1727:
1582:
1573:
1564:
1555:
1551:
1547:
1543:
1535:
1522:
1515:
1505:
1498:
1494:
1482:
1271:
1264:
1260:
1109:
833:
829:
590:
571:
538:
419:
415:
369:
272:
167:
111:
90:
78:
67:
33:
28:
26:
3001:: 920–926.
2958:: 196–203.
2827:: 365–371.
2777:Porosimetry
2486:fluorinated
2478:hydrophobic
2474:hydrophilic
94:temperature
69:wettability
3760:Hysteresis
3734:Categories
3613:(3): 273.
3364:2017-03-31
2834:1712.04703
2799:References
2767:Goniometer
2693:hysteresis
2492:surfaces.
1992:hysteresis
134:immiscible
81:hysteresis
44:between a
3707:137147527
3699:0931-5195
3531:: 29–49.
3494:1754-2189
3454:: 79–100.
3301:1531-7331
3256:0014-7672
3221:0019-7866
3056:2187-9745
3015:0167-7322
2980:104412970
2972:0167-7322
2899:116124581
2891:0261-0523
2716:balance.
2527:Precursor
2253:−
2184:κ
2048:θ
2044:
2026:θ
2022:
1954:θ
1950:
1926:θ
1922:
1913:−
1897:θ
1893:
1836:θ
1832:
1808:θ
1804:
1795:−
1779:θ
1775:
1670:θ
1666:
1637:θ
1633:
1608:
1591:θ
1541:method).
1466:θ
1463:
1450:−
1447:θ
1444:
1428:−
1425:θ
1422:
1393:γ
1385:γ
1380:−
1354:γ
1350:κ
1329:γ
1313:γ
1309:−
1295:γ
1285:θ
1282:
1230:γ
1222:γ
1194:γ
1190:κ
1162:γ
1146:γ
1142:−
1128:γ
1076:θ
1073:
1053:θ
1050:
1034:θ
1031:
1022:∓
1006:α
1003:
983:α
980:
964:α
961:
935:θ
932:
914:α
911:∓
908:θ
902:
893:±
884:α
881:
856:α
853:∓
850:θ
844:
771:γ
762:−
714:γ
710:κ
705:−
689:γ
673:γ
669:−
655:γ
502:γ
498:κ
477:γ
461:γ
457:−
443:γ
433:θ
430:
378:Δ
337:Δ
320:θ
316:
290:γ
244:θ
240:
223:γ
219:−
205:γ
201:−
187:γ
64:interface
40:) is the
3565:: 9–22.
3510:51605807
3502:29988109
3351:15571703
3134:18177886
3091:15323516
3071:Langmuir
2851:51916594
2760:See also
2714:Wilhelmy
2597:– (DDMS)
2546:– (FDTS)
2482:polymers
2462:metallic
2101:, noted
277:via the
275:adhesion
31:(symbol
3615:Bibcode
3331:Bibcode
3281:Bibcode
3242:: 546.
3157:Bibcode
3114:Bibcode
2792:Wetting
2741:fiber.
2480:. Many
2466:ceramic
1110:where
545:Newtons
49:surface
3723:
3705:
3697:
3687:
3508:
3500:
3492:
3406:
3349:
3299:
3254:
3219:
3132:
3089:
3054:
3013:
2978:
2970:
2932:964884
2930:
2920:
2897:
2889:
2849:
2608:100.0
2600:103.0
2589:105.0
2581:107.0
2573:108.0
2565:108.0
2557:110.0
2549:110.0
2538:118.0
2066:where
1728:where
1605:arccos
1574:θ
1565:θ
1556:θ
1523:θ
1521:– cos
1516:θ
1506:θ
1499:θ
1265:α
580:, and
539:where
370:where
168:θ
160:γ
149:γ
142:γ
122:liquid
120:: the
118:phases
51:and a
46:liquid
3740:Angle
3703:S2CID
3555:(PDF)
3506:S2CID
3358:(PDF)
3319:(PDF)
3186:(PDF)
2976:S2CID
2895:S2CID
2847:S2CID
2829:arXiv
2616:90.0
2470:oxide
2445:glass
158:) by
130:vapor
126:solid
61:vapor
53:solid
42:angle
3721:ISBN
3695:ISSN
3685:ISBN
3498:PMID
3490:ISSN
3404:ISBN
3347:PMID
3297:ISSN
3252:ISSN
3217:ISSN
3130:PMID
3087:PMID
3052:ISSN
3011:ISSN
2968:ISSN
2928:OCLC
2918:ISBN
2887:ISSN
2500:and
1571:and
1514:cos
586:V dP
547:and
27:The
3677:doi
3623:doi
3567:doi
3533:doi
3482:doi
3339:doi
3327:281
3289:doi
3244:doi
3209:doi
3165:doi
3122:doi
3110:319
3079:doi
3042:doi
3003:doi
2999:248
2960:doi
2956:281
2877:doi
2839:doi
2825:555
2674:CCD
2464:or
2041:cos
2019:cos
1941:cos
1919:cos
1884:sin
1823:cos
1801:cos
1766:sin
1663:cos
1630:cos
1454:cos
1435:cos
1419:cos
1279:cos
1269:):
1267:= 0
1070:cos
1047:cos
1028:sin
1000:cos
977:cos
958:sin
929:cos
899:sin
878:cos
841:cos
427:cos
313:cos
237:cos
3736::
3701:.
3693:.
3683:.
3656:,
3621:.
3611:17
3609:.
3605:.
3563:56
3561:.
3557:.
3527:.
3504:.
3496:.
3488:.
3478:13
3476:.
3472:.
3460:^
3450:.
3446:.
3427:.
3373:^
3345:.
3337:.
3325:.
3321:.
3295:.
3287:.
3277:39
3275:.
3250:.
3240:40
3238:.
3215:.
3205:28
3203:.
3163:.
3153:57
3151:.
3128:.
3120:.
3108:.
3085:.
3075:20
3073:.
3050:.
3036:.
3032:.
3009:.
2997:.
2974:.
2966:.
2954:.
2940:^
2926:.
2893:.
2885:.
2873:95
2871:.
2867:.
2845:.
2837:.
2823:.
2807:^
2695:.
2631:A
2504:.
2175::
2124:.
1504:–
576:,
281::
178::
162:LG
151:SL
144:SG
88:.
76:.
3709:.
3679::
3629:.
3625::
3617::
3575:.
3569::
3539:.
3535::
3529:1
3512:.
3484::
3452:4
3431:.
3412:.
3367:.
3341::
3333::
3303:.
3291::
3283::
3258:.
3246::
3223:.
3211::
3188:.
3171:.
3167::
3159::
3136:.
3124::
3116::
3093:.
3081::
3058:.
3044::
3038:6
3017:.
3005::
2982:.
2962::
2934:.
2901:.
2879::
2853:.
2841::
2831::
2412:.
2404:2
2400:/
2396:3
2392:)
2386:2
2379:y
2375:f
2369:+
2364:2
2357:x
2353:f
2347:+
2344:1
2341:(
2334:x
2331:x
2327:f
2323:)
2318:2
2311:y
2307:f
2301:+
2298:1
2295:(
2292:+
2287:y
2284:x
2280:f
2274:y
2270:f
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2260:f
2256:2
2248:y
2245:y
2241:f
2237:)
2232:2
2225:x
2221:f
2215:+
2212:1
2209:(
2201:2
2198:1
2193:=
2188:m
2163:)
2160:y
2157:,
2154:x
2151:(
2148:f
2112:a
2109:C
2082:r
2077:Y
2075:θ
2070:m
2068:θ
2052:Y
2038:r
2035:=
2030:m
1968:3
1959:R
1945:3
1937:+
1931:R
1916:3
1910:2
1902:R
1888:3
1876:=
1866:R
1861:r
1850:3
1841:A
1827:3
1819:+
1813:A
1798:3
1792:2
1784:A
1770:3
1758:=
1748:A
1743:r
1713:)
1704:R
1699:r
1695:+
1689:A
1684:r
1675:R
1657:R
1652:r
1648:+
1642:A
1624:A
1619:r
1612:(
1602:=
1596:c
1577:R
1568:A
1559:C
1553:(
1526:A
1519:R
1509:R
1502:A
1485:κ
1469:)
1458:3
1439:2
1431:2
1416:+
1413:2
1410:(
1401:G
1398:L
1389:3
1375:a
1372:1
1362:G
1359:L
1345:+
1337:G
1334:L
1321:L
1318:S
1303:G
1300:S
1288:=
1262:(
1247:.
1238:G
1235:L
1226:3
1217:=
1214:C
1210:,
1202:G
1199:L
1185:=
1182:B
1178:,
1170:G
1167:L
1154:L
1151:S
1136:G
1133:S
1121:=
1118:A
1094:)
1084:2
1080:)
1067:+
1064:1
1061:(
1056:)
1044:+
1041:2
1038:(
1014:2
1010:)
997:+
994:1
991:(
986:)
974:+
971:2
968:(
950:(
943:2
939:)
926:+
923:1
920:(
917:)
905:(
896:C
888:a
871:B
868:+
865:A
862:=
859:)
847:(
810:L
807:S
802:A
798:d
793:P
790:d
779:G
776:L
767:V
753:L
750:S
745:A
741:d
736:L
733:d
722:G
719:L
697:G
694:L
681:G
678:S
663:L
660:S
648:+
639:L
636:S
631:A
627:d
619:G
616:L
611:A
607:d
601:=
598:0
554:κ
549:a
541:κ
523:a
520:1
510:G
507:L
493:+
485:G
482:L
469:L
466:S
451:G
448:S
436:=
393:G
390:L
387:S
382:W
352:G
349:L
346:S
341:W
334:=
331:)
325:C
310:+
307:1
304:(
298:G
295:L
258:0
255:=
249:C
231:G
228:L
213:L
210:S
195:G
192:S
171:C
37:C
34:θ
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
