References
- Bonn D, Eggers J, Indekeu J, et al. Wetting and spreading. Rev Mod Phys. 2009;81(2):739–805. doi:10.1103/RevModPhys.81.739.
- Wu S. Polymer interface and adhesion. New York (NY): Marcel Dekker; 1982.
- Adamson AW. Physical chemistry of surfaces. Hoboken (NJ): Wiley; 1990.
- Berg JC. Wettability. In Schick MJ, Fowkes FM, editors. Surfactant science series. New York (NY): Marcel Dekker: 1993; Vol. 49.
- Hiemenz PC, Rajagopalan R. Principles of colloid and surface science. Boca Raton (FL): CRC Press; 1997.
- de Gennes P-G. Wetting; statics and dynamics. Rev Mod Phys. 1985;57(3):827–863. doi:10.1103/RevModPhys.57.827.
- Schonhorn H, Frisch HL, Kwei TK. Kinetics of wetting of surfaces by polymer melts. J Appl Phys. 1966;37(13):4967–4973. doi:10.1063/1.1708174.
- Kwei TK, Schonhorn H, Frisch HL. Kinetics of wetting of surfaces by polymer melts. J Colloid Interface Sci. 1968;28(3–4):543–546. doi:10.1016/0021-9797(68)90087-8.
- Strella S. Analysis of spreading of a viscous drop on a smooth surface. J Appl Phys. 1970;41(10):4242–4243. doi:10.1063/1.1658446.
- Radigan W, Ghiradella H, Frisch HL, et al. Kinetics of spreading of glass on fernico metal. J Colloid Interface Sci. 1974;49(2):241–248. doi:10.1016/0021-9797(74)90357-9.
- Greenspan HP. On the motion of a small viscous droplet that wets a surface. J Fluid Mech. 1978;84(01):125. (doi:10.1017/S0022112078000075.
- Tanner LH. The spreading of silicone oil drops on horizontal surfaces. J Phys D Appl Phys. 1979;12(9):1473–1484. doi:10.1088/0022-3727/12/9/009.
- Dussan VEB. On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu Rev Fluid Mech. 1979;11(1):371–400. doi:10.1146/annurev.fl.11.010179.002103.
- Lelah MD, Marmur A. Spreading kinetics of drops on glass. J Colloid Interface Sci. 1981;82(2):518–525. doi:10.1016/0021-9797(81)90393-3.
- Dodge FT. The spreading of liquid droplets on solid surfaces. J Colloid Interface Sci. 1988;121(1):154–160. doi:10.1016/0021-9797(88)90418-3.
- de Gennes P-G, Hua X, Levinson P. Dynamics of wetting: local contact angles. J Fluid Mech. 1990;212(1):55–63. doi:10.1017/S0022112090001859.
- Haley PJ, Miksis MJ. The effect of the contact line on droplet spreading. J Fluid Mech. 1991;223(1):57–81. doi:10.1017/S0022112091001337.
- Brenner M, Bertozzi A. Spreading of droplets on a solid surface. Phys Rev Lett. 1993;71(4):593–596. doi:10.1103/PhysRevLett.71.593.
- Extrand CW. Spontaneous spreading of viscous liquid drops. J Colloid Interface Sci. 1993;157(1):72–76. doi:10.1006/jcis.1993.1159.
- Starov VM, Kalinin VV, Chen J-D. Spreading of liquid drops over dry surfaces. Adv Colloid Interface Sci. 1994;50(1):187–221. doi:10.1016/0001-8686(94)80030-8.
- Chebbi R, Selim MS. Capillary spreading of liquid drops on solid surfaces. J Colloid Interface Sci. 1997;195(1):66–76. doi:10.1006/jcis.1997.5136.
- Alteraifi AM, Sasa BJ. Spreading of liquid drops over solid substrates: ‘like wets ’like. J Adhes Sci Technol. 2006;20(12):1333–1343. doi:10.1163/156856106778456546.
- Chebbi R. Dynamics of partial wetting. J Adhes Sci Technol. 2011;25(14):1767–1783. doi:10.1163/016942410X533408.
- Cherry BW, Holmes CM. Kinetics of wetting of surfaces by polymers. J Colloid Interface Sci. 1969;29(1):174–176. doi:10.1016/0021-9797(69)90367-1.
- Cherry BW. Polymer surfaces. Cambridge: Cambridge University Press; 1981.
- Blake TD, Haynes JM. Kinetics of liquid/liquid displacement. J Colloid Interface Sci. 1969;30(3):421–423. doi:10.1016/0021-9797(69)90411-1.
- Blake TD. Dynamic contact angles and wetting kinetics. In Wettability BJC, editor. Surfactant science series. Vol. 49. New York (NY): Marcel Dekker; 1993. p. 251–309.
- Marmur A. Equilibrium and spreading of liquids on solid surfaces. Adv Colloid Interface Sci. 1983;19(1–2):75–102. doi:10.1016/0001-8686(83)80004-9.
- Schrader ME. Young-Dupre revisited. Langmuir. 1995;11(9):3585–3589. doi:10.1021/la00009a049.
- Extrand CW. A thermodynamic model for wetting free energies from contact angles. Langmuir. 2003;19(3):646–649. doi:10.1021/la0259609.
- Starov VM, Velarde MG. Surface forces and wetting phenomena. J Phys Condens Matter. 2009;21(46):464121. doi:10.1088/0953-8984/21/46/464121.
- Madejski J. Solidification of droplets on a cold surface. Int J Heat Mass Trans. 1976;19(9):1009–1013. doi:10.1016/0017-9310(76)90183-6.
- Gu Y, Li D. A model for a liquid drop spreading on a solid surface. Colloids Surf A. 1998;142(2–3):243–256. doi:10.1016/S0927-7757(98)00358-6.
- Gu Y, Li D. Liquid drop spreading on solid surfaces at low impact speeds. Colloids Surf A. 2000;163(2–3):239–245. doi:10.1016/S0927-7757(99)00295-2.
- Erickson D, Blackmore B, Li D. An energy balance approach to modeling the hydrodynamically driven spreading of a liquid drop. Colloids Surf A. 2001;182(1–3):109–122. doi:10.1016/S0927-7757(00)00834-7.
- Li R, Ashgriz N, Chandra S. Maximum spread of droplet on solid surface: low Reynolds and weber numbers. J Fluids Eng. 2010;132(1):061302.
- Bormashenko E. Variational framework for defining contact angles: a general thermodynamic approach. J Adhes Sci Technol. 2020;34(2):219–230. doi:10.1080/01694243.2019.1663030.
- Extrand CW. Contact angles and hysteresis on surfaces with chemically heterogeneous islands. Langmuir. 2003;19(9):3793–3796. doi:10.1021/la0268350.
- Gao L, McCarthy TJ. How wenzel and cassie were wrong. Langmuir. 2007;23(7):3762–3765. doi:10.1021/la062634a.
- Extrand CW, Moon SI. Which controls wetting? Contact line versus interfacial area: simple experiments on capillary rise. Langmuir. 2012;28(44):15629–15633. doi:10.1021/la303808q.
- Extrand CW. Origins of wetting. Langmuir. 2016;32(31):7697–7706. doi:10.1021/acs.langmuir.6b01935.
- Hardy WB. The spreading of fluids on glass. Phil. Mag. 1919;38(223):49–55. doi:10.1080/14786440708635928.
- Bangham DH, Saweris Z. The behaviour of liquid drops and adsorbed films at cleavage surfaces of mica. Trans Faraday Soc. 1938;34(1):554–570. doi:10.1039/tf9383400554.
- Bascom WD, Cottington RL, Singleterry CR, et al. Dynamic surface phenomena in the spontaneous spreading of oils on solids. Adv Chem. 1964;43:355–379.
- Beaglehole D. Profiles of the precursor of spreading drops of siloxane oil on glass, fused silica, and mica. J Phys Chem. 1989;93(2):893–899. doi:10.1021/j100339a067.
- Heslot F, Fraysse N, Cazabat MA. Molecular layering in the spreading of wetting liquid drops. Nature. 1989;338(6217):640–642. doi:10.1038/338640a0.
- Hoang A, Kavehpour HP. Dynamics of nanoscale precursor film near a moving contact line of spreading drops. Phys Rev Lett. 2011;106(25):254501. doi:10.1103/PhysRevLett.106.254501.
- Wang H. From contact line structures to wetting dynamics. Langmuir. 2019;35(32):10233–10245. doi:10.1021/acs.langmuir.9b00294.
- Hubao A, Yang Z, Hu R, et al. Effect of solid–liquid interactions on substrate wettability and dynamic spreading of nanodroplets: a molecular dynamics study. J Phys Chem C. 2020;124(42):23260–23269. doi:10.1021/acs.jpcc.0c07919.
- Ma X, Lei J, Xu J. Line tension of nanodroplets on a concave surface. Langmuir. 2021;37(15):4432–4440. doi:10.1021/acs.langmuir.0c03489.
- Extrand CW. Relation between contact angle and the cross-sectional area of small, sessile liquid drops. Langmuir. 2006;22(20):8431–8434. doi:10.1021/la061325h.
- Details regarding the derivation of eq (6) can be found in the appendices.
- Weast RC. Handbook of chemistry and physics. 73rd ed. Boca Raton (FL): CRC: 1992. p. 93.
- DuPont Krytox VPF vacuum pump fluids, product information; H-58530; December, 2012.
- Bashforth F, Adams JC. An attempt to test the theories of capillary action by comparing the theoretical and measured forms of drops of fluid. Himayatnagar, Hyderabad: University Press; 1883.
- Ferguson A. On the theoretical shape of large bubbles and drops, with other allied problems. Phil Mag. 1913;25(148):507–520. doi:10.1080/14786440408634191.
- Ellefson BS, Taylor NW. Surface properties of fused salts and glasses: i. Sessile-drop method for determining surface tension and density of viscous liquids at high temperatures. J Am Ceramic Soc. 1938;21(6):193–205. doi:10.1111/j.1151-2916.1938.tb15764.x.
- Blaisedell BE. The physical properties of fluid interfaces of large radius of curvature. I. Integration of Laplace’s equation for the equilibrium meridian of a fluid of axial symmetry in a gravitational field. Numerical integration and tables for sessile drops of moderately large size. J Math Phys. 1940;19(1):186–216.
- Staicopolus DN. The computation of surface tension and of contact angle by the sessile-drop method. J Colloid Sci. 1962;17(5):439–447. doi:10.1016/0095-8522(62)90055-7.
- Butler JN, Bloom BH. A curve-fitting method for calculating interfacial tension from the shape of a sessile drop. Surf Sci. 1966;4(1):1–17. doi:10.1016/0039-6028(66)90063-X.
- Maze C, Burnet G. A non-linear regression method for calculating surface tension and contact angle from the shape of a sessile drop. Surf Sci. 1969;13(2):451–470. doi:10.1016/0039-6028(69)90204-0.
- Huh C, Scriven LE. Shapes of axisymmetric fluid interfaces of unbounded extent. J Colloid Interface Sci. 1969;30(3):323–337. doi:10.1016/0021-9797(69)90399-3.
- Padday JF. Theory of surface tension. In Matijević E, editor. Surface and colloid science. Vol. 1. Hoboken (NJ): Wiley; 1969. p. 39–248.
- Princen HM. The equilibrium shape of interfaces, drops and bubbles. Rigid and deformable particles at interfaces. In Matijević E, editor. Surface and colloid science. Vol. 2. Hoboken (NJ): Wiley, 1969. p. 1–84.
- Johnson RE, Jr., Dettre RH. Wettability and contact angles. In Matijević E, editor. Surface and colloid science. Vol. 2. Hoboken (NJ): Wiley; 1969. p. 85–153.
- Huh C, Reed RL. A method for estimating interfacial tensions and contact angles from sessile and pendant drop shapes. J Colloid Interface Sci. 1983;91(2):472–484. doi:10.1016/0021-9797(83)90361-2.
- Dimitrov AS, Kralchevsky PA, Nikolov AD, et al. Contact angle measurements with sessile drops and bubbles. J Colloid Interface Sci. 1991;145(1):279–282. doi:10.1016/0021-9797(91)90120-W.
- Chatterjee J. Limiting conditions for applying the spherical section assumption in contact angle estimation. J Colloid Interface Sci. 2003;259(1):139–147. doi:10.1016/s0021-9797(02)00198-4.
- Shapiro B, Moon H, Garrell RL, et al. Equilibrium behavior of sessile drops under surface tension, applied external fields, and material variations. J Appl Phys. 2003;93(9):5794–5811. doi:10.1063/1.1563828.
- Extrand CW, Moon SI. Contact angles of liquid drops on super hydrophobic surfaces: understanding the role of flattening of drops by gravity. Langmuir. 2010;26(22):17090–17099. doi:10.1021/la102566c.
- Extrand CW, Moon SI. When sessile drops are no longer small: transitions from spherical to fully flattened. Langmuir. 2010;26(14):11815–11822. doi:10.1021/la1005133.
- Srinivasan S, McKinley GH, Cohen RE. Assessing the accuracy of contact angle measurements for sessile drops on liquid-repellent surfaces. Langmuir. 2011;27(22):13582–13589. doi:10.1021/la2031208.
- Extrand CW, Moon SI. Experimental measurement of forces and energies associated with capillary rise in a vertical tube. J Colloid Interface Sci. 2013;407(1):488–492. doi:10.1016/j.jcis.2013.06.017.
- Extrand CW. Forces, pressures and energies associated with liquid rising in nonuniform capillary tubes. J Colloid Interface Sci. 2015;450(1):135–140. doi:10.1016/j.jcis.2015.03.007.
- Extrand CW. Meniscus formation in a vertical capillary tube. Langmuir. 2022;38(7):2346–2353. doi:10.1021/acs.langmuir.1c03226.
- Extrand CW. Energies associated with a meniscus along a flat vertical wall. Langmuir. 2022;38(45):13720–13727. doi:10.1021/acs.langmuir.2c01807.
- Beyer WH. Standard mathematical tables. 27th ed. Boca Raton (FL): CRC Press; 1984.