- Open Access
Wetting transition: Macroscopic roughness, static friction, and energy barrier
Phys. Rev. Research 7, 043093 – Published 23 October, 2025
DOI: https://doi.org/10.1103/ybmh-5k99
Abstract
When a droplet is deposited on a rough solid substrate, the classic Cassie-Wenzel theory (CWT) is often used to describe the wetting states. However, CWT fails to explain experimental observations of high static friction on hydrophobic surfaces with a critical roll-off angle close to ; the static friction is associated with the minimum energy required for the transition between the Cassie state and the Wenzel state. Here, we propose an alternative theory for calculating the static friction force of a droplet on a rough solid surface, based on a complete energy landscape method. Our results for static friction are orders of magnitude larger than those predicted by CWT and have been validated through quantitative comparisons with experiments.
Physics Subject Headings (PhySH)
Article Text
References (55)
- P.-G. de Gennes, Wetting: statics and dynamics, Rev. Mod. Phys. 57, 827 (1985).
- K. Koch, B. Bhushan, and W. Barthlott, Multifunctional surface structures of plants: An inspiration for biomimetics, Prog. Mater. Sci. 54, 137 (2009).
- F. Wang, Y. Wu, and B. Nestler, Wetting effect on patterned substrates, Adv. Mater. 35, 2210745 (2023).
- T. Young, III. An essay on the cohesion of fluids, Philos. Trans. R. Soc. London 95, 65 (1805).
- A. Cassie and S. Baxter, Wettability of porous surfaces, Trans. Faraday Soc. 40, 546 (1944).
- R. N. Wenzel, Resistance of solid surfaces to wetting by water, Ind. Eng. Chem. 28, 988 (1936).
- A. Lafuma and D. Quéré, Superhydrophobic states, Nat. Mater. 2, 457 (2003).
- G. Whyman, E. Bormashenko, and T. Stein, The rigorous derivation of young, Cassie–Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon, Chem. Phys. Lett. 450, 355 (2008).
- E. Bormashenko, R. Pogreb, G. Whyman, and M. Erlich, Cassie–Baxter wetting transition in vibrating drops deposited on rough surfaces: Is the dynamic Cassie-Baxter wetting transition a 2D or 1D Affair? Langmuir 23, 6501 (2007).
- J. Sun, P. Zhu, X. Yan, C. Zhang, Y. Jin, X. Chen, and Z. Wang, Robust liquid repellency by stepwise wetting resistance, Appl. Phys. Rev. 8, 031403 (2021).
- J. Wu, R. Ma, Z. Wang, and S. Yao, Do droplets always move following the wettability gradient? Appl. Phys. Lett. 98, 204104 (2011).
- Z. Guo, Y. Liu, D. Lohse, X. Zhang, and X. Zhang, Stability of micro-Cassie states on rough substrates, J. Chem. Phys. 142, 244704 (2015).
- J. M. Encarnación Escobar, D. García-González, I. Dević, X. Zhang, and D. Lohse, Morphology of evaporating sessile microdroplets on lyophilic elliptical patches, Langmuir 35, 2099 (2019).
- S. Peng, T. L. Mega, and X. Zhang, Collective effects in microbubble growth by solvent exchange, Langmuir 32, 11265 (2016).
- I. W. Park, J. M. Ribe, M. Fernandino, and C. A. Dorao, The criterion of the Cassie–Baxter and Wenzel wetting modes and the effect of elastic substrates on it, Adv. Mater. Interfaces 10, 2202439 (2023).
- A. Marmur, Wetting on hydrophobic rough surfaces: To be heterogeneous or not to be? Langmuir 19, 8343 (2003).
- A. Marmur and E. Bittoun, When Wenzel and Cassie are right: Reconciling local and global considerations, Langmuir 25, 1277 (2009).
- M. Reyssat and D. Quéré, Contact angle hysteresis generated by strong dilute defects, J. Phys. Chem. B 113, 3906 (2009).
- N. Gao, F. Geyer, D. W. Pilat, S. Wooh, D. Vollmer, H.-J. Butt, and R. Berger, How drops start sliding over solid surfaces, Nat. Phys. 14, 191 (2018).
- R. Tadmor, Open problems in wetting phenomena: Pinning retention forces, Langmuir 37, 6357 (2021).
- E. Bormashenko, Progress in understanding wetting transitions on rough surfaces, Adv. Colloid Interface Sci. 222, 92 (2015).
- G. Whyman and E. Bormashenko, Wetting transitions on rough substrates: General considerations, J. Adhes. Sci. Technol. 26, 207 (2012).
- C. Ishino, K. Okumura, and D. Quéré, Wetting transitions on rough surfaces, Europhys. Lett. 68, 419 (2004).
- M. Xu, G. Sun, and C.-J. Kim, Infinite lifetime of underwater superhydrophobic states, Phys. Rev. Lett. 113, 136103 (2014).
- P. Lv, Y. Xue, Y. Shi, H. Lin, and H. Duan, Metastable states and wetting transition of submerged superhydrophobic structures, Phys. Rev. Lett. 112, 196101 (2014).
- Y. Xiang, S. Huang, P. Lv, Y. Xue, Q. Su, and H. Duan, Ultimate stable underwater superhydrophobic state, Phys. Rev. Lett. 119, 134501 (2017).
- T. Koishi, K. Yasuoka, S. Fujikawa, T. Ebisuzaki, and X. C. Zeng, Coexistence and transition between Cassie and Wenzel state on pillared hydrophobic surface, Proc. Natl. Acad. Sci. USA 106, 8435 (2009).
- A. Giacomello, M. Chinappi, S. Meloni, and C. M. Casciola, Metastable wetting on superhydrophobic surfaces: Continuum and atomistic views of the Cassie-Baxter–Wenzel transition, Phys. Rev. Lett. 109, 226102 (2012).
- T.-H. Yen and C.-Y. Soong, Hybrid Cassie–Wenzel model for droplets on surfaces with nanoscale roughness, Phys. Rev. E 93, 022805 (2016).
- F. Wang, H. Zhang, and B. Nestler, Wetting phenomena: Line tension and gravitational effect, Phys. Rev. Lett. 133, 246201 (2024).
- F. Wang and B. Nestler, Wetting and contact-angle hysteresis: Density asymmetry and van der Waals force, Phys. Rev. Lett. 132, 126202 (2024).
- F. Wang, H. Zhang, Y. Wu, and B. Nestler, A thermodynamically consistent diffuse interface model for the wetting phenomenon of miscible and immiscible ternary fluids, J. Fluid Mech. 970, A17 (2023).
- J. Long, L. Pan, P. Fan, D. Gong, D. Jiang, H. Zhang, L. Li, and M. Zhong, Cassie-state stability of metallic superhydrophobic surfaces with various micro/nanostructures produced by a femtosecond laser, Langmuir 32, 1065 (2016).
- O. Bliznyuk, V. Veligura, E. S. Kooij, H. J. Zandvliet, and B. Poelsema, Metastable droplets on shallow-grooved hydrophobic surfaces, Phys. Rev. E 83, 041607 (2011).
- A. Promraksa, Y.-C. Chuang, and L.-J. Chen, Study on the wetting transition of a liquid droplet sitting on a square-array cosine wave-like patterned surface, J. Colloid Interface Sci. 418, 8 (2014).
- G. Whyman and E. Bormashenko, How to make the Cassie wetting state stable? Langmuir 27, 8171 (2011).
- M. Reyssat, J. M. Yeomans, and D. Quéré, Impalement of fakir drops, Europhys. Lett. 81, 26006 (2007).
- B. Bhushan and Y. C. Jung, Natural and biomimetic artificial surfaces for superhydrophobicity, self-cleaning, low adhesion, and drag reduction, Prog. Mater. Sci. 56, 1 (2011).
- D. Quéré, Wetting and roughness, Annu. Rev. Mater. Res. 38, 71 (2008).
- E. Bormashenko, Wetting of Real Surfaces (Walter de Gruyter GmbH & Co. KG, Leipzig, 2018), Vol. 19.
- B. Zhang, X. Chen, J. Dobnikar, Z. Wang, and X. Zhang, Spontaneous Wenzel to Cassie dewetting transition on structured surfaces, Phys. Rev. Fluids 1, 073904 (2016).
- K. Rykaczewski, A. T. Paxson, S. Anand, X. Chen, Z. Wang, and K. K. Varanasi, Multimode multidrop serial coalescence effects during condensation on hierarchical superhydrophobic surfaces, Langmuir 29, 881 (2013).
- T. Mouterde, G. Lehoucq, S. Xavier, A. Checco, C. T. Black, A. Rahman, T. Midavaine, C. Clanet, and D. Quéré, Antifogging abilities of model nanotextures, Nat. Mater. 16, 658 (2017).
- S. Peng, I. Devic, H. Tan, D. Lohse, and X. Zhang, How a surface nanodroplet sits on the rim of a microcap, Langmuir 32, 5744 (2016).
- D. Lohse and X. Zhang, Surface nanobubbles and nanodroplets, Rev. Mod. Phys. 87, 981 (2015).
- C. Furmidge, Studies at phase interfaces. I. The sliding of liquid drops on solid surfaces and a theory for spray retention, J. Colloid Sci. 17, 309 (1962).
- H. Zhang, H. Zhang, F. Wang, and B. Nestler, Exploration of contact angle hysteresis mechanisms: From microscopic to macroscopic, J. Chem. Phys. 161, 194705 (2024).
- F. Aurbach, F. Wang, and B. Nestler, Wetting phenomena of droplets and gas bubbles: Contact angle hysteresis based on varying liquid–solid and solid–gas interfacial tensions, J. Chem. Phys. 161, 164708 (2024).
- N. A. Patankar, Hysteresis with regard to Cassie and Wenzel states on superhydrophobic surfaces, Langmuir 26, 7498 (2010).
- T. Koishi, K. Yasuoka, S. Fujikawa, and X. C. Zeng, Measurement of contact-angle hysteresis for droplets on nanopillared surface and in the Cassie and Wenzel states: A molecular dynamics simulation study, ACS Nano 5, 6834 (2011).
- H. Y. Erbil, The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review, Surf. Sci. Rep. 69, 325 (2014).
- Existing models [50, 51, 52] erroneously equate the contact angles of the Wenzel and Cassie states with the advancing and receding contact angles, respectively, while completely neglecting the critical intermediate state—the saddle point configuration and its corresponding contact-angle characteristics.
- C. Lv, C. Yang, P. Hao, F. He, and Q. Zheng, Sliding of water droplets on microstructured hydrophobic surfaces, Langmuir 26, 8704 (2010).
- E. Blokhuis, Y. Shilkrot, and B. Widom, Young's law with gravity, Mol. Phys. 86, 891 (1995).
- J.-F. Joanny and P.-G. De Gennes, A model for contact angle hysteresis, J. Chem. Phys. 81, 552 (1984).