Solute transport and interface evolution in dissolutive wetting

  • JinHong Yang
  • QuanZi YuanEmail author
  • YaPu ZhaoEmail author


Dissolutive wetting, i.e., droplet wetting on dissolvable surfaces, is essential for various natural phenomena and industrial applications such as the formation of sinkholes, enhancing shale gas recovery, drug design, MEMS, and so on. It is difficult to predict the evolution of concentration field and solid-liquid interface owing to the coupled effects of wetting, diffusion, and convection. This study makes substantial progress by proposing a new theory based on Onsager’s variational principle and finding two modes of solute transport, i.e., shifting and lifting modes. Furthermore, we investigate the influence of wetting and dissolution coupling on the interface shape using a phase diagram. Using our theory, we can predict and inversely predict the interface evolution.

Key words

wetting diffusion solid-liquid interface concentration distribution 

List of variables




Saturation concentration


The initial concentration near origin


Boltzmann constant


Characteristic convective velocity


Height-averaged flow velocity


Mole volume of the solute


Capillary number


Shape factor


Diffusion coefficient


Potential energy


Concentration boundary-layer thickness


Lower height of the droplet


Upper height of the droplet


Characteristic length


Avogadro number


Pélect number


Droplet radius


Spreading coefficient




Droplet volume


Convective intensity


Mean volume concentration


Surface tension


Solvent viscosity


Contact angle


le Lower equilibrium contact angle


Upper equilibrium contact angle


Dissolution characteristic time


Diffusion characteristic time


Dissipation coefficient at the contact line


Energy dissipation


Viscosity dissipation


Dissipation at the contact line


Surface area of a solute molecular

Supplementary material

11433_2019_9425_MOESM1_ESM.doc (50 kb)
Solute transport and interface evolution in dissolutive wetting


  1. 1.
    W. Yang, H. T. Wang, T. F. Li, and S. X. Qu, Sci. China-Phys. Mech. Astron. 62, 014601 (2018).CrossRefGoogle Scholar
  2. 2.
    Z. P. Xu, and Q. S. Zheng, Sci. China-Phys. Mech. Astron. 61, 074601 (2018).ADSCrossRefGoogle Scholar
  3. 3.
    E. Mohtarami, A. Baghbanan, M. Eftekhari, and H. Hashemolhosseini, Theor. Appl. Fract. Mech. 89, 110 (2017).CrossRefGoogle Scholar
  4. 4.
    A. M. Hynes, H. Ashraf, J. K. Bhardwaj, J. Hopkins, I. Johnston, and J. N. Shepherd, Sens. Actuat. A-Phys. 74, 13 (1999).CrossRefGoogle Scholar
  5. 5.
    S. Biswas, J. Doherty, D. Saladukha, Q. Ramasse, D. Majumdar, M. Upmanyu, A. Singha, T. Ochalski, M. A. Morris, and J. D. Holmes, Nat. Commun. 7, 11405 (2016).ADSCrossRefGoogle Scholar
  6. 6.
    B. J. Carey, J. Z. Ou, R. M. Clark, K. J. Berean, A. Zavabeti, A. S. R. Chesman, S. P. Russo, D. W. M. Lau, Z. Q. Xu, Q. Bao, O. Kevehei, B. C. Gibson, M. D. Dickey, R. B. Kaner, T. Daeneke, and K. Kalantar-Zadeh, Nat. Commun. 8, 14482 (2017).ADSCrossRefGoogle Scholar
  7. 7.
    J. B. Dressman, G. L. Amidon, C. Reppas, and V. P. Shah, Pharmaceut. Res. 15, 11 (1998).CrossRefGoogle Scholar
  8. 8.
    L. Yin, B. Murray, and T. Singler, Acta Mater. 54, 3561 (2006).CrossRefGoogle Scholar
  9. 9.
    R. Hellmann, S. Cotte, E. Cadel, S. Malladi, L. S. Karlsson, S. Lozano-Perez, M. Cabié, and A. Seyeux, Nat. Mater. 14, 307 (2015).ADSCrossRefGoogle Scholar
  10. 10.
    J. A. Hyatt, and P. M. Jacobs, Geomorphology 17, 305 (1996).ADSCrossRefGoogle Scholar
  11. 11.
    W. F. Zhou, Eng. Geol. 31, 50 (1997).Google Scholar
  12. 12.
    L. Ristroph, J. Fluid Mech. 838, 1 (2018).ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    C. Cohen, M. Berhanu, J. Derr, and S. Courrech du Pont, Phys. Rev. Fluids 1, 050508 (2016).ADSCrossRefGoogle Scholar
  14. 14.
    Q. Z. Yuan, and Y. P. Zhao, Phys. Rev. Lett. 104, 246101 (2010).ADSCrossRefGoogle Scholar
  15. 15.
    Y. P. Zhao, Physical Mechanics of Surfaces and Interfaces (Science Press, Beijing, 2012).Google Scholar
  16. 16.
    D. Wheeler, J. A. Warren, and W. J. Boettinger, Phys. Rev. E 82, 051601 (2010), arXiv: 1006.4881.ADSCrossRefGoogle Scholar
  17. 17.
    E. Saiz, M. Benhassine, J. De Coninck, and A. P. Tomsia, Scripta Mater. 62, 934 (2010).CrossRefGoogle Scholar
  18. 18.
    J. Yang, Q. Yuan, and Y. P. Zhao, Int. J. Heat Mass Transfer 118, 201 (2018).CrossRefGoogle Scholar
  19. 19.
    P. Protsenko, O. Kozlova, R. Voytovych, and N. Eustathopoulos, J. Mater. Sci. 43, 5669 (2008).ADSCrossRefGoogle Scholar
  20. 20.
    O. Kozlova, R. Voytovych, P. Protsenko, and N. Eustathopoulos, J. Mater. Sci. 45, 2099 (2009).ADSCrossRefGoogle Scholar
  21. 21.
    N. Alleborn, and H. Raszillier, Chem. Eng. Sci. 59, 2071 (2004).CrossRefGoogle Scholar
  22. 22.
    P. Protsenko, J. P. Garandet, R. Voytovych, and N. Eustathopoulos, Acta Mater. 58, 6565 (2010).CrossRefGoogle Scholar
  23. 23.
    J. Chapuis, E. Romero, F. Soulié, C. Bordreuil, and G. Fras, Heat Mass Transfer 52, 2283 (2015).ADSCrossRefGoogle Scholar
  24. 24.
    X. Man, and M. Doi, Phys. Rev. Lett. 116, 066101 (2016), arXiv: 1602.04891.ADSCrossRefGoogle Scholar
  25. 25.
    P. G. de Gennes, Rev. Mod. Phys. 57, 827 (1985).ADSCrossRefGoogle Scholar
  26. 26.
    V. Stanek, and J. Szekely, Chem. Eng. Sci. 25, 699 (1970).CrossRefGoogle Scholar
  27. 27.
    J. R. Lister, G. G. Peng, and J. A. Neufeld, Phys. Rev. Lett. 111, 154501 (2013), arXiv: 1310.0484.ADSCrossRefGoogle Scholar
  28. 28.
    Q. Z. Yuan, J. H. Yang, Y. Sui, and Y. P. Zhao, Langmuir 33, 6464 (2017).CrossRefGoogle Scholar
  29. 29.
    X. H. Wang, W. H. Shen, X. F. Huang, J. L. Zang, and Y. P. Zhao, Sci. China-Phys. Mech. Astron. 60, 064612 (2017).ADSCrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Nonlinear MechanicsInstitute of Mechanics, Chinese Academy of SciencesBeijingChina
  2. 2.School of Engineering ScienceUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations