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Solute transport and interface evolution in dissolutive wetting

  • JinHong Yang
  • QuanZi YuanEmail author
  • YaPu Zhao
Article
  • 2 Downloads

Abstract

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

c

Concentration

cs

Saturation concentration

c0

The initial concentration near origin

kB

Boltzmann constant

uc

Characteristic convective velocity

uf

Height-averaged flow velocity

vmole

Mole volume of the solute

Ca

Capillary number

Cn

Shape factor

D

Diffusion coefficient

F

Potential energy

Ha

Concentration boundary-layer thickness

H1

Lower height of the droplet

Hu

Upper height of the droplet

L

Characteristic length

NA

Avogadro number

Pe

Pélect number

R

Droplet radius

S

Spreading coefficient

T

Temperature

V

Droplet volume

α

Convective intensity

ϕ

Mean volume concentration

γ

Surface tension

η

Solvent viscosity

θ

Contact angle

θ

le Lower equilibrium contact angle

θue

Upper equilibrium contact angle

τD

Dissolution characteristic time

τD

Diffusion characteristic time

ξ

Dissipation coefficient at the contact line

Φ

Energy dissipation

Φη

Viscosity dissipation

Φξ

Dissipation at the contact line

Ω

Surface area of a solute molecular

Supplementary material

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

References

  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

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