Controlling the Motion of Interfaces in Capillary Channels with Non-uniform Surface Wettability

Abstract

The use of self-driven flows in microfluidic devices attracts many researchers as the external flow-driving mechanism is diminished or eliminated. One of the mechanisms providing such motions is generating a pressure difference across interfaces as in the case of the motion in capillary tubes. The capillarity, namely, the pressure difference across the interface due to its curvature drives the motion. This pressure depends on the interaction with the capillary walls and is controlled if one varies the surface energy of the walls. In this study, we search for the effects of surface energy on the motion of interfaces in capillary-driven flow. To this end, we model the motion of fluid particles in a capillary channel and integrate the governing equations using the binary lattice Boltzmann method for the two-phase flow. We, first, validate our solver for canonical static and dynamic problems. We, then, discuss two main contributions; we show how to deviate the interface speed from the ones moving in channels with uniform wall energies and discuss the conditions under which such an interface stagnates (like a passive valve in a channel). Tuning the wettability of the channel walls, we provide a simple condition for stopping the interface: the summation of the equilibrium contact angles interface make with the channel walls at the bottom and top wall need to satisfy $\theta_{eq}^{top}+\theta_{eq}^{bot} \geq \pi$. Configurations and wetting properties of different wettability regions play major roles together

Keywords

• Capillarity
• Wetting
• Interfaces
• Microfluidics
• Lattice Boltzmann Method

Yüzey Islanabilirliği Üniform Olmayan Kılcal Kanallardaki Arayüzeylerin Hareketinin Kontrolü

Abstract

Mikroakışkan cihazlarda kendinden tahrikli akışların kullanımı, harici akış tahrik mekanizması azaltıldığı veya ortadan kaldırıldığı için birçok araştırmacının ilgisini çekmektedir. Bu tür hareketleri sağlayan mekanizmalardan biri de kılcal borulardaki harekette olduğu gibi arayüzeyler arasında bir basınç farkı oluşturmaktır. Kılcallık, yani giriş boyunca eğriliği nedeniyle oluşan basınç farkı, hareketi yönlendirir. Bu basınç kılcal duvarlarla etkileşime bağlıdır ve duvarların yüzey enerjisi değiştirilerek kontrol edilir. Bu çalışmada, yüzey enerjisinin kılcal tahrikli akıştaki arayüzlerin hareketi üzerindeki etkilerini araştırıyoruz. Bu amaçla, bir kılcal kanaldaki sıvı parçacıklarının hareketini modelliyoruz ve iki fazlı akış için ikili Lattice Boltzmann yöntemini kullanıyoruz. Öncelikle standart statik ve dinamik problemler için çözücümüzü doğruluyoruz. O halde iki ana katkıyı tartışıyoruz; arayüz hızının, tekdüze duvar enerjilerine sahip kanallarda hareket edenlerden nasıl saptırılacağını gösteriyoruz ve böyle bir arayüzün durduğu koşulları (bir kanaldaki pasif valf gibi) tartışıyoruz. Kanal duvarlarının ıslanabilirliğini ayarlayarak arayüzü durdurmak için basit bir koşul sağlıyoruz: arayüzün alt ve üst duvardaki kanal duvarlarıyla yaptığı denge temas açılarının toplamı $\theta_{eq}^{üst}+\theta_{eq}^{alt} \geq \pi$'yi karşılamalıdır. Farklı ıslanabilirlik bölgelerinin konfigürasyonları ve ıslanma özellikleri birlikte önemli rol oynar.

Keywords

• Kapilarite
• Islatma
• Arayüzey
• Mikroakışkanlar
• Lattice Boltzmann Metodu

References

1. [1] Darmanin, T. and Guittard, F., 2015. ‘Superhydrophobic and superoleophobic properties in nature’, Materials Today 18(5), 273–285. DOI: 10.1016/j.mattod.2015.01.001
2. [2] Kohonen, M. M., 2006. ‘Engineered wettability in tree capillaries’, Langmuir 22, 3148–3153. DOI: 10.1021/la052861x
3. [3] Barthlott, W., Neinhuis, C. 1997. ‘Purity of the sacred lotus, or escape from contamination in biological surfaces’, Planta 202, 1–8. DOI: 10.1007/s004250050096
4. [4] Parker, A. R. and Lawrance, C. R., 2001. ‘Water capture by a desert beetle’, Nature 414, 33–34. DOI: 10.1038/35102108
5. [5] Zheng, Y., Gao, X. and Jiang, L. 2007. ‘Directional adhesion of superhydrophobic butterfly wings’, Soft Matter 3, 178–182. DOI: 10.1039/B612667G
6. [6] Yager, P., Edwards, T., Fu, E., Helton, K., Nelson, K., Tam, M.R., Weigl, B.H. 2006. ‘Microfluidic diagnostic technologies for global public health’, Nature 442, 412–418. DOI: 10.1038/nature05064
7. [7] Sackmann, E.K., Fulton, A.L. and Beebe, D.J., 2014. ‘The present and future role of microfluidics in biomedical research’, Nature 507, 181–189. DOI: 10.1038/nature13118
8. [8] Yeo, L.Y., Chang, H.C., Chan, P.P.Y., and Friend, J.R. 2011. ‘Microfluidic devices for bioapplications’, Small 7(1), 12–48. DOI: 10.1002/smll.201000946

9. [9] Sonmez, I. and Cebeci, Y., 2004. ‘Investigation of relationship between critical surface tension of wetting and oil agglomeration recovery of barite’, Colloids and Surfaces A: Physicochem. Eng. Aspects 234, 27–33. DOI: 10.1016/j.colsurfa.2003.12.003
10. [10] Dupuis, A. and Yeomans, J.M., 2004. Lattice Boltzmann modelling of droplets on chemically heterogeneous surfaces. Future Generation Computer Systems, 20(6), pp.993-1001. DOI: 10.1016/j.future.2003.12.012
11. [11] Leopoldes, J., Dupuis, A., Bucknall, D.G. and Yeomans, J.M., 2003. ‘Jetting micronscale droplets onto chemically heterogeneous surfaces’, Langmuir 19, 9818–9822. DOI: 10.1021/la0353069
12. [12] Verberg, R., Pooley, C.M., Yeomans, J.M. and Balazs, A.C., 2004. ‘Pattern formation in binary fluids confined between rough, chemically heterogeneous surfaces’, Physical Review Letters 93(18). DOI: 10.1103/PhysRevLett.93.184501
13. [13] Au, A.K., Lai, H., Utela, B.R. and Folch, A., 2011. ‘Microvalves and micropumps for biomems’, Micromachines 2(2), 179–220. DOI: 10.3390/mi2020179
14. [14] Hilber, W., 2016. ‘Stimulus-active polymer actuators for next-generation microfluidic devices’, Applied Physics A 122(751). DOI: 10.1007/s00339-016-0258-6
15. [15] Arango, Y., Temiz, Y., Gökçe, O. and Delamarche, E., 2020. ‘Electro-actuated valves and self-vented channels enable programmable flow control and monitoring in capillary-driven microfluidics’, Science Advances 6(16). DOI: 10.1126/sciadv.aay8305
16. [16] Mahmud, M. S., Alo, A., Farshchian, B., Lee, G.-H. and Kim, N., 2022. ‘Pulsed laser ablation on polymethylmethacrylate (pmma) surfaces for capillary driven flows’, Surfaces and Interfaces 31, 101989. DOI: 10.1016/j.surfin.2022.101989
17. [17] Marmur, A., 1994a. ‘Contact angle hysteresis on heterogeneous smooth surfaces’, J. Colloid Interface Sci. 168(1), 40–46. DOI: 10.1006/jcis.1994.1391
18. [18] Marmur, A., 1994b. ‘Thermodynamic aspects of contact angle hysteresis’, Advances in Colloid and Interface Science 50, 121–141. DOI: 10.1016/0001-8686(94)80028-6
19. [19] Joanny, J.F. and De Gennes, P.G., 1984. ‘A model for contact angle hysteresis’, J. Chem. Phys. 81(552). DOI: 10.1063/1.447337
20. [20] Adamson, A. W. and Gast, A. P., 1997. ‘Physical chemistry of surfaces’, A Wiley-Interscience Publication 6th Edition.
21. [21] Sonmez, I. and Cebeci, Y., 2019. ‘Contact angle hysteresis in a microchannel: Statics’, Physical Review Fluids 4(044008). DOI: 10.1016/j.colsurfa.2003.12.003
22. [22] Kusumaatmaja, H. and Yeomans, J.M., 2007. ‘Modeling contact angle hysteresis on chemically patterned and superhydrophobic surfaces’, Langmuir 23(11), 6019–6032. DOI: 10.1021/la063218t
23. [23] Montes Ruiz-Cabello, F.J., Rodríguez-Valverde, M.A., Marmur, A. and Cabrerizo-Vílchez, M.A., 2011. ‘Comparison of sessile drop and captive bubble methods on rough homogeneous surfaces: A numerical study’, Langmuir 27(15), 9638–9643. DOI: 10.1021/la201248z
24. [24] Chang, X., Huang, H., Lu, X.Y. and Hou, J., 2022. ‘Width effect on contact angle hysteresis in a patterned heterogeneous microchannel’, J. Fluid Mech. 949(A15). DOI: 10.1017/jfm.2022.763
25. [25] Wang, X., Xu, B. and Chen, Z., 2020. ‘Numerical simulation of droplet dynamics on chemically heterogeneous surfaces by lattice boltzmann method’, International Journal of Numerical Methods for Heat and Fluid Flow 30(2), 607–624. DOI: 10.1108/HFF-03-2019-0259
26. [26] Iwahara, D., Shinto, H., Miyahara, M. and Higashitani, K., 2003. ‘Liquid drops on homogeneous and chemically heterogeneous surfaces: A two dimensional lattice boltzmann study’, Langmuir 19, 9086–9093. DOI: 10.1021/la034456g
27. [27] Tilehboni, S.M., Fattahi, E., Afrouzi, H.H. and Farhadi, M., 2015. ‘Numerical simulation of droplet detachment from solid walls under gravity force using lattice boltzmann method’, Journal of Molecular Liquids 212, 544–556. DOI: 10.1016/j.molliq.2015.10.007
28. [28] Park, C.S., Baek, S.Y., Lee, K.J. and Kim, S.W., 2003. ‘Two-phase flow in a gas-injected capillary tube’, Advances in Polymer Technology 22(4), 320–328. DOI: 10.1002/adv.10059
29. [29] Frisch, U., d'Humières, D., Hasslacher, B., Lallemand, P., Pomeau, Y. and Rivet, J.P., 2019. Lattice gas hydrodynamics in two and three dimensions. In Lattice Gas Methods for Partial Differential Equations. CRC Press, pp. 77-136.
30. [30] Dutka, F., Napiórkowski, M. and Dietrich, S., 2012. ‘Mesoscopic analysis of gibbs’ criterion for sessile nanodroplets on trapezoidal substrates’, The Journal of Chemical Physics 136(064702). DOI: 10.1063/1.3682775
31. [31] Kusumaatmaja, H., Pooley, C.M., Girardo, S., Pisignano, D. and Yeomans, J.M., 2008. ‘Capillary filling in patterned channels’, Physical Review E 77(067301). DOI: 10.1103/PhysRevE.77.067301
32. [32] Zhao, J., Chen, S. and Liu, Y., 2016. ‘Droplets motion on chemically/topographically heterogeneous surfaces’, Molecular Simulation 42, 1452–1459. DOI: 10.1080/08927022.2016.1198478
33. [33] Kusumaatmaja, H., 2008. ‘Lattice boltzmann studies of wetting and spreading on patterned surfaces’, University of Oxford D. Phil. Thesis.
34. [34] Zhang, J., Li, B. and Kwok, D.Y., 2009. ‘Metastable contact angles and selfpropelled drop movement on chemically, heterogeneous surfaces by a meanfield lattice boltzmann model’, Eur. Phys. J. Special Topics 171, 73–79. DOI: 10.1140/epjst/e2009-01013-y
35. [35] Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G. and Viggen, E.M., 2017a. The lattice Boltzmann method. Springer International Publishing, 10(978-3), pp.407-431.
36. [36] Kendon, V.M., Cates, M.E., Pagonabarraga, I., Desplat, J.C. and Bladon, P., 2001. ‘Inertial effects in three dimensional spinodal decomposition of a symmetric binary fluid mixture: a lattice boltzmann study’, J. Fluid Mech 440, 147–203. DOI: 10.1017/S0022112001004682
37. [37] Bray, A.J., 1994. ‘Theory of phase-ordering kinetics’, Advances in Physics 43(3), 357–459. DOI: 10.1080/00018739400101505
38. [38] Swift, M.R., Orlandini, E., Osborn, W.R. and Yeomans, J.M., 1996. ‘Lattice boltzmann simulations of liquid-gas and binary fluid systems’, Physical Review E. 54(5), 5041–5052. DOI: 10.1103/physreve.54.5041
39. [39] Briant, A.J. and Yeomans, J.M., 2004. ‘Lattice boltzmann simulations of contact line motion. ii. binary fluids’, Physical Review E 69(031603). DOI: 10.1103/PhysRevE.69.031603
40. [40] Krüger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G. and Viggen, E.M., 2017b. The lattice Boltzmann method. Springer International Publishing, 10(978-3), pp.65-66. [41] Bhatnagar, P.L., Gross, E.P. and Krook, M., 1954. ‘A model for collision processes in gases. i. small amplitude processes in charged and neutral one component systems’, Physical Review 94(3), 511–525. DOI: 10.1103/physrev.94.511
41. [42] Pooley, C.M., Kusumaatmaja, H. and Yeomans, J.M., 2008. ‘Contact line dynamics in binary lattice boltzmann simulations’, Physical Review E 78(056709). DOI: 10.1103/PhysRevE.78.056709
42. [43] Pooley, C.M., Kusumaatmaja, H. and Yeomans, J.M., 2009. ‘Modelling capillary filling dynamics using lattice boltzmann simulations’, Eur. Phys. J. Special Topics 171, 63–71. DOI: 10.1140/epjst/e2009-01012-0
43. [44] Ladd, A., 1994. ‘Numerical simulations of particulate suspensions via a discretized boltzmann equation. part 1. theoretical foundation’, Journal of Fluid Mechanics 271, 285. DOI: 10.1017/s0022112094001771
44. [45] Schrader, M., 1995. ‘Young-dupre revisited’, Langmuir 11, 3585–3589. DOI: 10.1021/la00009a049
45. [46] Washburn, E. W., 1921. ‘The dynamics of capillary flow’, The Physical Review 17(3), 273. DOI: 10.1103/PhysRev.17.273
46. [47] Cox, R., 1986. ‘The dynamics of the spreading of liquids on a solid surface. part 1. viscous flow.’, Journal of Fluid Mechanics 168(1), 169–194. DOI: 10.1017/s0022112086000332
47. [48] Voinov, O., 1977. ‘Hydrodynamics of wetting’, Fluid Dynamics 11(5), 714-721. DOI: 10.1007/bf01012963
48. [49] Latva-Kokko, M. and Rothman, D. H., 2007. ‘Scaling of dynamic contact angles in a lattice-boltzmann model’, Physical Review Letters 98(254503). DOI: 10.1103/PhysRevLett.98.254503
49. [50] Teng, P., Tian, D., Fu, H. and Wang, S., 2020. ‘Recent progress of electrowetting for droplet manipulation: from wetting to superwetting systems’, Mater. Chem. Front. 4(140). DOI: 10.1039/c9qm00458k
50. [51] Olanrewaju, A., Beaugrand, M., Yafia, M. and Juncker, D., 2018. ‘Capillary microfluidics in microchannels: from microfluidic networks to capillaric circuits’, Lab. Chip. 18(16), 2323–2347. DOI: 10.1039/c8lc00458g
51. [52] Mugele, F., Klingner, A., Buehrle, J., Steinhauser, D. and Herminghaus, S., 2005. ‘Electrowetting: a convenient way to switchable wettability patterns’, J. Phys.: Condens. Matter 17, 559–576. DOI: 10.1088/0953-8984/17/9/016