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Theoretical and Computational Fluid Dynamics

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12-07-2020 | Original Article

Phase-field modeling and computer simulation of the coffee-ring effect

Authors: Junxiang Yang, Hyundong Kim, Chaeyoung Lee, Sangkwon Kim, Jian Wang, Sungha Yoon, Jintae Park, Junseok Kim

Published in: Theoretical and Computational Fluid Dynamics | Issue 5-6/2020

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Abstract

In this study, we propose a novel computational model for simulating the coffee-ring phenomenon. The proposed method is based on a phase-field model and Monte Carlo simulation. We use the Allen–Cahn equation with a pinning boundary condition to model a drying droplet. The coffee particles inside the droplet move according to a random walk function with a truncated standard normal distribution under gravitational force. We perform both two-dimensional and three-dimensional computational experiments to demonstrate the accurate simulation of the coffee-ring phenomenon by the proposed model.

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Sobac, B., Brutin, D.: Thermal effects of the substrate on water droplet evaporation. Phys. Rev. E 86, 021602 (2012)

Leenaars, A.F.M., Huethorst, J.A.M., Van Oekel, J.J.: Marangoni drying: a new extremly clean drying process. Langmuir 6, 1701 (1990)

Brutin, D., Sobac, B., Loquet, B., Sampol, B.: Pattern formation in drying drops of blood. J. Fluid Mech. 667, 85–95 (2011)MATH

Sobac, B., Brutin, B.: Structural and evaporative evolutions in desiccating sessile drops of blood. Phys. Rev. E 84, 011603 (2011)

Kim, D., Jeong, S., Moon, J.: Organic thin film transistors with ink-jet printed metal nanoparticle electrodes of a reduced channel length by laser ablation. Appl. Phys. Lett. 91, 071114 (2006)

Jing, J., Reed, J., Huang, J., Hu, X., Clarke, V., Edington, J., Housman, D., Anantharaman, T.S., Huff, E.J., Mishra, B., Porter, B., Shenker, A., Wolfson, E., Hiort, C., Kantor, R., Aston, C., Schwartz, D.C.: Automated high resolution optical mapping using arrayed, fluid-fixed DNA molecules. Proc. Natl. Acad. Sci. 95, 8046 (1998)

Lal, S., Clare, S.E., Halas, N.J.: Nanoshell-enabled photothermal cancer therapy: impending clinical impact. Acc. Chem. Res. 41, 1842–1851 (2008)

Skirtach, A.G., Dejugnat, C., Braun, D., Susha, A.S., Rogach, A.L., Parak, W.J., Mohwald, H., Sukhorukov, G.B.: The role of metal nanoparticles in remote release of encapsulated materials. Nano. Lett. 5, 1371–1377 (2005)

Mugele, F., Baret, J.C.: Electrowetting: from basics to applications. J. Phys.: Condens. Matter 17, R705–R774 (2005)

10.

Murade, C.U., Oh, J.M., van den Ende, D., Mugele, F.: Electrowetting driven optical switch and tunable aperture. Opt. Express 19, 15525–15531 (2011)

11.

Chang, S.Y.P., Chao, Y.C.: icroemulsion polymerization of microlatex in sublimation ink for cotton fabric ink jet printing. J. Appl. Polym. Sci. 122, 1872–1881 (2011)

12.

Xue, C.H., Shi, M.M., Chen, H.Z., Wu, G., Wang, M.: Preparation and application of nanoscale microemulsion as binder for fabric inkjet printing. Colloid. Surf. A 287, 147–152 (2006)

13.

Kim, J.Y., Cho, K., Ryu, S.A., Kim, S.Y., Weon, B.M.: Crack formation and prevention in colloidal drops. Sci. Rep. 5, 13166 (2015)

14.

Tornero, A.F., Blasco, M.G., Azqueta, M.C., Acevedo, C.F., Castro, C.S., López, S.R.: Antimicrobial ecological waterborne paint based on novel hybrid nanoparticles of zinc oxide partially coated with silver. Prog. Org. Coat. 121, 130–141 (2018)

15.

Wu, Y., Lavernia, E.J.: Interaction mechanisms between ceramic particles and atomized metallic droplets. Metallurg. Trans. A 23, 2923–2937 (1992)

16.

Qu, R., Zhang, W., Liu, N., Zhang, Q., Liu, Y., Li, X., Wei, Y., Feng, L.: Antioil Ag\(_3\)PO\(_4\) nanoparticle/polydopamine/Al\(_2\)O\(_3\) sandwich structure for complex wastewater treatment: dynamics catalysis under natural light. ACS Sustain. Chem. Eng. 6, 8019–8028 (2018)

17.

Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Nagel, S.R., Witten, T.A.: Capillary flow as the cause of ring stains from dried liquid drops. Nature 389, 827–829 (1997)

18.

Conway, J., Korns, H., Fisch, M.R.: Evaporation kinematics of polystyrene bead suspensions. Langmuir 13, 426–431 (1997)

19.

Weon, B.M., Je, J.H.: Self-pinning by colloids confined at a contact line. Phys. Rev. Lett. 110, 028303 (2013)

20.

Bhardwaj, R., Feng, X., Attinger, D.: Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study. New J. Phys. 11, 075020 (2009)

21.

Boneberg, J., Burmeister, F., Schäfle, C., Leiderer, P., Reim, D., Fery, A., Herminghaus, S.: The formation of nano-dot and nano-ring structures in colloidal monolayer lithography. Langmuir 13, 7080–7084 (1997)

22.

Ondarçuhu, T., Joachim, C.: Drawing a single nanofibre over hundreds of microns. Europhys. Lett. 42, 215–220 (1998)

23.

Denkov, N.D., Velev, O.D., Kralchevsky, P.A., Ivanov, I.B., Yoshimura, H., Nagayama, K.: Mechanism of formation of two-dimensional crystals from latex particles on substrates. Langmuir 8, 3183–3190 (1992)

24.

Dimitrov, A.S., Dushkin, C.D., Yoshimura, H., Nagayama, K.: Observations of latex particle two-dimensional-crystal nucleation in wetting films on mercury, glass, and mica. Langmuir 10, 432–440 (1994)

25.

Vakaralski, I.U., Marston, J.O., Thoroddsen, S.T.: Foam-film-stabilized liquid bridge networks in evaporative lithography and wet granular matter. Langmuir 29, 4966–4973 (2013)

26.

Deegan, R.D.: Pattern formation on drying drops. Phys. Rev. E 61, 475–485 (2000)

27.

Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Nagel, S.R., Witten, T.A.: Contact line deposits in an evaporating drop. Phys. Rev. E 62, 756–765 (2000)

28.

Hu, H., Larson, R.G.: Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B 110, 7090–7094 (2006)

29.

Kim, H.S., Park, S.S., Hagelberg, F.: Computational approach to drying a nanoparticle-suspended liquid droplet. J. Nanopart. Res. 13, 59–68 (2011)

30.

Stannard, A.: Dewetting-mediated pattern formation in nanoparticle assemblies. J. Phys. Condens. Matter 23, 083001 (2011)

31.

Robbins, M.J., Archer, A.J., Thiele, U.: Modelling the evaporation of thin films of colloidal suspensions using dynamical density functional theory. J. Phys. Condens. Matter 23, 415102 (2011)

32.

Gupta, D., Peters, M.H.: A Brownian dynamics simulation of aerosol deposition onto spherical collectors. J. Colloid. Interface Sci. 104, 375–389 (1985)

33.

Chen, J.C., Kim, A.S.: Brownian dynamics, molecular dynamics, and Monte Carlo modeling of colloidal systems. Adv. Colloid. Interface Sci. 112, 159–173 (2004)

34.

Yunker, P.J., Still, T., Lohr, M.A., Yodh, A.G.: Suppression of the coffee-ring effect by shape-dependent capillary interactions. Nature 476, 308–311 (2011)

35.

Zhou, B., Heider, Y., Ma, S., Markert, B.: Phase-field-based modeling of the gelation process of biopolymer droplets in 3D bioprinting. Comput. Mech. 63, 1187–1202 (2019)MathSciNetMATH

36.

Shao, Y., Duan, Q., Qiu, S.: Adaptive consistent element-free Galerkin method for phase-field model of brittle fracture. Comput. Mech. 64, 741–767 (2019)MathSciNetMATH

37.

Yin, B., Kaliske, M.: Fracture simulation of viscoelastic polymers by the phase-field method. Comput. Mech. 65, 293–309 (2020)MathSciNet

38.

Chiu, P.H.: A coupled phase field framework for solving incompressible two-phase flows. J. Comput. Phys. 392, 115–140 (2019)MathSciNet

39.

Soligo, G., Roccon, A., Soldati, A.: Mass-conservation-improved phase field models for turbulent multiphase flow simulation. Acta Mech. 230, 683–696 (2019)MathSciNetMATH

40.

Zhu, G., Kou, J., Sun, S., Yao, J., Li, F.: Numerical approximation of a phase-field surfactant model with fluid flow. J. Sci. Comput. 80, 223–247 (2019)MathSciNetMATH

41.

Lee, H.G., Yang, J., Kim, J.: Pinning boundary conditions for phase-field models. Commun. Nonlinear Sci. Numer. Simul. 82, 105060 (2020)MathSciNet

42.

Kim, J.: Phase-field models for multi-component fluid flows. Commun. Comput. Phys. 12, 613–661 (2012)MathSciNetMATH

43.

Long, J., Luo, C., Yu, Q., Li, Y.: An unconditional stable compact fourth-order finite difference scheme for three dimensional Allen-Cahn equation. Comput. Math. Appl. 77, 1042–1054 (2019)MathSciNetMATH

44.

Saka, H., Bengston, R.D., Reichl, L.E.: Relaxation of Brownian particles in a gravitational field. Am. J. Phys. 77, 240–243 (2009)

45.

Barr, D.R., Sherrill, E.T.: Mean and variance of truncated normal distributions. Am. Stat. 53, 357–361 (1999)

46.

Codling, E.A., Bearon, R.N., Thorn, G.J.: Diffusion about the mean drift location in a biased random walk. Ecology 91, 3106–3113 (2010)

47.

Mazzeo, D., Oliveti, G., Labonia, E.: Estimation of wind speed probability density function using a mixture of two truncated normal distributions. Renew. Energy 115, 1260–1280 (2018)

48.

Shur, V.Y., Bykov, D.A., Mingaliev, E.A., Tyurnina, A.E., Burban, G.V., Kadushnikov, R.M., Mizgulin, V.V.: Coffee ring effect during drying of colloid drop: experiment and computer simulation. Ferroelectrics 476, 47–53 (2015)

49.

Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Nagel, S.R., Witten, T.A.: Capillary flows as the cause of ring stains from dried liquid drops. Nature 389, 827–829 (1997)

Title: Phase-field modeling and computer simulation of the coffee-ring effect
Authors: Junxiang Yang
Hyundong Kim
Chaeyoung Lee
Sangkwon Kim
Jian Wang
Sungha Yoon
Jintae Park
Junseok Kim
Publication date: 12-07-2020
Publisher: Springer Berlin Heidelberg
Published in: Theoretical and Computational Fluid Dynamics / Issue 5-6/2020
Print ISSN: 0935-4964
Electronic ISSN: 1432-2250
DOI: https://doi.org/10.1007/s00162-020-00544-w

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