Combined Probabilistic Methods for Droplet Drying Simulations
Wolak Wiktor, Drzewiński Andrzej, Marć Maciej, Najder-Kozdrowska Lidia, Dudek Mirosław R. *
University of Zielona Góra
Institute of Physics
ul. Szafrana 4a, 65-069 Zielona Góra, Poland∗E-mail: m.dudek@if.uz.zgora.pl
Received:
Received: 15 November 2021; revised: 16 December 2021; accepted: 18 December 2021; published online: 29 December 2021
DOI: 10.12921/cmst.2021.0000032
Abstract:
The rapidly developing 3D printing and the related fabrication of ultra-thin layers in various industries have resulted in the need for theoretical methods for describing large-area systems of growing nanostructures. The specificity of these issues is the presence of multi-particle systems characterized by the coexistence of particles with a wide range of sizes typical for ions, nanoparticles, and their agglomerates. A particular example would be an aqueous nano-colloidal suspension drying on a substrate as a self-assembling deposit. It should be emphasized here that the development of deposit patterning control techniques is one of the most important challenges for the thin film industry. In this paper we show that probabilistic methods can be successfully used to model such systems. To this aim, the combined master equation and Monte Carlo methods were used for computer simulation of a drying droplet in the case of a low concentration salt solution.The novelty of this approach is to show the possibility of computer simulation for a microscopic system while simulating large-scale processes affecting microscopic processes. The numerical results were additionally supported by experimental data.
Key words:
deposit patterning, drying droplet, master equation, Monte Carlo
References:
[1] R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Capillary flow as the cause of ring stains from dried liquid drops, Nature 389, 827–829 (1997).
[2] R.G. Larson, Re-Shaping the Coffee Ring, Angew. Chem. Int. Ed. 51, 2546–2548 (2012).
[3] P.J. Yunker, T. Still, M.A. Lohr, A.G. Yodh, Suppression of the coffee-ring effect by shape-dependent capillary interactions, Nature 476, 308–311 (2011).
[4] D. Soltman, V. Subramanian, Inkjet-Printed Line Morphologies and Temperature Control of the Coffee Ring Effect, Langmuir 24, 2224–2231 (2008).
[5] A. Crivoi, F. Duan, Three-dimensional Monte Carlo model of the coffee-ring effect in evaporating colloidal droplets, Sci. Rep. 4, 4310 (2014).
[6] H.K. Christenson, N.H. Thomson, The nature of the air-cleaved mica surface, Surf. Sci. Rep. 71, 367–390 (2016).
[7] H. Hu, R.G. Larson, Evaporation of a Sessile Droplet on a Substrate, J. Phys. Chem. B 106, 1334–1344 (2002).
[8] H. Okada, S.N. Atluri, Computational and Experimental Simulations in Engineering, Mechanisms and Machine Science 75 (2020).
[9] J. Desarnaud, H. Derluyn, J. Carmeliet, D. Bonn, N. Shahid-zadeh, Hopper Growth of Salt Crystals, J. Phys. Chem. Lett. 9, 2961–2966 (2018).
[10] T. Vicsek, Fractal growth phenomena, World Scientific Publishing Co. Pte. Ltd. (1992).
[11] G.F. Harrington, J.M. Campbell, H.K. Christenson, Crystal Patterns Created by Rupture of a Thin Film, Cryst. Growth Des. 13, 5062–5067 (2013).
The rapidly developing 3D printing and the related fabrication of ultra-thin layers in various industries have resulted in the need for theoretical methods for describing large-area systems of growing nanostructures. The specificity of these issues is the presence of multi-particle systems characterized by the coexistence of particles with a wide range of sizes typical for ions, nanoparticles, and their agglomerates. A particular example would be an aqueous nano-colloidal suspension drying on a substrate as a self-assembling deposit. It should be emphasized here that the development of deposit patterning control techniques is one of the most important challenges for the thin film industry. In this paper we show that probabilistic methods can be successfully used to model such systems. To this aim, the combined master equation and Monte Carlo methods were used for computer simulation of a drying droplet in the case of a low concentration salt solution.The novelty of this approach is to show the possibility of computer simulation for a microscopic system while simulating large-scale processes affecting microscopic processes. The numerical results were additionally supported by experimental data.
Key words:
deposit patterning, drying droplet, master equation, Monte Carlo
References:
[1] R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Capillary flow as the cause of ring stains from dried liquid drops, Nature 389, 827–829 (1997).
[2] R.G. Larson, Re-Shaping the Coffee Ring, Angew. Chem. Int. Ed. 51, 2546–2548 (2012).
[3] P.J. Yunker, T. Still, M.A. Lohr, A.G. Yodh, Suppression of the coffee-ring effect by shape-dependent capillary interactions, Nature 476, 308–311 (2011).
[4] D. Soltman, V. Subramanian, Inkjet-Printed Line Morphologies and Temperature Control of the Coffee Ring Effect, Langmuir 24, 2224–2231 (2008).
[5] A. Crivoi, F. Duan, Three-dimensional Monte Carlo model of the coffee-ring effect in evaporating colloidal droplets, Sci. Rep. 4, 4310 (2014).
[6] H.K. Christenson, N.H. Thomson, The nature of the air-cleaved mica surface, Surf. Sci. Rep. 71, 367–390 (2016).
[7] H. Hu, R.G. Larson, Evaporation of a Sessile Droplet on a Substrate, J. Phys. Chem. B 106, 1334–1344 (2002).
[8] H. Okada, S.N. Atluri, Computational and Experimental Simulations in Engineering, Mechanisms and Machine Science 75 (2020).
[9] J. Desarnaud, H. Derluyn, J. Carmeliet, D. Bonn, N. Shahid-zadeh, Hopper Growth of Salt Crystals, J. Phys. Chem. Lett. 9, 2961–2966 (2018).
[10] T. Vicsek, Fractal growth phenomena, World Scientific Publishing Co. Pte. Ltd. (1992).
[11] G.F. Harrington, J.M. Campbell, H.K. Christenson, Crystal Patterns Created by Rupture of a Thin Film, Cryst. Growth Des. 13, 5062–5067 (2013).
