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2017 | OriginalPaper | Chapter

Transmission Probability of Diffusing Particles—A Case Study

Authors : Kinnari Shah, Nuggehalli M. Ravindra

Published in: TMS 2017 146th Annual Meeting & Exhibition Supplemental Proceedings

Publisher: Springer International Publishing

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Abstract

A diffusing particle is subjected to a variety of collisions that lead to a random or Brownian motion. The aim of this study is to compute the transmission probability and highlight the visualization of Brownian motion under the conditions of varying viscosity, particle size and temperature. As a preliminary study, two simulation results such as transport of diluted species and particle based approach have been compared and the transmission probability is computed by a particle based approach. We validate our results with Stokes-Einstein equation and Fang and Ning’s experimental and theoretical work and show that the transmission probability increases with decrease in viscosity and particle size and increase in temperature. The obtained results also describe the Brownian motion for various particle sizes, viscosity and temperature.

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Literature
1.
go back to reference S.C. Glotzer, M.J. Solomon, N.A. Kotov, AIChE J. 50(12), 2978–2985 (2004)CrossRef S.C. Glotzer, M.J. Solomon, N.A. Kotov, AIChE J. 50(12), 2978–2985 (2004)CrossRef
3.
go back to reference J.N. Israelachvili, Intermolecular and Surface Forces, 2nd edn. (Academic Press, Amsterdam, 2003), p. 450 J.N. Israelachvili, Intermolecular and Surface Forces, 2nd edn. (Academic Press, Amsterdam, 2003), p. 450
4.
go back to reference A.P. Alivisatos, P.F. Barbara, A.W. Castleman, J. Chang, D.A. Dizon, M.L. Klein, G.L. McLendon, J.S. Miller, M.A. Ratner, P.J. Rossky, S.I. Stupp, M.E. Thompson, Adv. Mater. 10, 1297 (1998)CrossRef A.P. Alivisatos, P.F. Barbara, A.W. Castleman, J. Chang, D.A. Dizon, M.L. Klein, G.L. McLendon, J.S. Miller, M.A. Ratner, P.J. Rossky, S.I. Stupp, M.E. Thompson, Adv. Mater. 10, 1297 (1998)CrossRef
5.
go back to reference K.M. Chen, X. Jiang, L.C. Kimerling, P.T. Hammond, Langmuir, 16(2000), 7825–7834 K.M. Chen, X. Jiang, L.C. Kimerling, P.T. Hammond, Langmuir, 16(2000), 7825–7834
6.
7.
go back to reference J. Schmitt, P. Machtle, D. Eck, H. Mohwald, C.A. Helm, Langmuir 15, 3256 (1999)CrossRef J. Schmitt, P. Machtle, D. Eck, H. Mohwald, C.A. Helm, Langmuir 15, 3256 (1999)CrossRef
10.
go back to reference M. Trau, S. Sankaran, D.A. Saville, I.A. Aksay, Nature 374, 437–439 (1995)CrossRef M. Trau, S. Sankaran, D.A. Saville, I.A. Aksay, Nature 374, 437–439 (1995)CrossRef
11.
12.
go back to reference H.X. He, H. Zhang, Q.G. Li, T. Zhu, S.F.Y. Li, Z.F. Liu, Langmuir 16, 3846–3851 (2000)CrossRef H.X. He, H. Zhang, Q.G. Li, T. Zhu, S.F.Y. Li, Z.F. Liu, Langmuir 16, 3846–3851 (2000)CrossRef
13.
go back to reference P. Jiang, J.F. Bertone, K.S. Hwang, V.L. Colvin, Chem. Mater. 11, 2132–2140 (1999)CrossRef P. Jiang, J.F. Bertone, K.S. Hwang, V.L. Colvin, Chem. Mater. 11, 2132–2140 (1999)CrossRef
14.
go back to reference R.G. Freeman, K.C. Grabar, K.J. Allison, R.M. Bright, J.A. Divas, A.P. Guthrie, M.B. Hommer, M.A. Jackson, P.C. Smith, D.G. Walter, M.J. Natan, Science 267, 1629–1632 (1995)CrossRef R.G. Freeman, K.C. Grabar, K.J. Allison, R.M. Bright, J.A. Divas, A.P. Guthrie, M.B. Hommer, M.A. Jackson, P.C. Smith, D.G. Walter, M.J. Natan, Science 267, 1629–1632 (1995)CrossRef
15.
16.
go back to reference H.X. He, W. Huang, H. Zhang, Q.G. Li, F.Y.S. Li, Z.F. Liu, Langmuir 16, 517 (2000)CrossRef H.X. He, W. Huang, H. Zhang, Q.G. Li, F.Y.S. Li, Z.F. Liu, Langmuir 16, 517 (2000)CrossRef
17.
18.
go back to reference N. Aubry, P. Singh, M. Janjua and S. Nudurupati, Proc. Natl. Acad. Sci. U.S.A. 105 (2008), 3711–3714; N. Aubry, and P. Singh, Phys. Rev. E, 77 (2008), 056302 N. Aubry, P. Singh, M. Janjua and S. Nudurupati, Proc. Natl. Acad. Sci. U.S.A. 105 (2008), 3711–3714; N. Aubry, and P. Singh, Phys. Rev. E, 77 (2008), 056302
19.
go back to reference D.Y.C. Chan, J.D. Henry Jr., L.R. White, J. Colloid Interface Sci. 79, 410 (1981)CrossRef D.Y.C. Chan, J.D. Henry Jr., L.R. White, J. Colloid Interface Sci. 79, 410 (1981)CrossRef
21.
go back to reference M. Janjua, S. Nudurupati, P. Singh, N. Aubry, Electrophoresis 32, 518–526 (2011)CrossRef M. Janjua, S. Nudurupati, P. Singh, N. Aubry, Electrophoresis 32, 518–526 (2011)CrossRef
23.
go back to reference N. Aubry, P. Singh, M. Janjua, S. Nudurupati, Proc. Natl. Acad. Sci. U.S.A. 105, 3711–3714 (2008)CrossRef N. Aubry, P. Singh, M. Janjua, S. Nudurupati, Proc. Natl. Acad. Sci. U.S.A. 105, 3711–3714 (2008)CrossRef
24.
go back to reference N. Bowden, A. Terfort, J. Carbeck, G.M. Whitesides, Science 276(5310), 233–235 (1997)CrossRef N. Bowden, A. Terfort, J. Carbeck, G.M. Whitesides, Science 276(5310), 233–235 (1997)CrossRef
25.
go back to reference C.D. Dushkin, K. Nagayama, T. Miwa, P.A. Kralchevsky, Langmuir 9, 3695–3701 (1993)CrossRef C.D. Dushkin, K. Nagayama, T. Miwa, P.A. Kralchevsky, Langmuir 9, 3695–3701 (1993)CrossRef
28.
go back to reference V.I. Tikhonov, M.A. Mironov, Markov Processes (Sov. Radio, Moscow, 1977) V.I. Tikhonov, M.A. Mironov, Markov Processes (Sov. Radio, Moscow, 1977)
29.
go back to reference S.A. Akhmanov, Yu.E. D’yakov, A.S. Chirkin, Introduction to Statistical Radio Physics and Optics (Nauka, Moscow, 1981) S.A. Akhmanov, Yu.E. D’yakov, A.S. Chirkin, Introduction to Statistical Radio Physics and Optics (Nauka, Moscow, 1981)
30.
go back to reference B.V. Gnedenko, in Theory of Probability (Fizmatgiz, Moscow, 1961; Central Books, London, 1970), ed. by V.I. Bogachev, Gaussian Measures (Nauka, Moscow, 1997) B.V. Gnedenko, in Theory of Probability (Fizmatgiz, Moscow, 1961; Central Books, London, 1970), ed. by V.I. Bogachev, Gaussian Measures (Nauka, Moscow, 1997)
31.
go back to reference I.I. Gikhman, A.V. Skorokhod, Introduction to the Theory of Random Processes (Nauka, Moscow, 1965; Saunders, Philadelphia, 1969) I.I. Gikhman, A.V. Skorokhod, Introduction to the Theory of Random Processes (Nauka, Moscow, 1965; Saunders, Philadelphia, 1969)
32.
go back to reference R. Elliott, Stochastic Calculus Applications (Springer, Berlin, 1983; Mir, Moscow, 1986) R. Elliott, Stochastic Calculus Applications (Springer, Berlin, 1983; Mir, Moscow, 1986)
33.
go back to reference A.N. Borodin, P. Salminen, Handbook on Brownian Motion (Birkhäuser Verlag, Basel, 1996; Lan’, St.Petersburg, 2000) A.N. Borodin, P. Salminen, Handbook on Brownian Motion (Birkhäuser Verlag, Basel, 1996; Lan’, St.Petersburg, 2000)
34.
35.
go back to reference H.Y. Fang, M. Ning, J. Hydrodyn. 26(6), 875–881 (2014) H.Y. Fang, M. Ning, J. Hydrodyn. 26(6), 875–881 (2014)
36.
go back to reference Brownian Motion, Solved COMSOL Multiphys. 5, 2 (2015) Brownian Motion, Solved COMSOL Multiphys. 5, 2 (2015)
37.
go back to reference M. Hossain, K. Shah, D. Ju, S. Gurupatham, I.S. Fischer, P. Singh, ASME 2013 Fluids Engineering Summer Meeting (FEDSM 2013), 7–11 July 2013, Nevada, USA M. Hossain, K. Shah, D. Ju, S. Gurupatham, I.S. Fischer, P. Singh, ASME 2013 Fluids Engineering Summer Meeting (FEDSM 2013), 7–11 July 2013, Nevada, USA
38.
Metadata
Title
Transmission Probability of Diffusing Particles—A Case Study
Authors
Kinnari Shah
Nuggehalli M. Ravindra
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-51493-2_72

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