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Title: Inclusion of line tension effect in classical nucleation theory for heterogeneous nucleation: A rigorous thermodynamic formulation and some unique conclusions

Abstract

A rigorous thermodynamic formulation of the geometric model for heterogeneous nucleation including line tension effect is missing till date due to the associated mathematical hurdles. In this work, we develop a novel thermodynamic formulation based on Classical Nucleation Theory (CNT), which is supposed to illustrate a systematic and a more plausible analysis for the heterogeneous nucleation on a planar surface including the line tension effect. The appreciable range of the critical microscopic contact angle (θ{sub c}), obtained from the generalized Young’s equation and the stability analysis, is θ{sub ∞} < θ{sub c} < θ′ for positive line tension and is θ{sub M} < θ{sub c} < θ{sub ∞} for negative line tension. θ{sub ∞} is the macroscopic contact angle, θ′ is the contact angle for which the Helmholtz free energy has the minimum value for the positive line tension, and θ{sub M} is the local minima of the nondimensional line tension effect for the negative line tension. The shape factor f, which is basically the dimensionless critical free energy barrier, becomes higher for lower values of θ{sub ∞} and higher values of θ{sub c} for positive line tension. The combined effect due to the presence of the triple line andmore » the interfacial areas (f{sup L} + f{sup S}) in shape factor is always within (0, 3.2), resulting f in the range of (0, 1.7) for positive line tension. A formerly presumed appreciable range for θ{sub c}(0 < θ{sub c} < θ{sub ∞}) is found not to be true when the effect of negative line tension is considered for CNT. Estimation based on the property values of some real fluids confirms the relevance of the present analysis.« less

Authors:
;  [1]
  1. Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302 (India)
Publication Date:
OSTI Identifier:
22415515
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 142; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FLUIDS; FLUORINE IONS; FREE ENERGY; INCLUSIONS; NUCLEATION; PARTIAL DIFFERENTIAL EQUATIONS; PHASE STABILITY; SURFACES

Citation Formats

Singha, Sanat K., Das, Prasanta K., E-mail: pkd@mech.iitkgp.ernet.in, and Maiti, Biswajit. Inclusion of line tension effect in classical nucleation theory for heterogeneous nucleation: A rigorous thermodynamic formulation and some unique conclusions. United States: N. p., 2015. Web. doi:10.1063/1.4914141.
Singha, Sanat K., Das, Prasanta K., E-mail: pkd@mech.iitkgp.ernet.in, & Maiti, Biswajit. Inclusion of line tension effect in classical nucleation theory for heterogeneous nucleation: A rigorous thermodynamic formulation and some unique conclusions. United States. doi:10.1063/1.4914141.
Singha, Sanat K., Das, Prasanta K., E-mail: pkd@mech.iitkgp.ernet.in, and Maiti, Biswajit. Sat . "Inclusion of line tension effect in classical nucleation theory for heterogeneous nucleation: A rigorous thermodynamic formulation and some unique conclusions". United States. doi:10.1063/1.4914141.
@article{osti_22415515,
title = {Inclusion of line tension effect in classical nucleation theory for heterogeneous nucleation: A rigorous thermodynamic formulation and some unique conclusions},
author = {Singha, Sanat K. and Das, Prasanta K., E-mail: pkd@mech.iitkgp.ernet.in and Maiti, Biswajit},
abstractNote = {A rigorous thermodynamic formulation of the geometric model for heterogeneous nucleation including line tension effect is missing till date due to the associated mathematical hurdles. In this work, we develop a novel thermodynamic formulation based on Classical Nucleation Theory (CNT), which is supposed to illustrate a systematic and a more plausible analysis for the heterogeneous nucleation on a planar surface including the line tension effect. The appreciable range of the critical microscopic contact angle (θ{sub c}), obtained from the generalized Young’s equation and the stability analysis, is θ{sub ∞} < θ{sub c} < θ′ for positive line tension and is θ{sub M} < θ{sub c} < θ{sub ∞} for negative line tension. θ{sub ∞} is the macroscopic contact angle, θ′ is the contact angle for which the Helmholtz free energy has the minimum value for the positive line tension, and θ{sub M} is the local minima of the nondimensional line tension effect for the negative line tension. The shape factor f, which is basically the dimensionless critical free energy barrier, becomes higher for lower values of θ{sub ∞} and higher values of θ{sub c} for positive line tension. The combined effect due to the presence of the triple line and the interfacial areas (f{sup L} + f{sup S}) in shape factor is always within (0, 3.2), resulting f in the range of (0, 1.7) for positive line tension. A formerly presumed appreciable range for θ{sub c}(0 < θ{sub c} < θ{sub ∞}) is found not to be true when the effect of negative line tension is considered for CNT. Estimation based on the property values of some real fluids confirms the relevance of the present analysis.},
doi = {10.1063/1.4914141},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 10,
volume = 142,
place = {United States},
year = {2015},
month = {3}
}