A Variational approach to thin film hydrodynamics of binary mixtures

Xinpeng Xu; Uwe Thiele; Tiezheng Qian

doi:10.1088/0953-8984/27/8/085005

A Variational approach to thin film hydrodynamics of binary mixtures

Xinpeng Xu, Uwe Thiele, Tiezheng Qian

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager's variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager's reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory-Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.

Original language	English
Article number	085005
Journal	Journal of Physics Condensed Matter
Volume	27
Issue number	8
DOIs	https://doi.org/10.1088/0953-8984/27/8/085005
State	Published - 4 Mar 2015
Externally published	Yes

Keywords

binary mixtures
capillarity
liquid thin films
liquidsolid interfaces
modeling
wettability

Access to Document

10.1088/0953-8984/27/8/085005

Cite this

@article{d1855607bad240f8b2469a144e2cfef1,

title = "A Variational approach to thin film hydrodynamics of binary mixtures",

abstract = "In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager's variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager's reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory-Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.",

keywords = "binary mixtures, capillarity, liquid thin films, liquidsolid interfaces, modeling, wettability",

author = "Xinpeng Xu and Uwe Thiele and Tiezheng Qian",

note = "Publisher Copyright: {\textcopyright} 2015 IOP Publishing Ltd.",

year = "2015",

month = mar,

day = "4",

doi = "10.1088/0953-8984/27/8/085005",

language = "英语",

volume = "27",

journal = "Journal of Physics Condensed Matter",

issn = "0953-8984",

publisher = "IOP Publishing Ltd.",

number = "8",

}

TY - JOUR

T1 - A Variational approach to thin film hydrodynamics of binary mixtures

AU - Xu, Xinpeng

AU - Thiele, Uwe

AU - Qian, Tiezheng

PY - 2015/3/4

Y1 - 2015/3/4

N2 - In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager's variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager's reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory-Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.

AB - In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager's variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager's reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory-Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.

KW - binary mixtures

KW - capillarity

KW - liquid thin films

KW - liquidsolid interfaces

KW - modeling

KW - wettability

UR - http://www.scopus.com/inward/record.url?scp=84922570099&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/27/8/085005

DO - 10.1088/0953-8984/27/8/085005

M3 - 文章

AN - SCOPUS:84922570099

SN - 0953-8984

VL - 27

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

IS - 8

M1 - 085005

ER -

A Variational approach to thin film hydrodynamics of binary mixtures

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this