TY - JOUR
T1 - A Variational approach to thin film hydrodynamics of binary mixtures
AU - Xu, Xinpeng
AU - Thiele, Uwe
AU - Qian, Tiezheng
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work is supported by Hong Kong RGC Grant No 604013. T Qian and U Thiele would like to thank the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge for the Research Program 'Mathematical Modelling and Analysis of Complex Fluids and Active Media in Evolving Domains' in which this work was initiated.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2015/2/4
Y1 - 2015/2/4
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.
UR - http://hdl.handle.net/10754/600242
UR - https://iopscience.iop.org/article/10.1088/0953-8984/27/8/085005
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 - Article
C2 - 25651053
SN - 0953-8984
VL - 27
SP - 085005
JO - Journal of Physics: Condensed Matter
JF - Journal of Physics: Condensed Matter
IS - 8
ER -