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Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants

Published online by Cambridge University Press:  27 September 2019

Guangpu Zhu Open the ORCID record for Guangpu Zhu [Opens in a new window] ,
Jisheng Kou ,
Bowen Yao ,
Yu-shu Wu ,
Jun Yao  and
Shuyu Sun
Guangpu Zhu
Affiliation:
Research Center of Multiphase Flow in Porous Media, School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China
Jisheng Kou
Affiliation:
School of Civil Engineering, Shaoxing University, Shaoxing 312000, Zhejiang, China School of Mathematics and Statistics, Hubei Engineering University, Xiaogan 432000, Hubei, China
Bowen Yao
Affiliation:
Department of Petroleum Engineering, Colorado School of Mines, 1600 Arapahoe Street, Golden, CO 80401, USA
Yu-shu Wu
Affiliation:
Department of Petroleum Engineering, Colorado School of Mines, 1600 Arapahoe Street, Golden, CO 80401, USA
Jun Yao*
Affiliation:
Research Center of Multiphase Flow in Porous Media, School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China
Shuyu Sun*
Affiliation:
Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia
*
†Email addresses for correspondence: rcogfr_upc@126.com, shuyu.sun@kaust.edu.sa
†Email addresses for correspondence: rcogfr_upc@126.com, shuyu.sun@kaust.edu.sa
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Abstract

Droplet dynamics on a solid substrate is significantly influenced by surfactants. It remains a challenging task to model and simulate the moving contact line dynamics with soluble surfactants. In this work, we present a derivation of the phase-field moving contact line model with soluble surfactants through the first law of thermodynamics, associated thermodynamic relations and the Onsager variational principle. The derived thermodynamically consistent model consists of two Cahn–Hilliard type of equations governing the evolution of interface and surfactant concentration, the incompressible Navier–Stokes equations and the generalized Navier boundary condition for the moving contact line. With chemical potentials derived from the free energy functional, we analytically obtain certain equilibrium properties of surfactant adsorption, including equilibrium profiles for phase-field variables, the Langmuir isotherm and the equilibrium equation of state. A classical droplet spread case is used to numerically validate the moving contact line model and equilibrium properties of surfactant adsorption. The influence of surfactants on the contact line dynamics observed in our simulations is consistent with the results obtained using sharp interface models. Using the proposed model, we investigate the droplet dynamics with soluble surfactants on a chemically patterned surface. It is observed that droplets will form three typical flow states as a result of different surfactant bulk concentrations and defect strengths, specifically the coalescence mode, the non-coalescence mode and the detachment mode. In addition, a phase diagram for the three flow states is presented. Finally, we study the unbalanced Young stress acting on triple-phase contact points. The unbalanced Young stress could be a driving or resistance force, which is determined by the critical defect strength.

JFM classification

Interfacial Flows (free surface): Contact lines Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 327 - 359
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Copyright
© 2019 Cambridge University Press 

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