Volume 25, Issue 2
Three-Phase Model of Visco-Elastic Incompressible Fluid Flow and Its Computational Implementation

Shixin Xu, Mark Alber & Zhiliang Xu

Commun. Comput. Phys., 25 (2019), pp. 586-624.

Published online: 2018-10

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  • Abstract

Energetic Variational Approach is used to derive a novel thermodynamically consistent three-phase model of a mixture of Newtonian and visco-elastic fluids. The model which automatically satisfies the energy dissipation law and is Galilean invariant, consists of coupled Navier-Stokes and Cahn-Hilliard equations. Modified General Navier Boundary Condition with fluid elasticity taken into account is also introduced for using the model to study moving contact line problems. Energy stable numerical scheme is developed to solve system of model equations efficiently. Convergence of the numerical scheme is verified by simulating a droplet sliding on an inclined plane under gravity. The model can be applied for studying various biological or biophysical problems. Predictive abilities of the model are demonstrated by simulating deformation of venous blood clots with different visco-elastic properties and experimentally observed internal structures under different biologically relevant shear blood flow conditions.

  • Keywords

Phase field method, Energetic Variational Approach, multi-phase flow, visco-elasticity, variable density, slip boundary condition, deformation of blood clot, thrombus.

  • AMS Subject Headings

92C05, 92C10, 65M12, 35Q35, 35Q92

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-586, author = {}, title = {Three-Phase Model of Visco-Elastic Incompressible Fluid Flow and Its Computational Implementation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {2}, pages = {586--624}, abstract = {

Energetic Variational Approach is used to derive a novel thermodynamically consistent three-phase model of a mixture of Newtonian and visco-elastic fluids. The model which automatically satisfies the energy dissipation law and is Galilean invariant, consists of coupled Navier-Stokes and Cahn-Hilliard equations. Modified General Navier Boundary Condition with fluid elasticity taken into account is also introduced for using the model to study moving contact line problems. Energy stable numerical scheme is developed to solve system of model equations efficiently. Convergence of the numerical scheme is verified by simulating a droplet sliding on an inclined plane under gravity. The model can be applied for studying various biological or biophysical problems. Predictive abilities of the model are demonstrated by simulating deformation of venous blood clots with different visco-elastic properties and experimentally observed internal structures under different biologically relevant shear blood flow conditions.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0167}, url = {http://global-sci.org/intro/article_detail/cicp/12764.html} }
TY - JOUR T1 - Three-Phase Model of Visco-Elastic Incompressible Fluid Flow and Its Computational Implementation JO - Communications in Computational Physics VL - 2 SP - 586 EP - 624 PY - 2018 DA - 2018/10 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2017-0167 UR - https://global-sci.org/intro/article_detail/cicp/12764.html KW - Phase field method, Energetic Variational Approach, multi-phase flow, visco-elasticity, variable density, slip boundary condition, deformation of blood clot, thrombus. AB -

Energetic Variational Approach is used to derive a novel thermodynamically consistent three-phase model of a mixture of Newtonian and visco-elastic fluids. The model which automatically satisfies the energy dissipation law and is Galilean invariant, consists of coupled Navier-Stokes and Cahn-Hilliard equations. Modified General Navier Boundary Condition with fluid elasticity taken into account is also introduced for using the model to study moving contact line problems. Energy stable numerical scheme is developed to solve system of model equations efficiently. Convergence of the numerical scheme is verified by simulating a droplet sliding on an inclined plane under gravity. The model can be applied for studying various biological or biophysical problems. Predictive abilities of the model are demonstrated by simulating deformation of venous blood clots with different visco-elastic properties and experimentally observed internal structures under different biologically relevant shear blood flow conditions.

Shixin Xu, Mark Alber & Zhiliang Xu. (2020). Three-Phase Model of Visco-Elastic Incompressible Fluid Flow and Its Computational Implementation. Communications in Computational Physics. 25 (2). 586-624. doi:10.4208/cicp.OA-2017-0167
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