Volume 1, Issue 1
Molecular Hydrodynamics of the Moving Contact Line in Two-phase Immiscible Flows

Tiezheng Qian, Xiao-Ping Wang & Ping Sheng

DOI:

Commun. Comput. Phys., 1 (2006), pp. 1-52.

Published online: 2006-01

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  • Abstract

The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible fluids intersects the solid wall. Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition, since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line. In this paper we first present an introductory review of the problem. We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow, from molecular dynamics (MD) simulations to continuum hydrodynamics calculations. Through extensive MD studies and detailed analysis, we have uncovered the slip boundary condition governing the moving contact line, denoted the generalized Navier boundary condition. We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results down to the molecular scale. These results serve to affirm the validity of the generalized Navier boundary condition, as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.

  • Keywords

Inverse problems viscoelastic models wave propagation in biotissue statistical models

  • AMS Subject Headings

34A55 35R30 74J25 62J02 93A30

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COPYRIGHT: © Global Science Press

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@Article{CiCP-1-1, author = {}, title = {Molecular Hydrodynamics of the Moving Contact Line in Two-phase Immiscible Flows}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {1}, pages = {1--52}, abstract = {

The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible fluids intersects the solid wall. Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition, since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line. In this paper we first present an introductory review of the problem. We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow, from molecular dynamics (MD) simulations to continuum hydrodynamics calculations. Through extensive MD studies and detailed analysis, we have uncovered the slip boundary condition governing the moving contact line, denoted the generalized Navier boundary condition. We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results down to the molecular scale. These results serve to affirm the validity of the generalized Navier boundary condition, as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7949.html} }
TY - JOUR T1 - Molecular Hydrodynamics of the Moving Contact Line in Two-phase Immiscible Flows JO - Communications in Computational Physics VL - 1 SP - 1 EP - 52 PY - 2006 DA - 2006/01 SN - 1 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7949.html KW - Inverse problems KW - viscoelastic models KW - wave propagation in biotissue KW - statistical models AB -

The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible fluids intersects the solid wall. Decades ago it was already known that the moving contact line is incompatible with the no-slip boundary condition, since the latter would imply infinite dissipation due to a non-integrable singularity in the stress near the contact line. In this paper we first present an introductory review of the problem. We then present a detailed review of our recent results on the contact-line motion in immiscible two-phase flow, from molecular dynamics (MD) simulations to continuum hydrodynamics calculations. Through extensive MD studies and detailed analysis, we have uncovered the slip boundary condition governing the moving contact line, denoted the generalized Navier boundary condition. We have used this discovery to formulate a continuum hydrodynamic model whose predictions are in remarkable quantitative agreement with the MD simulation results down to the molecular scale. These results serve to affirm the validity of the generalized Navier boundary condition, as well as to open up the possibility of continuum hydrodynamic calculations of immiscible flows that are physically meaningful at the molecular level.

Tiezheng Qian, Xiao-Ping Wang & Ping Sheng. (1970). Molecular Hydrodynamics of the Moving Contact Line in Two-phase Immiscible Flows. Communications in Computational Physics. 1 (1). 1-52. doi:
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