# A mixed formulation of a sharp interface model of stokes flow with moving contact lines

- Volume: 48, Issue: 4, page 969-1009
- ISSN: 0764-583X

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topWalker, Shawn W.. "A mixed formulation of a sharp interface model of stokes flow with moving contact lines." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.4 (2014): 969-1009. <http://eudml.org/doc/273319>.

@article{Walker2014,

abstract = {Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking level) and allows for moving contact lines and contact angle hysteresis and pinning through a variational inequality. Moreover, the formulation can be extended to include non-linear contact line motion models. We prove the well-posedness of the time semi-discrete system and fully discrete method using appropriate choices of finite element spaces. A formal energy law is derived for the semi-discrete and fully discrete formulations and preliminary error estimates are also given. Simulation results are presented for a droplet in multiple configurations to illustrate the method.},

author = {Walker, Shawn W.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {mixed method; Stokes equations; surface tension; contact line motion; contact line pinning; variational inequality; well-posedness},

language = {eng},

number = {4},

pages = {969-1009},

publisher = {EDP-Sciences},

title = {A mixed formulation of a sharp interface model of stokes flow with moving contact lines},

url = {http://eudml.org/doc/273319},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Walker, Shawn W.

TI - A mixed formulation of a sharp interface model of stokes flow with moving contact lines

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 4

SP - 969

EP - 1009

AB - Two-phase fluid flows on substrates (i.e. wetting phenomena) are important in many industrial processes, such as micro-fluidics and coating flows. These flows include additional physical effects that occur near moving (three-phase) contact lines. We present a new 2-D variational (saddle-point) formulation of a Stokesian fluid with surface tension that interacts with a rigid substrate. The model is derived by an Onsager type principle using shape differential calculus (at the sharp-interface, front-tracking level) and allows for moving contact lines and contact angle hysteresis and pinning through a variational inequality. Moreover, the formulation can be extended to include non-linear contact line motion models. We prove the well-posedness of the time semi-discrete system and fully discrete method using appropriate choices of finite element spaces. A formal energy law is derived for the semi-discrete and fully discrete formulations and preliminary error estimates are also given. Simulation results are presented for a droplet in multiple configurations to illustrate the method.

LA - eng

KW - mixed method; Stokes equations; surface tension; contact line motion; contact line pinning; variational inequality; well-posedness

UR - http://eudml.org/doc/273319

ER -

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