Viscous flow over a chemically patterned surface

Sprittles, James E.; Shikhmurzaev, Yulii D.

doi:10.1103/physreve.76.021602

Cited by 13 publications

(12 citation statements)

References 25 publications

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“…A userfriendly step-by-step guide specifying the entire implementation can be found in Sprittles and Shikhmurzaev [19]. The same code has previously been used to simulate the flow of liquids over chemically patterned surfaces [30,31], where it was shown how the effect of variable wettability of the solid surface on the flow of an adjacent fluid can be described in the framework of continuum mechanics, in agreement with the results of molecular dynamics simulations [32,33].…”

Section: Numerical Resultsmentioning

confidence: 59%

Viscous flow in domains with corners: Numerical artifacts, their origin and removal

Sprittles

Shikhmurzaev

2011

Computer Methods in Applied Mechanics and Engineering

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a b s t r a c tViscous flows in domains with boundaries forming two-dimensional corners are considered. We examine the case where on each side of the corner the boundary condition for the tangential velocity is formulated in terms of stress. It is shown that computing such flows numerically by straightforwardly applying welltested algorithms (and numerical codes based on their use, such as COMSOL Multiphysics) can lead to spurious multivaluedness and mesh-dependence in the distribution of the fluid's pressure. The origin of this difficulty is that, near a corner formed by smooth parts of the boundary, in addition to the solution of the formulated inhomogeneous problem, there also exists an eigensolution. For obtuse corner angles this eigensolution (a) becomes dominant and (b) has a singular radial derivative of velocity at the corner. Despite the bulk pressure in the eigensolution being constant, when the derivatives of the velocity are singular, numerical errors in the velocities calculation near the corner give rise to pressure spikes, whose magnitude increases as the mesh is refined. A method is developed that uses the knowledge about the eigensolution to remove the artifacts in the pressure distribution. The method is first explained in the simple case of a Stokes flow in a corner region and then generalized for the Navier-Stokes equations applied to describe steady and unsteady free-surface flows encountered in problems of dynamic wetting.

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Section: Numerical Resultsmentioning

confidence: 59%

Viscous flow in domains with corners: Numerical artifacts, their origin and removal

Sprittles

Shikhmurzaev

2011

Computer Methods in Applied Mechanics and Engineering

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“…Estimates for the material constants have been obtained by comparing the theory to experiments in dynamic wetting, e.g. in [33], but could just as easily have been taken from an entirely different process in which interface formation is key to describing the dynamics of the flow [34,35,36,37]. In other words, once obtained for a particular liquid in one set of experiments, the material constants determined can be used to describe all phenomena involving the same fluid in which interface formation dynamics 'kicks in'.…”

Section: The Interface Formation Modelmentioning

confidence: 99%

Finite element simulation of dynamic wetting flows as an interface formation process

Sprittles

Shikhmurzaev

2013

Journal of Computational Physics

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A mathematically challenging model of dynamic wetting as a process of interface formation has been, for the first time, fully incorporated into a numerical code based on the finite element method and applied, as a test case, to the problem of capillary rise. The motivation for this work comes from the fact that, as discovered experimentally more than a decade ago, the key variable in dynamic wetting flows -the dynamic contact angle -depends not just on the velocity of the three-phase contact line but on the entire flow field/geometry. Hence, to describe this effect, it becomes necessary to use the mathematical model that has this dependence as its integral part. A new physical effect, termed the 'hydrodynamic resist to dynamic wetting', is discovered where the influence of the capillary's radius on the dynamic contact angle, and hence on the global flow, is computed. The capabilities of the numerical framework are then demonstrated by comparing the results to experiments on the unsteady capillary rise, where excellent agreement is obtained. Practical recommendations on the spatial resolution required by the numerical scheme for a given set of non-dimensional similarity parameters are provided, and a comparison to asymptotic results available in limiting cases confirms that the code is converging to the correct solution. The appendix gives a userfriendly step-by-step guide specifying the entire implementation and allowing the reader to easily reproduce all presented results, including the benchmark calculations.

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“…In the present work, the problem formulated in Section 2 has been considered using part of a finite-element-based numerical platform which has been developed to simulate a range of microfluidic capillary flows and has already been used to obtain new results for the flow of liquids over surfaces of varying wettability [15,16]. The idea here, is to modify the finiteelement's basis function Φ p associated with the pressure at the corner point.…”

Section: Numerical Resultsmentioning

confidence: 99%

Viscous flows in corner regions: Singularities and hidden eigensolutions

Sprittles¹,

Shikhmurzaev²

2011

Numerical Methods in Fluids

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Numerical issues arising in computations of viscous flows in corners formed by a liquid-fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the `moving contact-line problem' and gives rise to a logarithmic singularity of pressure, requires a certain modification of the standard finite-element method. This modification appears to be insufficient above a certain critical value of the corner angle where the numerical solution becomes mesh-dependent. As shown, this is due to an eigensolution, which exists for all angles and becomes dominant for the supercritical ones. A method of incorporating the eigensolution into the numerical method is described that makes numerical results mesh-independent again. Some implications of the unavoidable finiteness of the mesh size in practical applications of the finite element method in the context of the present problem are discussed.Comment: Submitted to the International Journal for Numerical Methods in Fluid

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Viscous flow over a chemically patterned surface

Cited by 13 publications

References 25 publications

Viscous flow in domains with corners: Numerical artifacts, their origin and removal

Viscous flow in domains with corners: Numerical artifacts, their origin and removal

Finite element simulation of dynamic wetting flows as an interface formation process

Viscous flows in corner regions: Singularities and hidden eigensolutions

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