Singularities at the moving contact line. Mathematical, physical and computational aspects

Shikhmurzaev, Yulii D.

doi:10.1016/j.physd.2006.03.003

Cited by 64 publications

(53 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…30,32 The approach outlined above removes the unphysical singularities in the mathematical description of the coalescence process and allows one to treat it in a regular way, as just one of many fluid mechanics phenomena. The developed model (which came to be known as "interface formation model" or, for brevity, IFM) unifies the mathematical modelling of such seemingly different phenomena as coalescence, 30 breakup of liquid threads 30,33 and free films, 34 as well as dynamic wetting; [35][36][37][38] an exposition of the fundamentals of the theory of capillary flows with forming/disappearing interfaces can be found in Ref. 39.…”

Section: E Coalescence As An Interface Formation/disappearance Processmentioning

confidence: 99%

Coalescence of liquid drops: Different models versus experiment

Sprittles¹,

Shikhmurzaev²

2012

Physics of Fluids

117

View full text Add to dashboard Cite

The process of coalescence of two identical liquid drops is simulated numerically in the framework of two essentially different mathematical models, and the results are compared with experimental data on the very early stages of the coalescence process reported recently. The first model tested is the 'conventional' one, where it is assumed that coalescence as the formation of a single body of fluid occurs by an instant appearance of a liquid bridge smoothly connecting the two drops, and the subsequent process is the evolution of this single body of fluid driven by capillary forces. The second model under investigation considers coalescence as a process where a section of the free surface becomes trapped between the bulk phases as the drops are pressed against each other, and it is the gradual disappearance of this 'internal interface' that leads to the formation of a single body of fluid and the conventional model taking over. Using the full numerical solution of the problem in the framework of each of the two models, we show that the recently reported electrical measurements probing the very early stages of the process are better described by the interface formation/disappearance model. New theory-guided experiments are suggested that would help to further elucidate the details of the coalescence phenomenon. As a by-product of our research, the range of validity of different 'scaling laws' advanced as approximate solutions to the problem formulated using the conventional model is established.

show abstract

Section: E Coalescence As An Interface Formation/disappearance Processmentioning

confidence: 99%

Coalescence of liquid drops: Different models versus experiment

Sprittles¹,

Shikhmurzaev²

2012

Physics of Fluids

117

View full text Add to dashboard Cite

show abstract

“…(2)), although in some cases the local value of the surface tension may differ from its equilibrium value so that the local angle will not be h e . For instance, c will differ from its equilibrium value if the fluid motion affects the distribution of tensio-active molecules on the interface; other theories involving variable surface tensions have also been proposed [26]. Heterogeneities or roughness of the interface affect the observed contact angles at scales larger than that of the surface imperfections.…”

Section: ð2þmentioning

confidence: 99%

A mesh-dependent model for applying dynamic contact angles to VOF simulations

Afkhami

Zaleski

Bussmann

2009

Journal of Computational Physics

222

178

View full text Add to dashboard Cite

a b s t r a c tTypical VOF algorithms rely on an implicit slip that scales with mesh refinement, to allow contact lines to move along no-slip boundaries. As a result, solutions of contact line phenomena vary continuously with mesh spacing; this paper presents examples of that variation. A mesh-dependent dynamic contact angle model is then presented, that is based on fundamental hydrodynamics and serves as a more appropriate boundary condition at a moving contact line. This new boundary condition eliminates the stress singularity at the contact line; the resulting problem is thus well-posed and yields solutions that converge with mesh refinement. Numerical results are presented of a solid plate withdrawing from a fluid pool, and of spontaneous droplet spread at small capillary and Reynolds numbers.Published by Elsevier Inc.

show abstract

“…Even though this approach has been very successful in solving many fluid mechanics problems, when it comes to the MCL problem, the no-slip condition adopted at the liquid-solid boundary will lead to singularity in shear stress distribution at the vicinity of the MCL front, which poses a serious challenge in solving the MCL problem (e.g. [1][2][3][4][5][6]). …”

Section: Introductionmentioning

confidence: 99%

On multiscale moving contact line theory

Fan

2015

Proc. R. Soc. A.

View full text Add to dashboard Cite

In this paper, a multiscale moving contact line (MMCL) theory is presented and employed to simulate liquid droplet spreading and capillary motion. The proposed MMCL theory combines a coarse-grained adhesive contact model with a fluid interface membrane theory, so that it can couple molecular scale adhesive interaction and surface tension with hydrodynamics of microscale flow. By doing so, the intermolecular force, the van der Waals or double layer force, separates and levitates the liquid droplet from the supporting solid substrate, which avoids the shear stress singularity caused by the noslip condition in conventional hydrodynamics theory of moving contact line. Thus, the MMCL allows the difference of the surface energies and surface stresses to drive droplet spreading naturally. To validate the proposed MMCL theory, we have employed it to simulate droplet spreading over various elastic substrates. The numerical simulation results obtained by using MMCL are in good agreement with the molecular dynamics results reported in the literature.

show abstract

Singularities at the moving contact line. Mathematical, physical and computational aspects

Cited by 64 publications

References 37 publications

Coalescence of liquid drops: Different models versus experiment

Coalescence of liquid drops: Different models versus experiment

A mesh-dependent model for applying dynamic contact angles to VOF simulations

On multiscale moving contact line theory

Contact Info

Product

Resources

About