Wetting: Inverse Dynamic Problem and Equations for Microscopic Parameters

Voinov, O. V.

doi:10.1006/jcis.2000.6726

Cited by 18 publications

(7 citation statements)

References 11 publications

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“…We also note that at the transition the condition (30) yields η I ∼ Ca 2/3 l c , and that we used essentially the same matching argument as Derjaguin [42] and Landau and Levich [41]. This can also be compared to the prediction of Voinov [55] which is similar but with a constant C(0) differing from that obtained by asymptotic matching.…”

Section: General Casementioning

confidence: 74%

Transition in a numerical model of contact line dynamics and forced dewetting

Afkhami

Buongiorno

Guion

et al. 2018

Journal of Computational Physics

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We investigate the transition to a Landau-Levich-Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier-Stokes equations with surface tension. We use a discretization of the capillary forces near the receding contact line that yields an equilibrium for a specified contact angle θ ∆ called the numerical contact angle. Despite the well-known contact line singularity, dynamic simulations can proceed without any explicit additional numerical procedure. We investigate angles from 15 • to 110 • and capillary numbers from 0.00085 to 0.2 where the mesh size ∆ is varied in the range of 0.0035 to 0.06 of the capillary length l c . To interpret the results, we use Cox's theory which involves a microscopic distance r m and a microscopic angle θ e . In the numerical case, the equivalent of θ e is the angle θ ∆ and we find that Cox's theory also applies. We introduce the scaling factor or gauge function φ so that r m = ∆/φ and estimate this gauge function by comparing our numerics to Cox's theory. The comparison provides a direct assessment of the agreement of the numerics with Cox's theory and reveals a critical feature of the numerical treatment of contact line dynamics: agreement is poor at small angles while it is better at large angles. This scaling factor is shown to depend only on θ ∆ and the viscosity ratio q. In the case of small θ e , we use the prediction by Eggers [Phys. Rev. Lett., vol. 93, pp 094502, 2004] of the critical capillary number for the Landau-Levich-Derjaguin forced dewetting transition. We generalize this prediction to large θ e and arbitrary q and express the critical capillary number as a function of θ e and r m . This implies also a prediction of the critical capillary number for the numerical case as a function of θ ∆ and φ. The theory involves a logarithmically small parameter = 1/ ln(l c /r m ) and is thus of moderate accuracy. The numerical results are however in approximate agreement in the general case, while good agreement is reached in the small θ ∆ and q case. An analogy can be drawn between the numerical contact angle condition and a regularization of the Navier-Stokes equation by a partial Navier-slip model. The analogy leads to a value for the numerical length scale r m proportional to the slip length. Thus the microscopic length found in the simulations is a kind of numerical slip length in the vicinity of the contact line. The knowledge of this microscopic length scale and the associated gauge function can be used to realize grid-independent simulations that could be matched to microscopic physics in the region of validity of Cox's theory. This version of the paper includes the corrections indicated in [1].

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Section: General Casementioning

confidence: 74%

Transition in a numerical model of contact line dynamics and forced dewetting

Afkhami

Buongiorno

Guion

et al. 2018

Journal of Computational Physics

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“…The mathematical model of the contact line is quite general but also rather simplistic. Alternative models [5,6] are possible within the framework of Equation (3) and will be investigated and contrasted. This model can also be calibrated and validated by comparison with laboratory experiments.…”

Section: Discussionmentioning

confidence: 99%

“…Detailed mathematical analyses of this problem and alternative mathematical models appear in the literature, e.g. References [5,6]. In general these models may be expressed in the form…”

Section: Mathematical Modelmentioning

confidence: 99%

Finite element simulation of three‐dimensional free‐surface flow problems with dynamic contact lines

Walkley

Gaskell

Jimack

et al. 2004

Numerical Methods in Fluids

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SUMMARYAn arbitrary Lagrangian-Eulerian (ALE) ÿnite element method is described for the solution of threedimensional free-surface ow problems. The focus of this work is on extending the algorithm to include a dynamic contact line model allowing the uid free surface, in the steady case, to form a prespeciÿed static contact angle with a solid boundary and, in the transient case, to move along the solid boundary. This widens the applicability of the algorithm to important industrial applications such as forced spreading of uids and gravity-driven ow on inclined surfaces.

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“…The contact angle hysteresis is affected by solid surface including surface inhomogeneity, surface roughness and impurities on the surface (Carey 2008). The mechanisms of wetting behaviour of pure liquid on the solid have not been completely revealed (Carey 2008), and several models from hydrodynamic (Gennes 1985;Voinov 2000;Bonn et al 2009), and molecular kinetics aspects (Bertrand et al 2009;Blake 2006;Blake and De Coninck 2002;Blake and Haynes 1969;Cherry and Holmes 1969) have been proposed. For instance, the molecular kinetic model considers what happens in the immediate vicinity of moving contact line within the moving three phase zone through the process of attachment or detachment of fluid molecules to or from the substrate (Blake 2006).…”

Section: Introductionmentioning

confidence: 99%

The effect of gold nanoparticles on the spreading of triple line

Vafaei

Wen

2010

Microfluid Nanofluid

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The work reports a unique phenomenon of gold nanoparticles on the formation of gas bubbles. The welldefined gold nanofluids prevent the spreading of triple line during bubble formation, i.e. the triple line is pinned somewhere around the middle of the tube wall during the rapid bubble formation stage whereas it spreads to the outer edge of the tube for pure liquid. Compared with pure liquid, adding nanoparticles raises bubble frequency and reduces departure bubble volume. Different to other observations of bubble dynamics in nanofluids under evaporation or boiling conditions, which are caused by the surface modification due to particle sedimentation, this work reveals an inherent feature of enhanced pinning of triple lines for well-defined nanofluids, which bears extensive implications to a number of nanoparticle-associated interfacial phenomena.

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Wetting: Inverse Dynamic Problem and Equations for Microscopic Parameters

Cited by 18 publications

References 11 publications

Transition in a numerical model of contact line dynamics and forced dewetting

Transition in a numerical model of contact line dynamics and forced dewetting

Finite element simulation of three‐dimensional free‐surface flow problems with dynamic contact lines

The effect of gold nanoparticles on the spreading of triple line

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