Non-isothermal spreading of a thin liquid film on an inclined plane

Lopez, Patrice; Bankoff, S. G.; Miksis, Michael J.

doi:10.1017/s0022112096007914

Cited by 46 publications

(33 citation statements)

References 20 publications

(30 reference statements)

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“…The nondimensional problem for the weak-slip regime is therefore 4 Re * (∂ t u + u∂ x u + w∂ z u) = −∂ x p + 2 ∂ xx u + ∂ zz u, (2.10a) 6 Re * (∂ t w + u∂ x w + w∂ z w) = −∂ z p + 4 ∂ xx w + 2 ∂ zz w, (2.10b)…”

Section: Weak-slip Regimementioning

confidence: 99%

“…See also [4] for a different derivation. We observe that the weak-and the strong-slip regimes represent two distinguished limits in the sense that they represent two scalings which are richer than other slip regimes.…”

Section: Strong-slip Regimementioning

confidence: 99%

“…For film thicknesses in the range of a few micrometers and larger, the choice of the boundary condition at the solid substrate enters only weakly in that it does not influence the eventual appearance of instabilities, such as formation of fingers at the three-phase contact-line; see for example [2][3][4][5]. For other applications, such as for the dewetting of a nano-scale thin polymer film on a hydrophobic substrate the boundary condition at the substrate appears to have a crucial influence on the dynamics and morphology of the film.…”

Section: Introductionmentioning

confidence: 99%

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Lubrication Models with Small to Large Slip Lengths

2005

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A set of lubrication models for the thin film flow of incompressible fluids on solid substrates is derived and studied. The models are obtained as asymptotic limits of the Navier-Stokes equations with the Navier-slip boundary condition for different orders of magnitude for the slip-length parameter. Specifically, the influence of slip on the dewetting behavior of fluids on hydrophobic substrates is investigated here. Matched asymptotics are used to describe the dynamic profiles for dewetting films and comparison is given with computational simulations. The motion of the dewetting front shows transitions from being nearly linear in time for no-slip to t 2/3 as the slip is increased. For much larger slip lengths the front motion appears to become linear again. Correspondingly, the dewetting profiles undergo a transition from oscillatory to monotone decay into the uniform film layer for large slip. Increasing the slip further, to very large values, is associated with an increasing degree of asymmetry in the structure of the dewetting ridge profile.

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Section: Weak-slip Regimementioning

confidence: 99%

Section: Strong-slip Regimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lubrication Models with Small to Large Slip Lengths

2005

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“…However, this leads to a stress singularity at the moving contact line, which is inherited by the resulting fourth-order lubrication equation for h. To resolve this problem, the equations are regularized for example by allowing b = 0, with b being orders of magnitude smaller than the height of the actual film, or by prescribing a precursor near the contact line having orders of magnitude smaller height compared to h. Also, one can take the underlying intermolecular potential between the liquid and the substrate into account, which stabilizes a very thin (precursor) film near the contact line, with a thickness close to where the potential has its minimum. The actual choice of regularization near the contact line enters only weakly in the solution as h → 0 and does not influence the eventual stability dynamics; see for example [1,[9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Linear stability analysis of a sharp-interface model for dewetting thin films

2008

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The stability of the receding front at the growing rim of a thin liquid film dewetting from a substrate is studied. The underlying forces that drive the dewetting motion are given by the intermolecular potential between the liquid film and the substrate. The role of slippage in the emerging instability is studied via a sharp-interface model for the dewetting thin film, which is derived from the lubrication model via matched asymptotic expansions. Using the separation of the time-scale for the slow growth of the rim and the time-scale on which the rim destabilises, the sharp-interface results are compared to earlier results for the lubrication model and good agreement for the unstable modes is obtained. The main advantage of the sharp-interface model is that it allows for the derivation of traveling solutions for the base state and subsequently a systematic linear stability analysis via normal modes. Interestingly, unlike the dispersion relations that are typically encountered for the well-known finger-instability in thin-film flows, where the dependence of the growth rate on the wave number is quadratic, here it is linear.Keywords Asymptotic methods · High-order nonlinear boundary-value problems · Sharp-interface model · Stability analysis · Thin liquid films

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“…Because disturbances to the film cannot extend beyond the contact line for the slip model, and because the contact slope is fixed in most applications of that model, the amount and duration of the nonmodal amplification are significantly less than for the precursor film model considered here. These restrictions on the slip model can be at least partially overcome by allowing disturbances to the slip coefficient 61 and by formulating the problem in terms of a speed-dependent contact angle 62 that can adjust to perturbations. There are meaningful differences between perturbations to the precursor film and slip coefficient due to the wetting properties of the liquid, however.…”

Section: -7mentioning

confidence: 99%

Transient dynamics and structure of optimal excitations in thermocapillary spreading: Precursor film model

2006

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Linearized modal stability theory has shown that the thermocapillary spreading of a liquid film on a homogeneous, completely wetting surface can produce a rivulet instability at the advancing front due to formation of a capillary ridge. Mechanisms that drain fluid from the ridge can stabilize the flow against rivulet formation. Numerical predictions from this analysis for the film speed, shape, and most unstable wavelength agree remarkably well with experimental measurements even though the linearized disturbance operator is non-normal, which allows transient growth of perturbations. Our previous studies using a more generalized nonmodal stability analysis for contact lines models describing partially wetting liquids ͑i.e., either boundary slip or van der Waals interactions͒ have shown that the transient amplification is not sufficient to affect the predictions of eigenvalue analysis. In this work we complete examination of the various contact line models by studying the influence of an infinite and flat precursor film, which is the most commonly employed contact line model for completely wetting films. The maximum amplification of arbitrary disturbances and the optimal initial excitations that elicit the maximum growth over a specified time, which quantify the sensitivity of the film to perturbations of different structure, are presented. While the modal results for the three different contact line models are essentially indistinguishable, the transient dynamics and maximum possible amplification differ, which suggests different transient dynamics for completely and partially wetting films. These differences are explained by the structure of the computed optimal excitations, which provides further basis for understanding the agreement between experiment and predictions of conventional modal analysis.

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Non-isothermal spreading of a thin liquid film on an inclined plane

Cited by 46 publications

References 20 publications

Lubrication Models with Small to Large Slip Lengths

Lubrication Models with Small to Large Slip Lengths

Linear stability analysis of a sharp-interface model for dewetting thin films

Transient dynamics and structure of optimal excitations in thermocapillary spreading: Precursor film model

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