1996
DOI: 10.1017/s0022112096007914
|View full text |Cite
|
Sign up to set email alerts
|

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

Abstract: A thin layer of liquid advancing over a dry, heated, inclined plate is studied. A lubrication model with contact line motion is derived. The plate is at constant temperature, and the surface Biot number is specified. The steady-state solution is obtained numerically. In addition, the steady-state solution is studied analytically in the neighbourhood of the contact line. A linear stability analysis about the steady state is then performed. The effects of gravity, thermocapillarity and contact line motion are di… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

7
26
0

Year Published

2003
2003
2023
2023

Publication Types

Select...
4
3

Relationship

0
7

Authors

Journals

citations
Cited by 46 publications
(33 citation statements)
references
References 20 publications
7
26
0
Order By: Relevance
“…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 2 more Smart Citations
“…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%
See 1 more Smart Citation
“…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%
“…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%