Generalized linear stability of noninertial coating flows over topographical features

Davis, Jeffrey M.; Troian, Sandra M.

doi:10.1063/1.1945627

Cited by 28 publications

(20 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…24,25 Discrete modes are similarly absent for relevant q for isothermal flows over topography. 40,41 The effect of varying the steepness ␦ of the topography S I on the film profile and its linear stability is shown in Fig. 4 for M = 17, Bi= 0.01, D = 1, and a = 2.…”

Section: A Base Profiles and Linear Stabilitymentioning

confidence: 99%

“…The dispersion relation is that of the continuous spectrum, ␤ =−q 4 , as for isothermal flows over topography. 40,41 There are critical values ␦ c1 and ␦ c2 analogous to D c1 and D c2 .…”

Section: A Base Profiles and Linear Stabilitymentioning

confidence: 99%

“…Such ridges that form in response to step-down, mound, and trench features are stable to transverse perturbations. 40,41 The nonlinear evolution equations for the local thickness of liquid films flowing over surfaces with nonuniform heating, 20 topographical features, 38 and both types of heterogeneity 4,47 have been derived previously using a longwave lubrication analysis, so only a brief derivation is given here. A linear variation in surface tension with temperature is assumed, ␥͑T ͒ = ␥ 0 − ␥ T ͑T − T ϱ ͒, where ␥ T = ‫␥ץ‬ / ‫ץ‬T Ͼ 0 and ␥ 0 is the surface tension at the ambient temperature T ϱ .…”

Section: Problem Formulationmentioning

confidence: 99%

“…[37][38][39] Noninertial coating flows over isothermal substrates with topographical features exhibit similar capillary ridges to the locally heated films but are stable to perturbations due to the restoring flow generated by the capillary pressure gradient induced by the features. 40,41 It was shown from boundary integral solutions of the unsimplified equations of Stokes flow 42 that the film closely follows the topography for capillary numbers ͑Ca͒ that are O͑1͒ or larger but a pronounced capillary ridge develops near the feature for smaller Ca. The Stokes flow results agree well with lubrication theory for CaϽ 10 −2 .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

Tiwari¹,

Davis²

2010

Physics of Fluids

Self Cite

View full text Add to dashboard Cite

A long-wave lubrication analysis is used to study the influence of topographical features on the linear stability of noninertial coating flows over a locally heated surface. Thin liquid films flowing over surfaces with localized heating develop a pronounced ridge at the upstream edge of the heater. This ridge becomes unstable to transverse perturbations above a critical Marangoni number and evolves into an array of rivulets even in the limit of noninertial flow. Similar fluid ridges form near topographical variations on isothermal surfaces, but these ridges are stable to perturbations. The influence of basic topographical features on the stability of the locally heated film is analyzed. In contrast to its destabilizing influence on liquid films resting on heated, horizontal walls, even such nonoptimized topography is found to be effective at stabilizing the flowing film with respect to rivulet formation and subsequent rupture. Optimal topographical features that suppress variations in the free-surface shape are also determined. The critical Marangoni number at the instability threshold increases substantially with appropriate topography even for nonzero Biot numbers. An energy analysis is used to provide insight into the mechanism by which the topography stabilizes the flow. Because the stabilizing effect of the topographical features is only weakly sensitive to the governing parameters and particular temperature profile, the use of such features could be a simple alternative in applications to more complicated methods of stabilization.

show abstract

Section: A Base Profiles and Linear Stabilitymentioning

confidence: 99%

Section: A Base Profiles and Linear Stabilitymentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

Tiwari¹,

Davis²

2010

Physics of Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…Davis & Troian (2005), for example, have revealed the key role of recirculating streamlines on the stability of free surface disturbances. Wet, low viscosity coatings typically found in multi-layer coating systems are also particularly prone to becoming disturbed by drying-air, Cohen & Gutoff (1992).…”

Section: Introductionmentioning

confidence: 99%

Drying air-induced disturbances in multi-layer coating systems

Ikin

Thompson

2007

Chemical Engineering Science

View full text Add to dashboard Cite

A range of new experimental techniques is developed to quantify drying-air induced disturbances on low viscosity single and multi-layer coating systems. Experiments on prototype slide-bead coating systems show that the surface disturbances take the form of a wavelike pattern and quantify precisely how its amplitude increases rapidly with wet thickness and decreases with viscosity. Heat transfer measurements show that the redistribution of water to form an additional lower viscosity carrier layer while increasing the solids concentration of the upper layer or layers enables the maximum drying rate, for which drying-air induced surface disturbances are acceptably small, to be increased with significant commercial benefits.

show abstract

Beating capillarity in thin film flows

Sellier

Panda

2009

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYThe combination of substrate unevenness and capillarity is known to induce far-reaching perturbations at the free surface of thin liquid films. These might be undesired and this paper explores the possibility to control the free surface of thin liquid films to give it a prescribed profile by a suitable design of the underlying substrate. This corresponds to the inverse of the widely studied forward problem, which considers the effect of substrate unevenness on a free surface. Assuming that the steady free surface profile can be described by the lubrication approximation, this optimal control problem is shown to be governed by a first-order partial differential equation, which is solved numerically using the method of characteristics. The proposed method is successfully tested for a range of desired free surface profiles and the domain of existence of a solution to the inverse problem is probed. Expectedly, it is shown that, owing to surface tension, not all free surface profiles can be achieved but in some cases capillarity can be beaten and a prescribed free surface profile obtained.

show abstract

Generalized linear stability of noninertial coating flows over topographical features

Cited by 28 publications

References 33 publications

Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

Stabilization of thin liquid films flowing over locally heated surfaces via substrate topography

Drying air-induced disturbances in multi-layer coating systems

Beating capillarity in thin film flows

Contact Info

Product

Resources

About