Theory of drag out of liquids on flat plates

White, David A.; Tallmadge, John A.

doi:10.1016/0009-2509(65)80041-0

Cited by 160 publications

(94 citation statements)

References 3 publications

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“…There is a large body of literature devoted to different improvements and extensions of the Landau-Levich law. 1 Gravity corrections were accounted for by White and Tallmadge, 2 and their incorrect approximation of the normal stress was corrected in the work of Spiers et al 3 Later, Wilson 4 put ad hoc treatments by previous authors on the ground of systematic perturbation theory, establishing Eq. ͑1͒ as the leading term in an asymptotic expansion for small Ca.…”

Section: Introductionmentioning

confidence: 99%

Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

Krechetnikov

Homsy

2005

Physics of Fluids

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In this work we present an experimental study of deviations from the classical Landau-Levich law in the problem of dip coating. Among the examined causes leading to deviations are the nature of the liquid-gas and liquid-solid interfaces. The thickness of the coating film created by withdrawal of a plate from a bath was measured gravimetrically over a wide range of capillary numbers for both smooth and well-characterized rough substrates, and for clean and surfactant interface cases. In view of the dependence of the lifetime of a film on the type of liquid and substrate, and liquid-gas and liquid-solid interfaces, we characterized the range of measurability of the film thickness in the parameter space defined by the withdrawal capillary number, the surfactant concentration, and substrate roughness size. We then study experimentally the effect of a film thickening due to the presence of surfactants. Our recent theory based on a purely hydrodynamic role of the surface active substance suggests that there is a sorption-controlled coating regime in which Marangoni effects should lead to film thinning. However, our experiments conducted in this regime demonstrate film thickening, calling into question the conventional wisdom, which is that Marangoni stresses ͑as accounted by the conventional interfacial boundary conditions͒ lead to film thickening. Next we examine the effect of well-characterized substrate roughness on the coated film thickness, which also reveals its influence on wetting-related processes and an effective boundary condition at the wall. In particular, it is found that roughness results in a significant thickening of the film relative to that on a smooth substrate and a different power of capillary number than the classical Landau-Levich law.

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Section: Introductionmentioning

confidence: 99%

Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

Krechetnikov

Homsy

2005

Physics of Fluids

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“…The majority of experimental and theoretical studies [6][7][8][9][10][11][12][13][14][15][16][17][18] have focused exclusively on chemically homogeneous surfaces. As the number of techniques available for microfabrication and micropatterning grows, there is interest in selectively coating or ''inking'' chemically patterned surfaces for use as chemical microreactors.…”

Section: Introductionmentioning

confidence: 99%

Selective dip-coating of chemically micropatterned surfaces

Darhuber

Troian

Davis

et al. 2000

Journal of Applied Physics

143

129

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We characterize the selective deposition of liquid microstructures on chemically heterogeneous surfaces by means of dip coating processes. The maximum deposited film thickness depends critically on the speed of withdrawal as well as the pattern size, geometry, and angular orientation. For vertically oriented hydrophilic strips, we derive a hydrodynamic scaling relation for the deposited film thickness which agrees very well with interferometric measurements of dip-coated liquid lines. Due to the lateral confinement of the liquid, our scaling relation differs considerably from the classic Landau-Levich formula for chemically homogeneous surfaces. Dip coating is a simple method for creating large area arrays of liquid microstructures for applications involving chemical analysis and synthesis, biochemical assays, or wet printing of liquid polymer or ink patterns.

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“…͑11͒, therefore requires Bo͑3Ca͒ −1/3 Ӷ 1, which is more stringent than the constraint gh ϱ 2 / ␥ Ӷ 1 ͑equivalent to BoCa 2/3 Ӷ 1͒ given by Darhuber et al 12 At leading order, the free surface shape is therefore governed by 3 ͑ − ͒ = − ϱ , ͑12͒ subject to the boundary condition → ϱ as → −ϱ. As → ϱ, − → C S , which is a constant that can be found by numerically integrating Eq.…”

mentioning

confidence: 98%

“…[1][2][3][4][5][6][7][8][9] More recently, as microfabrication has become common and microfluidic applications have increased, the dip coating technique has been used to achieve selective material deposition on micropatterned surfaces. [10][11][12][13] In particular, the experimental investigation of the dip coating of vertical, wetting stripes on a nonwetting planar surface by Darhuber et al 12 has demonstrated that fluid confinement by chemical surface patterning strongly affects the thickness of the entrained liquid film.…”

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confidence: 99%

Asymptotic analysis of liquid films dip-coated onto chemically micropatterned surfaces

Davis

2005

Physics of Fluids

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The dip coating of chemically heterogeneous surfaces is a useful technique for attaining selective material deposition. For the case of vertical, wetting stripes surrounded by nonwetting regions, experiments have demonstrated that the thickness of the entrained film on the stripes is significantly different than on homogeneous surfaces because of the lateral confinement of the liquid. In the present work, the asymptotic matching of equations based on lubrication theory is used to determine the film thickness, and necessary restrictions on the capillary and Bond numbers are provided. The predictions are in excellent agreement with the existing experimental data, and the classical Landau–Levich formula for homogeneous surfaces is recovered from the analysis in the limit of very wide stripes.

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Theory of drag out of liquids on flat plates

Cited by 160 publications

References 3 publications

Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

Experimental study of substrate roughness and surfactant effects on the Landau-Levich law

Selective dip-coating of chemically micropatterned surfaces

Asymptotic analysis of liquid films dip-coated onto chemically micropatterned surfaces

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