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

Davis, Jeffrey M.

doi:10.1063/1.1850751

Cited by 21 publications

(22 citation statements)

References 22 publications

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“…12,19 This linkage of the capillary ridge to instability is also supported by results from recent studies of liquid film dynamics on chemically patterned substrates. Liquid confinement to a narrow wetting strip induces a significant transverse curvature of the free surface, 20,21 which suppresses the capillary ridge and fingering instability. 22,23 By contrast, Kalliadasis and Homsy 24 recently found that the stationary capillary ridge near an isolated topographical step-down is asymptotically stable to transverse perturbations.…”

Section: Introductionmentioning

confidence: 99%

Generalized linear stability of noninertial coating flows over topographical features

Davis

Troian

2005

Physics of Fluids

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The transient evolution of perturbations to steady lubrication flow over a topographically patterned surface is investigated via a nonmodal linear stability analysis of the non-normal disturbance operator. In contrast to the capillary ridges that form near moving contact lines, the stationary capillary ridges near trenches or elevations have only stable eigenvalues. Minimal transient amplification of perturbations occurs, regardless of the magnitude or steepness of the topographical features. The absence of transient amplification and the stability of the ridge are explained on physical grounds. By comparison to unstable ridge formation on smooth, flat, and homogeneous surfaces, the lack of closed, recirculating streamlines beneath the capillary ridge is linked to the linear stability.

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Section: Introductionmentioning

confidence: 99%

Generalized linear stability of noninertial coating flows over topographical features

Davis

Troian

2005

Physics of Fluids

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“…The mean curvature in the static meniscus region therefore reduces to 2 = 0, and the exact meniscus profile need not be determined explicitly. 19 Evaluating 2 along the centerline of the stripe ͑y =0͒ and noting that the free surface must be symmetric ͑and that h x → 0 at the top of the static meniscus to match the dynamic meniscus͒ reveals that h xx + h yy → 0 is the desired limiting behavior at the top of the static meniscus to which the solution in the dynamic meniscus should be matched. For the surfactant concentration, ⌫ → ⌫ 0 .…”

Section: Static Meniscusmentioning

confidence: 99%

“…Also, in this static meniscus region, for BoӶ 1, the liquid-vapor interface within several stripe widths of the wall is a minimal surface with zero mean curvature ͑2 =0͒. 19 In order to neglect gravity in Eq. ͑23͒, it was required that BoӶ Ca 1/3 .…”

Section: Static Meniscusmentioning

confidence: 99%

“…This restriction also makes the viscous contributions to the normal stress balance negligible, which allows for a more tractable analysis. Because CaӶ 1, an x = const cross section of the free surface of the liquid along the stripe must be an arc of a circle, 19 which within the lubrication approximation simplifies to a parabolic cap. The introduction of ĥ͑x , ŷ͒ = ĥ͑x͓͒1−4͑ŷ / W ͒ 2 ͔ reduces the analysis to a onedimensional asymptotic matching problem for the entrained film thickness at the centerline of the stripe, ĥ͑x͒ϵĥ͑x , ŷ =0͒.…”

Section: Governing Equationsmentioning

confidence: 99%

“…1,3,5,6 Davis 19 performed the first theoretical analysis of the dip coating of vertical, wetting stripes of width W on an otherwise nonwetting, planar surface using a matched asymptotic analysis. For sufficiently narrow stripes ͑gW 2 / 0 Ӷ 1͒, he derived an equation for the centerline thickness of the liquid film entrained on the wetting stripes, 19 h ϱ = 0.356W Ca 1/3 . ͑2͒…”

Section: Introductionmentioning

confidence: 99%

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Theoretical analysis of the effect of insoluble surfactant on the dip coating of chemically micropatterned surfaces

Tiwari

Davis

2006

Physics of Fluids

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Microfluidic flow on chemically heterogeneous surfaces is a useful technique with applications ranging from selective material deposition to the self-assembly of nanostructures. The recent theoretical analysis by Davis ͓Phys. Fluids 17, 038101 ͑2005͔͒ of the dip coating of a pure fluid onto vertical, wetting stripes surrounded by nonwetting regions quantified the experimentally observed deviations from the classical Landau-Levich result due to lateral confinement of the fluid by chemical surface patterning. In this present work, the analysis of dip coating of these heterogeneous surfaces is extended to a liquid containing an insoluble surfactant. Using matched asymptotic expansions based on lubrication theory in the limit of a small capillary number, the thickness of the deposited liquid film and the surfactant concentration in the deposited monolayer are predicted for a wide range of fluid properties and process parameters. The increase in the deposited film thickness is shown analytically to be limited by a multiplicative factor of 4 1/3 times the result for a pure liquid. Numerical results demonstrate that the thickening due to Marangoni effects is nonmonotonic in the capillary number because of the competition between viscous stresses, Marangoni stresses, and surface diffusion.

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Gradient Droplet Arrays by Acceleration‐Mode Dip‐Coating

Mandsberg

Shneidman

Jensen

et al. 2022

Adv Materials Inter

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Droplet microarray technology is of great interest in biology and chemistry as it allows for significant reactant savings and massive parallelization of experiments. Upon scaling down the footprint of each droplet in an array, it becomes increasingly challenging to produce the array drop‐by‐drop. Therefore, techniques for parallelized droplet production are developed, e.g., dip‐coating of biphilic substrates. However, it is in general difficult to tailor the characteristics of individual droplets, such as size and content, without updating the substrate. Here, the method of dip‐coating of uniformly patterned biphilic substrates in so‐called “acceleration‐mode” to produce droplet arrays featuring gradients in droplet height for fixed droplet footprint is developed. The results herein present this method applied to produce drops with base diameters varying over orders of magnitude, from as high as 6 mm to as small as 50 µm; importantly, the experimentally measured power‐law‐dependency of volume on capillary‐number matches analytical theory for droplet formation on heterogenous substrates though the precise quantitative values likely differ due to 2D substrate patterning. Gradient characteristics, including average droplet volume, steepness of the gradient, and its monotonicity, can all be tuned by changing the dip‐coating parameters, thus providing a robust method for high‐throughput screening applications and experiments.

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

Cited by 21 publications

References 22 publications

Generalized linear stability of noninertial coating flows over topographical features

Generalized linear stability of noninertial coating flows over topographical features

Theoretical analysis of the effect of insoluble surfactant on the dip coating of chemically micropatterned surfaces

Gradient Droplet Arrays by Acceleration‐Mode Dip‐Coating

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