Droplet motion on inclined heterogeneous substrates

Savva, Nikos; Kalliadasis, Serafim

doi:10.1017/jfm.2013.201

Cited by 67 publications

(54 citation statements)

References 75 publications

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“…By assuming that the dynamics is quasi-static, we have utilised the method of matched asymptotic expansions to deduce a set of IDEs for the evolution of the two droplet fronts in the limit of long oscillation periods. This analysis, which was verified by numerous numerical experiments performed throughout this work, was largely based on the recent work of the present authors on inclined heterogeneous substrates (Savva & Kalliadasis 2013). It is important to emphasise that even though we assumed the presence of slip in our model, our results can be easily mapped to other types of models that are commonly used to relax the stress singularity occurring at a moving contact line (see, for example Sibley et al 2012Sibley et al , 2013b.…”

Section: Discussionsupporting

confidence: 70%

“…Even though our model does not incorporate the effects of contact angle hysteresis by prescribing advancing and receding contact angles, that would pin the droplet fronts, the use of heterogeneities can yield hysteresis like-effects. Besides, we also ascribe to the view that heterogeneities are the principal source of contact angle hysteresis (see also discussion on non-vibrating droplets on inclined substrates, Savva & Kalliadasis 2013).…”

Section: Hysteresis-like Effectsmentioning

confidence: 81%

“…The aim of the present study is to present a combined analytical and numerical investigation of the 2D droplet dynamics in the presence of substrate vibrations and heterogeneities, by extending the work of Savva & Kalliadasis (2013) on inclined heterogeneous substrates (hereinafter referred to as SK) to include the effects of substrate vibrations. We focus on a regime of low-frequency vibrations as done previously (see , e.g.…”

Section: Introductionmentioning

confidence: 99%

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Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates

Savva

Kalliadasis

2014

J. Fluid Mech.

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We present a theoretical investigation of the effects of low-frequency vibrations on the motion of two-dimensional droplets on heterogeneous substrates in the presence of gravity and substrate heterogeneities, both chemical and topographical. A combined analytical and numerical approach is undertaken, extending the work of Savva & Kalliadasis on inclined heterogeneous substrates (J. Fluid Mech., vol. 725, 2013, p. 462) to include the effects of substrate vibrations and obtain, via a matching procedure and under the quasistatic assumption, evolution equations for the moving fronts. These equations are then invoked in a wide variety of case studies. It is demonstrated that vertically vibrated horizontal ratcheted substrates can induce unidirectional motion; for inclined substrates, we focus on a number of qualitative aspects of the peculiar vibration-induced climbing of droplets reported in experiments by Brunet, Eggers & Deegan (Phys. Rev. Lett., vol. 99, 2007, 144501). We examine the effects of weak inertia on the dynamics, deduce analytical criteria for the uphill motion in the limit of weak gravitational and vibrational effects, and demonstrate that substrate heterogeneities may be utilised to enhance droplet transport.

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Section: Discussionsupporting

confidence: 70%

Section: Hysteresis-like Effectsmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

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Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates

Savva

Kalliadasis

2014

J. Fluid Mech.

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“…In all cases we found that the drop moves down the incline with a constant speed which increases monotonically with the tilt angle. [Remarkably, in a 2D study of a drop on an inclined (chemically heterogeneous) substrate, Savva and Kalliadasis (2013) also find that the drop can move with a constant velocity.] At each instant in time, droplet profiles were recorded based on the ˜ φ = 1 / 2 isosurface.…”

Section: The Contact Anglementioning

confidence: 99%

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

Lamorgese

Mauri

2016

International Journal of Multiphase Flow

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a b s t r a c tA weakly nonlocal phase-field model is used to define the surface tension in liquid binary mixtures in terms of the composition gradient in the interfacial region so that, at equilibrium, it depends linearly on the characteristic length that defines the interfacial width. Contrary to previous works suggesting that the surface tension in a phase-field model is fixed, we define the surface tension for a curved interface and far-from-equilibrium conditions as the integral of the free energy excess (i.e., above the thermodynamic component of the free energy) across the interface profile in a direction parallel to the composition gradient. Consequently, the nonequilibrium surface tension can be widely different from its equilibrium value under dynamic conditions, while it reduces to its thermodynamic value for a flat interface at local equilibrium. In nonequilibrium conditions, the surface tension changes with time: during mixing, it decreases as the inverse square root of time, while in the linear regime of spinodal decomposition, it increases exponentially to its equilibrium value, as nonlinear effects saturate the exponential growth. In addition, since temperature gradients modify the steepness of the concentration profile in the interfacial region, they induce gradients in the nonequilibrium surface tension, leading to the Marangoni thermocapillary migration of an isolated drop. Similarly, Marangoni stresses are induced in a composition gradient, leading to diffusiophoresis. We also review results on the nonequilibrium surface tension for a wall-bound pendant drop near detachment, which help to explain a discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart from a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we present new results from phase-field simulations of the motion of an isolated droplet down an incline in gravity, showing that dynamic contact angle hysteresis can be explained in terms of the nonequilibrium surface tension.

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“…The possibility of using chemically heterogeneous surfaces (CHS) to guide wetting drops along certain directions has recently attracted much attention both theoretically [24][25][26][27][28][29][30][31][32] and experimentally [33][34][35][36][37][38]. In these studies, the driving force is provided by the down-plane component of the drop weight F g = ρVgsinα, acting on a drop of volume V and density ρ sliding down an inclined plane tilted by an angle α (see Figure 3).…”

Section: Basic Principlesmentioning

confidence: 99%

Drop mobility on chemically heterogeneous and lubricant-impregnated surfaces

Mistura

2017

Advances in Physics: X

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Controlling the motion of liquid drops in contact with a solid surface has broad technological implications in many different areas ranging from textiles to microfluidics and heat exchangers. The wettability of a surface is determined by specifying the apparent contact angle and contact angle hysteresis (CAH) that depend on the surface chemistry and morphology. The presence of chemical inhomogeneity and morphological disorder usually increases CAH. A liquid substrate, whose surface is atomically flat and homogenous, is then expected to exhibit a very low CAH. Low CAH determines high drop mobility, while high CAH favours drop pinning. Very slippery surfaces with exceptional omniphobicity are obtained by impregnating a textured solid with a lubricant. To guide and control the motion of drops, the solid surface can be decorated with suitable chemical patterns. In this review, we briefly outline the main results obtained in the past few years to passively control drop motion and produce robust omniphobic surfaces, highlighting some of the most promising applications of these novel functional surfaces.

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Droplet motion on inclined heterogeneous substrates

Cited by 67 publications

References 75 publications

Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates

Low-frequency vibrations of two-dimensional droplets on heterogeneous substrates

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

Drop mobility on chemically heterogeneous and lubricant-impregnated surfaces

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