Studies at phase interfaces. I. The sliding of liquid drops on solid surfaces and a theory for spray retention

Furmidge, C. G. L.

doi:10.1016/0095-8522(62)90011-9

Cited by 986 publications

(803 citation statements)

References 5 publications

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“…21 Here we assumed that half the drop (the trailing edge) meets the solid with a receding angle θ r while the other half (the leading edge) joins it with an advancing angle θ a , which was shown to be a realistic approximation. 22 Hence, the value of the contact angle hysteresis ∆cos θ can be deduced from the measurement of R. We display the corresponding results in Figure 3, as a function of the pillar density φ.…”

Section: Introductionmentioning

confidence: 99%

Contact Angle Hysteresis Generated by Strong Dilute Defects

2009

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Water on solid decorated with hydrophobic defects (such as micropillars) often stays at the top of the defects in a so-called fakir state, which explains the superhydrophobicity observed in such case, provided that the density of defects is small enough. Here we show that this situation provides an ideal frame for studying the contact angle hysteresis; the phase below the liquid is "perfect" and slippery (it is air), contrasting with pillars' tops whose edges form strong pining sites for the contact line. This model system thus allows us to study the hysteresis as a function of the density of defects and to compare it to the classical theory by Joanny and de Gennes, which is based on very similar hypothesis.

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Section: Introductionmentioning

confidence: 99%

Contact Angle Hysteresis Generated by Strong Dilute Defects

2009

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“…Owing to the difficulty of the three-dimensional flow problem, this study was limited to fluids and droplets of equal viscosity and computations were performed for a limited range of parameter values. More significantly, the prescription of contact lines of elliptical planform is an approximation which does not strictly conform to observations (Furmidge 1962) or to the asymptotic theory of Dussan (1987).…”

Section: Introductionmentioning

confidence: 99%

Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows

Dimitrakopoulos

Higdon

1997

J. Fluid Mech.

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The yield conditions for the displacement of fluid droplets from solid boundaries are studied through a series of numerical computations. The study includes gravitational and interfacial forces, but is restricted to two-dimensional droplets and low-Reynoldsnumber flow. A comprehensive study is conducted, covering a wide range of viscosity ratio λ, Bond number B d , capillary number Ca and contact angles θ A and θ R . The yield conditions for drop displacement are calculated and the critical shear rates are presented as functions Ca(λ, B d , θ A , ∆θ) where ∆θ = θ A − θ R is the contact angle hysteresis. The numerical solutions are based on the spectral boundary element method, incorporating a novel implementation of Newton's method for the determination of equilibrium free surface profiles. The numerical results are compared with asymptotic theories (Dussan 1987) based on the lubrication approximation. While excellent agreement is found in the joint asymptotic limits ∆θ θ A 1, the useful range of the lubrication models proves to be extremely limited. The critical shear rate is found to be sensitive to viscosity ratio with qualitatively different results for viscous and inviscid droplets. Gravitational forces normal to the solid boundary have a significant effect on the displacement process, reducing the critical shear rate for viscous drops and increasing the rate for inviscid droplets. The low-viscosity limit λ → 0 is shown to be a singular limit in the lubrication theory, and the proper scaling for Ca at small λ is identified.

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“…This formula was also derived a few years later by Frenkel (1948) through a minimization of the total energy of the system. Since then, a number of authors (see, for example Furmidge 1962;Dussan 1985;Quéré 1998;Miwa et al 2000; ElSherbini & Jacobi 2004a) proposed generalizations of (1.1) to account specifically on the steady, slow motion of rounded droplets at small inclination angles, deducing a phenomenological scaling law to explain their observations (see also Podgorski et al 2001;Le Grand et al 2005, in which both rounded and cusped droplets are investigated). To address the dynamic problem numerically, a broad range of methodologies were utilized, ranging from precursor film models (e.g.…”

Section: Introductionmentioning

confidence: 99%

Droplet motion on inclined heterogeneous substrates

Savva

Kalliadasis

2013

J. Fluid Mech.

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We consider the static and dynamic behaviour of two-dimensional droplets on inclined heterogeneous substrates. We utilize an evolution equation for the droplet thickness based on the long-wave approximation of the Stokes equations in the presence of slip. Through a singular perturbation procedure, evolution equations for the location of the two moving fronts are obtained under the assumption of quasistatic dynamics. The deduced equations, which are verified by direct comparisons with numerical solutions to the governing equation, are scrutinized in a variety of dynamic and equilibrium settings. For example, we demonstrate the possibility for stick-slip dynamics, substrate-induced hysteresis, the uphill motion of the droplet for sufficiently strong chemical gradients and the existence of a critical inclination angle beyond which the droplet can no longer be supported at equilibrium. Where possible, analytical expressions are obtained for various quantities of interest, which are also verified by appropriate numerical experiments.

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Studies at phase interfaces. I. The sliding of liquid drops on solid surfaces and a theory for spray retention

Cited by 986 publications

References 5 publications

Contact Angle Hysteresis Generated by Strong Dilute Defects

Contact Angle Hysteresis Generated by Strong Dilute Defects

Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows

Droplet motion on inclined heterogeneous substrates

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