Rolling droplets

Mahadevan, L.; Pomeau, Yves

doi:10.1063/1.870107

Cited by 335 publications

(382 citation statements)

References 10 publications

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“…Previous studies (Dell'Aversana et al 1997;Neitzel & Dell'Aversana 2002;Savino et al 2003) have pointed out that in these conditions the underside of the drop may deform such that the height of the gap is not constant. We avoid such geometrical complexities by treating the gap as a cylindrical disk with height h(t) and radius R d , where R d = R 2 /l c is the effective contact radius (Mahadevan & Pomeau 1999), and l c = √ σ /ρ o g is the capillary length of the oil; an approximation one expects to be valid provided Bo = ρ o gR 2 /σ < 1. In our experiments Bo = 0.17 and R d = 0.25 mm 0.4R.…”

Section: Lubrication Flow Within the Air Gapmentioning

confidence: 99%

Thermal delay of drop coalescence

et al. 2017

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We present the results of a combined experimental and theoretical study of drop coalescence in the presence of an initial temperature difference T 0 between a drop and a bath of the same liquid. We characterize experimentally the dependence of the residence time before coalescence on T 0 for silicone oils with different viscosities. Delayed coalescence arises above a critical temperature difference T c that depends on the fluid viscosity: for T 0 > T c , the delay time increases as T 2/3 0 for all liquids examined. This observed dependence is rationalized theoretically through consideration of the thermocapillary flows generated within the drop, the bath and the intervening air layer.

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Section: Lubrication Flow Within the Air Gapmentioning

confidence: 99%

Thermal delay of drop coalescence

et al. 2017

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“…A common observation of a droplet on an inclined substrate is that it appears to remain stationary as the inclination angle is increased, until a critical inclination angle † Email address for correspondence: s.kalliadasis@imperial.ac.uk is reached beyond which the substrate can no longer support the droplet at equilibrium and it slides downhill at a nearly constant speed (rolling motion is also possible for sufficiently hydrophobic substrates; see Mahadevan & Pomeau 1999;Richard & Quéré 1999). By increasing the inclination angle even further, cusp formation is eventually observed at the rear of the droplet, which may lead to breakup due to instabilities and the shedding of droplets (Podgorski, Flesselles & Limat 2001;Ben Amar, Cummings & Pomeau 2003;Limat & Stone 2004;Le Grand, Daerr & Limat 2005;Snoeijer et al 2005Snoeijer et al , 2007.…”

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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“…We hoped that the study of the synthesis and manipulation by aphids of non-wetting droplets might improve the possibility for the use of such droplets in human applications. We therefore drew on our newly gained knowledge of the unique properties of these nonwetting droplets (Mahadevan & Pomeau 1999;Richard & Quéré 1999;Aussillous & Quéré 2001), to determine if these properties might enhance aphid hygiene.…”

Section: Introductionmentioning

confidence: 99%

How aphids lose their marbles

Pike

Richard

Foster

et al. 2002

Proc. R. Soc. Lond. B

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136

104

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Insects provide examples of many cunning stratagems to cope with the challenges of living in a world dominated by surface forces. Despite being the current masters of the land environment, they are at constant risk of being entrapped in liquids, which they prevent by having waxy and hairy surfaces. The problem is particularly acute in an enclosed space, such as a plant gall. Using secreted wax to ef ciently parcel and transport their own excrement, aphids were able to solve this problem 200 Myr ago. Here, we report on the physical and physiological signi cance of this ingenious solution. The secreted powdery wax has three distinct roles: (i) it is hydrophobic, (ii) it creates a microscopically rough inner gall surface made of weakly compacted wax needles making the gall ultra-hydrophobic, and (iii) it coats the honeydew droplets converting them into liquid marbles, that can be rapidly and ef ciently moved.

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Rolling droplets

Cited by 335 publications

References 10 publications

Thermal delay of drop coalescence

Thermal delay of drop coalescence

Droplet motion on inclined heterogeneous substrates

How aphids lose their marbles

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