Ostwald ripening of droplets: The role of migration

Glasner, Karl; Otto, Félix; Rump, Tobias; Slepčev, Dejan

doi:10.1017/s0956792508007559

Cited by 38 publications

(74 citation statements)

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“…Additionally, using essentially a mixture of the gradient flow structure approach and asymptotic analysis, the one-as well as the two-dimensional case for M(h) = h q , q > 0 has recently been considered in [32]. Within the context of thin liquid films the relevant case here is M(h) = h 2 , the intermediate-slip model, apart form the more frequently considered no-slip case when M(h) = h 3 .…”

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confidence: 99%

Coarsening dynamics of slipping droplets

Kitavtsev

Wagner

2009

J Eng Math

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The late-phase dewetting process of nanoscopic thin polymer films on hydrophobized substrates using some recently derived lubrication models that take account of large slippage at the polymer-substrate interface is studied. The late phase of this process is characterized by the slow-time coarsening dynamics of arrays of droplets that remain after rupture and the initial dewetting phases. For this situation a reduced system of ordinary differential equations is derived from the lubrication model for large slippage using asymptotic analysis. This extends known results for the no-slip case. On the basis of the reduced model, the role of the slippage as a control parameter for droplet migration is analysed and several new qualitative effects for the coarsening process are identified.

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confidence: 99%

Coarsening dynamics of slipping droplets

Kitavtsev

Wagner

2009

J Eng Math

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“…In [11], Glasner et al studied the same problem using energy arguments and heuristically obtained the same result. Other results in [9,11] include that the collision mechanism can be as important as the ripening and can induce similar growth rates of characteristic sizes. No rigorous result is known so far for the power-logarithmic law (1.1).…”

Section: Introductionmentioning

confidence: 73%

“…In [9] and [11], it is pointed out that the motion of the droplet bases is determined by the mobility in the nonlinear thin film Equation (2.1). When the power 0 < q < 3, the influence of the mobility of the droplets are minor compared to the ripening process.…”

Section: Formal Derivation Of the Mean Field Modelmentioning

confidence: 99%

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On the Ostwald ripening of thin liquid films

Dai

2011

Communications in Mathematical Sciences

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Abstract. Dewetting instabilities cause a thin liquid film coating a solid substrate to rupture and finally form complex patterns, which are quasiequilibrium parabolic droplets connected by an ultra thin residual film. During the Ostwald ripening process, droplets exchange mass through the residual thin film without touching each other. Bigger ones grow while smaller ones shrink and disappear. As a result the total number of droplets N (t) decreases while the average size increases. For the physically realistic case when the underlying substrate is two dimensional, it is predicted that the average volume of droplets V follows a temporal power-logarithmic law: V 4/3 lnV ∼ ct. We propose a mean field model for the Ostwald ripening of 2D thin films and define a structural time scale ts, which is heuristically similar to t. In this mean field model we rigorously prove that V can not grow faster than the power-logarithmic law in ts in the average sense, as long as the droplets are well separated.Key words. Thin film equation, coarsening, Ostwald ripening, mean field models.AMS subject classifications. 35B40, 76A20, 35K25, 35K55, 35Q80. IntroductionDue to the dewetting instabilities, a thin liquid film coating a solid substrate goes through complicated morphological changes and ultimately forms complex nonlinear patterns in the late stage. The patterns are essentially quasi-static fluid droplets connected by an ultra thin residual film. Droplets may exchange mass through a diffusion field in the ultra thin film. Smaller ones shrink and collapse while bigger ones grow. This mechanism is called Ostwald ripening, as it is similar to what happens in phase transitions (see, e.g., [22]). Meanwhile, droplets may move around and collide to form bigger ones. These two mechanisms cause coarsening phenomena to occur where we observe the decrease of the total number of droplets and an increase in the average droplet size and the average distance between droplets.For the simplified case when the underlying substrate is one-dimensional, the coarsening dynamics of the thin film was studied by Glasner and Witelski [10,12] using asymptotic analysis methods. Heuristic arguments and numerical simulations suggest that under both mechanisms the number of droplets N (t) decreases following a temporal power law N (t) ∼ ct −2/5 . As a consequence, the average distance between drops grows as a temporal power law t 2/5 and the average height and width of drops grow as t 1/5 . The size distribution of droplets was studied in [13] by considering a mean field model when the ripening mechanism dominates. Their numerical simulations indicate that the power law for N (t) holds in the average sense when self-similarity of the size distribution is not attained. In [2], we studied the mean field model in [13] and rigorously proved that in the average sense N (t) can not decrease faster than the t −2/5 power law. When the underlying substrate is two dimensional, which is the physically realistic case, the situation becomes much more complicated. It is s...

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“…This promotes the presence of metallic Ag nanoparticles within the fi lms, which may have been formed by the photoreduction of oxidized silver dissolved in the TiO 2 matrix followed by coalescence [ 33 ] or Ostwald ripening processes. [ 39 ] The observed resonance around 650 nm in Figure 5 (7 of 9) 1500134 wileyonlinelibrary.com…”

Section: Multicolor Photochromic Behaviormentioning

confidence: 99%

Magnetron Sputtering Deposition of Ag/TiO₂ Nanocomposite Thin Films for Repeatable and Multicolor Photochromic Applications on Flexible Substrates

Diop

Simonot

Destouches

et al. 2015

Adv Materials Inter

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It is reported on a reactive magnetron sputtering‐based deposition method to synthesize, at room temperature, photochromic nanocomposite thin films consisting of Ag nanoparticles sandwiched between nanoporous TiO2 layers. The fabrication process is compatible with large‐scale production and functional flexible substrates. It is shown that when TiO2 is deposited in the metallic mode, the formation of Ag metal nanoparticles induces localized surface plasmon resonances in the visible range and therefore the as‐deposited samples are colored. In contrast, when TiO2 is deposited in the compound mode, the trilayer samples are colorless because silver oxidizes during TiO2 deposition. It is demonstrated that the colorless samples can be colored under ultraviolet (UV) laser exposure at 244 nm due to the reduction of oxidized silver and the formation of metallic Ag nanoparticles. Moreover, irradiation at 647 nm wavelength of colored samples (as‐prepared or after UV exposure) gives rise to changes in the particle morphology that strongly modifies the film absorbance and results in a color transition from blue to orange. The choice of the irradiation wavelength allows controlling the color saturation of the sample up to the complete discoloration by using a visible laser at 488 nm. All these photochromic mechanisms are repeatable during cyclic processes.

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Ostwald ripening of droplets: The role of migration

Cited by 38 publications

References 17 publications

Coarsening dynamics of slipping droplets

Coarsening dynamics of slipping droplets

On the Ostwald ripening of thin liquid films

Magnetron Sputtering Deposition of Ag/TiO₂ Nanocomposite Thin Films for Repeatable and Multicolor Photochromic Applications on Flexible Substrates

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Ostwald ripening of droplets: The role of migration

Cited by 38 publications

References 17 publications

Coarsening dynamics of slipping droplets

Coarsening dynamics of slipping droplets

On the Ostwald ripening of thin liquid films

Magnetron Sputtering Deposition of Ag/TiO2 Nanocomposite Thin Films for Repeatable and Multicolor Photochromic Applications on Flexible Substrates

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Product

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About

Magnetron Sputtering Deposition of Ag/TiO₂ Nanocomposite Thin Films for Repeatable and Multicolor Photochromic Applications on Flexible Substrates