Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations

Durán-Olivencia, Miguel A.; Gvalani, Rishabh S.; Kalliadasis, Serafim; Pavliotis, Grigorios A.

doi:10.1007/s10955-018-2200-0

Cited by 32 publications

(31 citation statements)

References 81 publications

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“…Numerical solutions to the SLE offer much broader applicability than the analytic results described above, and can be obtained at a small fraction of the computational cost of MD. A set of closely related stochastic equations are well studied for thin-film flows [26][27][28][29][30] and thermally activated vapor-bubble nucleation [31]. But, surprisingly, there are no detailed numerical SLE studies in the literature for liquid thread rupture.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture

2020

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The instability and rupture of nanoscale liquid threads is shown to strongly depend on thermal fluctuations. These fluctuations are naturally occurring within molecular dynamics (MD) simulations and can be incorporated via fluctuating hydrodynamics into a stochastic lubrication equation (SLE). A simple and robust numerical scheme is developed for the SLE that is validated against MD for both the initial (linear) instability and the nonlinear rupture process. Particular attention is paid to the rupture process and its statistics, where the "double-cone" profile reported by Moseler and Landmann [Science 289, 1165 (2000)] is observed, as well as other distinct profile forms depending on the flow conditions. Comparison to the Eggers' similarity solution [Phys. Rev. Lett. 89, 084502 (2002)], a power law of the minimum thread radius against time to rupture, shows agreement only at low surface tension; indicating that surface tension cannot generally be neglected when considering rupture dynamics.

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Section: Introductionmentioning

confidence: 99%

Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture

2020

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“…[1] is, inter alia, physically relevant for noise-driven rupture of liquid films on substrates. So far, typically films have been considered which are either linearly unstable with respect to small fluctuations of the interface or where the rupture proceeds via hole nucleation in the presence of disjoining pressure [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Here and in Ref.…”

Section: Introductionmentioning

confidence: 99%

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Groß¹

2018

J. Stat. Mech.

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A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards-Wilkinson equation with non-conserved noise and the Mullins-Herring equation with conserved noise. The profile is subject to either periodic or Dirichlet (no-flux) boundary conditions. We determine the noise-driven time-evolution of the profile between an initially flat configuration and the instant at which the profile reaches a given height M for the first time. The shape of the averaged profile agrees well with the prediction of weak-noise theory (WNT), which describes the most-likely trajectory to a fixed first-passage time. Furthermore, in agreement with WNT, on average the profile approaches the height M algebraically in time, with an exponent that is essentially independent of the boundary conditions. However, the actual value of the dynamic exponent turns out to be significantly smaller than predicted by WNT. This "renormalization" of the exponent is explained in terms of the entropic repulsion exerted by the impenetrable boundary on the fluctuations of the profile around its most-likely path. The entropic repulsion mechanism is analyzed in detail for a single (fractional) Brownian walker, which describes the anomalous diffusion of a tagged monomer of the interface as it approaches the absorbing boundary. The present study sheds light on the accuracy and the limitations of the weak-noise approximation for the description of the full first-passage dynamics.

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“…[33][34][35]. Thin-film equation based models are also widely used [2,[19][20][21][22] and if thermal fluctuations are important, these can also be incorporated, creating stochastic thin-film equation models [36,37]. Macroscopic scale approaches include just directly solving the Navier-Stokes equations or via methods such as lattice-Boltzmann [38].…”

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confidence: 99%

Kinetic Monte Carlo and hydrodynamic modeling of droplet dynamics on surfaces, including evaporation and condensation

2019

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We present a lattice-gas (generalised Ising) model for liquid droplets on solid surfaces. The time evolution in the model involves two processes: (i) Single-particle moves which are determined by a kinetic Monte Carlo algorithm. These incorporate into the model particle diffusion over the surface and within the droplets and also evaporation and condensation, i.e. the exchange of particles between droplets and the surrounding vapour. (ii) Larger-scale collective moves, modelling advective hydrodynamic fluid motion, determined by considering the dynamics predicted by a thin-film equation. The model enables us to relate how macroscopic quantities such as the contact angle and the surface tension depend on the microscopic interaction parameters between the particles and with the solid surface. We present results for droplets joining, spreading, sliding under gravity, dewetting, the effects of evaporation, the interplay of diffusive and advective dynamics, and how all this behaviour depends on the temperature and other parameters. * Electronic address: A.J. Archer@lboro.ac.uk arXiv:1906.08121v1 [cond-mat.soft] 19 Jun 2019 is to use Monte Carlo methods to simulate the dynamic properties of Hamiltonian systems [18]. However, it is not clear to us that one should enforce detailed balance when constructing coarse grained models of such non-equilibrium systems, since droplets on surfaces are highly dissipative systems, due to the evaporation, the strong coupling to the substrate, etc. Of course, at equilibrium, there should be detailed balance in the model.To model collective hydrodynamic motion in our model, we generate large-scale collective particle moves by considering the dynamics that is predicted by a thin-film equation. This is a time evolution equation for the liquid film thickness profile h, i.e. the height of the liquid-vapour interface above the surface [2,[19][20][21][22]. This equation is derived from the Navier-Stokes equations for a film of liquid on a surface by making a long-wave approximation, which greatly simplifies the analysis. When generating these 'thin-film moves', we first determine the liquid film height profile from the configuration of occupied lattice sites, we then evolve the thin-film equation for a short amount of time, and then map back to the lattice. In our model, an important quantity is the parameter λ, defined below in Eq. (13), which is proportional to the ratio of the number of KMC attempted particle moves to the number of thin-film moves. When λ = 0, our model reduces to just evolving the thin-film equation, whilst in the limit λ → ∞, our model is a pure KMC model. Therefore, this parameter λ ∝ D/η, where D is a single-particle diffusion coefficient and η is the viscosity.Key quantities that characterises how a liquid wets a surface are the spreading parameter S = γ sv − (γ sl + γ lv ), where γ sv , γ sl , and γ lv are the solid-vapour, solid-liquid and liquid-vapour interfacial tensions, respectively [2], and also the contact angle θ, which is given by Young's equation [2]:The...

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Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations

Cited by 32 publications

References 81 publications

Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture

Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture

First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect

Kinetic Monte Carlo and hydrodynamic modeling of droplet dynamics on surfaces, including evaporation and condensation

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