Finite-time thin film rupture driven by modified evaporative loss

Ji, Hangjie; Witelski, Thomas P.

doi:10.1016/j.physd.2016.10.002

Cited by 22 publications

(22 citation statements)

References 55 publications

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“…There are many forms of disjoining pressure reported in literature and different choices of disjoining pressure cause different flow behavior in a thin film [35,36]. The disjoining pressure for the system considered here is the classical φ = A/(6π h 3 ), obtained by integrating the attractive part of 12-6 LJ potential over a semi-infinitely extended substrate (the repulsive part makes a negligible contribution to the linear stability growth), where A is the Hamaker constant equal to the difference between the Hamaker constant of the liquid film itself and the liquid-solid interactions, i.e., A = A ll − A ls [28,37].…”

Section: Stochastic Thin-film Equationmentioning

confidence: 99%

Molecular simulation of thin liquid films: Thermal fluctuations and instability

2019

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The instability of a thin liquid film on a solid surface is studied both by molecular dynamics simulations (MD) and a stochastic thin-film equation (STF), which models thermal fluctuations with white noise. A linear stability analysis of the STF allows us to derive a power spectrum for the surface fluctuations, which is quantitatively validated against the spectrum observed in MD. Thermal fluctuations are shown to be critical to the dynamics of nanoscale films. Compared to the classical instability mechanism, which is driven by disjoining pressure, fluctuations (a) can massively amplify the instability, (b) cause the fluctuation wavelength that is dominant to evolve in time (a single fastest-growing mode does not exist), and (c) decrease the critical wavelength so that classically stable films can be ruptured.

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Section: Stochastic Thin-film Equationmentioning

confidence: 99%

Molecular simulation of thin liquid films: Thermal fluctuations and instability

2019

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“…We follow the approach in [24,43] and perturb the uniform film by an infinitesimal Fourier mode disturbance…”

Section: Stability Of Spatially Uniform Filmsmentioning

confidence: 99%

“…The phase plane for the second-order steady state solutions satisfying(24) in the critical case with 0 < P0 < P . The homoclinic orbit in solid line corresponds to the droplet solution in…”

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confidence: 99%

Instability and dynamics of volatile thin films

Witelski

2018

Phys. Rev. Fluids

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Volatile viscous fluids on partially-wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low Reynolds number lubrication approximation incorporating surface tension, intermolecular effects and evaporative fluxes. Parameter ranges for evaporationdominated and condensation-dominated regimes and a critical case are identified. Interfacial instabilities driven by the competition between the disjoining pressure and evaporative effects are studied via linear stability analysis. Transient pattern formation in nearly-flat evolving films in the critical case is investigated. In the weak evaporation limit unstable modes of finite amplitude non-uniform steady states lead to rich droplet dynamics, including flattening, symmetry breaking, and droplet merging. Numerical simulations show long time behaviors leading to evaporation or condensation are sensitive to transitions between film-wise and drop-wise dynamics.

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“…The nonlinear case q = −ψ(h)∇h can be made somewhat like the thin-film equation. For example if ψ(h) = κ(h 3 + βh −3 ), then the PDE resembles the case of a thin fluid film subject to van der Waals forces; this situation was studied in Winter et al [47] and many other places (e.g., [26]).…”

Section: Nonlinear Diffusionmentioning

confidence: 99%

Simulation of parabolic flow on an eye-shaped domain with moving boundary

2018

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During the upstroke of a normal eye blink, the upper lid moves and paints a thin tear film over the exposed corneal and conjunctival surfaces. This thin tear film may be modeled by a nonlinear fourth-order PDE derived from lubrication theory. A challenge in the numerical simulation of this model is to include both the geometry of the eye and the movement of the eyelid. A pair of orthogonal and conformal maps transform a square into an approximate representation of the exposed ocular surface of a human eye. A spectral collocation method on the square produces relatively efficient solutions on the eye-shaped domain via these maps. The method is demonstrated on linear and nonlinear second-order diffusion equations and shown to have excellent accuracy as measured pointwise or by conservation checks. Future work will use the method for thin-film equations on the same type of domain.

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Finite-time thin film rupture driven by modified evaporative loss

Cited by 22 publications

References 55 publications

Molecular simulation of thin liquid films: Thermal fluctuations and instability

Molecular simulation of thin liquid films: Thermal fluctuations and instability

Instability and dynamics of volatile thin films

Simulation of parabolic flow on an eye-shaped domain with moving boundary

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