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Nanoscale interfacial flows with thermal fluctuations and slip
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Zhang, Yixin (2021) Nanoscale interfacial flows with thermal fluctuations and slip. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3714729
Abstract
In this thesis, we present theoretical studies and molecular dynamics (MD) simulations of nanoscale interfacial flows taking the crucial effects of thermal fluctuations and slip into account.
Adopting a long-wave approximation to Fluctuating Hydrodynamics, we derive stochastic lubrication equations (SLEs) for planar films and annular films with slip modelled. It is found that Navier's slip condition has to be modified by including a random stress at the boundary and relating its covariance with slip.
This `long-wave' paradigm used to derive the SLEs has the inherent problem of being inaccurate for dynamics of interfacial waves with short wavelengths. We thus propose a Langevin equation to overcome this inadequacy, based on the Ornstein-Uhlenbeck process and classic Capillary Wave Theory (CWT).
Using the SLE, we investigate the effects of thermal fluctuations on the instability of dewetting nanofilms. A linear stability analysis of the SLE allows us to derive a power spectrum for the surface waves, which is quantitatively validated against the spectrum observed in MD. Thermal fluctuations are shown to be critical to the instability of nanoscale films. Compared to the classical instability mechanism, which is driven by disjoining pressure, fluctuations (a) massively amplify the instability, (b) create a time-dependent fastest growing wavenumber, and (c) increase the critical wavenumber so that classically stable films can be ruptured.
The proposed Langevin model can describe both the growth of capillary wave spectra and the relaxation of capillary wave correlations, with the former providing a time scale for the surface to reach thermal equilibrium. The capillary spectra of planar films are found to advance towards a static spectrum described by CWT, with the roughness of the surface W increasing as a power law of time W _ t1=8 before saturation. However, the spectra of an annular film (with outer radius h0) are unbounded for dimensionless wavenumber qh0 < 1 due to the Rayleigh-Plateau instability. Slip is shown to accelerate the growth of spectra for both kinds of films.
Temporal correlations of interfacial Fourier modes for nanofilms on anisotropic slip substrates, measured at thermal equilibrium in MD, demonstrate that (i) larger slip lengths lead to a faster decay in wave correlations, and (ii) unlike on isotropic-slip substrates, the time correlations of waves on anisotropic-slip substrates are wavedirection dependent. These findings can be well predicted by the Langevin model with a newly derived dispersion relation considering the anisotropic-slip condition.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QC Physics Q Science > QD Chemistry T Technology > TA Engineering (General). Civil engineering (General) |
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Library of Congress Subject Headings (LCSH): | Thin films, Thin films -- Effect of temperature on, Solid-liquid interfaces, Interfaces (Physical sciences) -- Mathematical models, Computational fluid dynamics, Molecular dynamics, Nanofluids | ||||
Official Date: | June 2021 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | School of Engineering | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Lockerby, Duncan A. ; Sprittles, James E. ; Lockerby, Duncan A. | ||||
Format of File: | |||||
Extent: | xiii, 114 leaves : illustrations | ||||
Language: | eng |
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