1
|
MacDowell LG. Surface tension of bulky colloids, capillarity under gravity, and the microscopic origin of the Kardar-Parisi-Zhang equation. Phys Rev E 2023; 108:L022801. [PMID: 37723748 DOI: 10.1103/physreve.108.l022801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 07/26/2023] [Indexed: 09/20/2023]
Abstract
Experimental measurements of the surface tension of colloidal interfaces have long been in conflict with computer simulations. In this Letter we show that the surface tension of colloids as measured by surface fluctuations picks up a gravity-dependent contribution which removes the discrepancy. The presence of this term puts a strong constraint on the structure of the interface which allows one to identify corrections to the fundamental equation of equilibrium capillarity and deduce bottom up the microscopic origin of a growth model with close relation to the Kardar-Parisi-Zhang equation.
Collapse
Affiliation(s)
- Luis G MacDowell
- Departamento de Química-Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, 28040 Madrid, Spain
| |
Collapse
|
2
|
Łapiński M, Kozioł R, Skubida W, Winiarz P, Mahjoub Yahia Elhassan R, Sadowski W, Kościelska B. Transformation of bimetallic Ag-Cu thin films into plasmonically active composite nanostructures. Sci Rep 2023; 13:10107. [PMID: 37344514 DOI: 10.1038/s41598-023-37343-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Accepted: 06/20/2023] [Indexed: 06/23/2023] Open
Abstract
Formation of plasmonically active silver, copper and composite silver-copper nanostructures were studied in this paper. Metallic nanostructures were fabricated by thermal disintegration, so called dewetting, of the thin films in an argon atmosphere. The formation process of the nanostructures was in-situ observed by a novel method, based on resistance measurements. The influence of the material and thickness of the initial thin film on temperature of their disintegration was investigated. Electrical measurements were validated by scanning electron microscopy observations, while metallic the behavior of nanostructures was studied by XPS method. The formation of silver-copper nanocomposite structures was confirmed by UV-vis spectroscopy. Plasmon resonance with two characteristic peaks for nanocomposite structures was observed.
Collapse
Affiliation(s)
- Marcin Łapiński
- Institute of Nanotechnology and Materials Engineering, Advanced Materials Center, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233, Gdańsk, Poland.
| | - Robert Kozioł
- Institute of Nanotechnology and Materials Engineering, Advanced Materials Center, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233, Gdańsk, Poland
| | - Wojciech Skubida
- Institute of Nanotechnology and Materials Engineering, Advanced Materials Center, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233, Gdańsk, Poland
| | - Piotr Winiarz
- Department of Hydrogen Energy, Faculty of Energy and Fuels, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059, Kraków, Poland
| | - Rowa Mahjoub Yahia Elhassan
- Institute of Nanotechnology and Materials Engineering, Advanced Materials Center, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233, Gdańsk, Poland
- Department of Physical and Chemical Science, University of L'Aquila, Via Vetoio 10, 67100, L'Aquila, Italy
| | - Wojciech Sadowski
- Institute of Nanotechnology and Materials Engineering, Advanced Materials Center, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233, Gdańsk, Poland
| | - Barbara Kościelska
- Institute of Nanotechnology and Materials Engineering, Advanced Materials Center, Gdansk University of Technology, ul. G. Narutowicza 11/12, 80-233, Gdańsk, Poland
| |
Collapse
|
3
|
Liu J, Zhao C, Lockerby DA, Sprittles JE. Thermal capillary waves on bounded nanoscale thin films. Phys Rev E 2023; 107:015105. [PMID: 36797965 DOI: 10.1103/physreve.107.015105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.
Collapse
Affiliation(s)
- Jingbang Liu
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Chengxi Zhao
- Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
| | - Duncan A Lockerby
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - James E Sprittles
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| |
Collapse
|
4
|
Zitz S, Scagliarini A, Harting J. Lattice Boltzmann simulations of stochastic thin film dewetting. Phys Rev E 2021; 104:034801. [PMID: 34654097 DOI: 10.1103/physreve.104.034801] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Accepted: 08/11/2021] [Indexed: 11/07/2022]
Abstract
We study numerically the effect of thermal fluctuations and of variable fluid-substrate interactions on the spontaneous dewetting of thin liquid films. To this aim, we use a recently developed lattice Boltzmann method for thin liquid film flows, equipped with a properly devised stochastic term. While it is known that thermal fluctuations yield shorter rupture times, we show that this is a general feature of hydrophilic substrates, irrespective of the contact angle θ. The ratio between deterministic and stochastic rupture times, though, decreases with θ. Finally, we discuss the case of fluctuating thin film dewetting on chemically patterned substrates and its dependence on the form of the wettability gradients.
Collapse
Affiliation(s)
- S Zitz
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, Fürther Strasse 248, 90429 Nürnberg, Germany.,Department of Chemical and Biological Engineering, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany
| | - A Scagliarini
- Institute for Applied Mathematics "M. Picone" (IAC), Consiglio Nazionale delle Ricerche (CNR), Via dei Taurini 19, 00185 Rome, Italy.,INFN, sezione Roma "Tor Vergata", via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - J Harting
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy, Forschungszentrum Jülich, Fürther Strasse 248, 90429 Nürnberg, Germany.,Department of Chemical and Biological Engineering and Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Fürther Straße 248, 90429 Nürnberg, Germany
| |
Collapse
|
5
|
Zhang Y, Sprittles JE, Lockerby DA. Nanoscale thin-film flows with thermal fluctuations and slip. Phys Rev E 2020; 102:053105. [PMID: 33327206 DOI: 10.1103/physreve.102.053105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 10/10/2020] [Indexed: 06/12/2023]
Abstract
The combined effects of thermal fluctuations and liquid-solid slip on nanoscale thin-film flows are investigated using stochastic lubrication equations (SLEs). The previous no-slip SLE for films on plates is extended to consider slip effects and a new SLE for films on fibers is derived, using a long-wave approximation to fluctuating hydrodynamics. Analytically derived capillary spectra, which evolve in time, are found from the new SLEs and compared to molecular dynamics simulations. It is shown that thermal fluctuations lead to the generation and growth of surface waves, and slip accelerates this growth. SLEs developed here provide useful tools to study nanoscale film dewetting, nanofiber coating, and liquid transport using nanofibers.
Collapse
Affiliation(s)
- Yixin Zhang
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - James E Sprittles
- Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Duncan A Lockerby
- School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
| |
Collapse
|
6
|
Numerical Picard Iteration Methods for Simulation of Non-Lipschitz Stochastic Differential Equations. Symmetry (Basel) 2020. [DOI: 10.3390/sym12030383] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, we present splitting approaches for stochastic/deterministic coupled differential equations, which play an important role in many applications for modelling stochastic phenomena, e.g., finance, dynamics in physical applications, population dynamics, biology and mechanics. We are motivated to deal with non-Lipschitz stochastic differential equations, which have functions of growth at infinity and satisfy the one-sided Lipschitz condition. Such problems studied for example in stochastic lubrication equations, while we deal with rational or polynomial functions. Numerically, we propose an approximation, which is based on Picard iterations and applies the Doléans-Dade exponential formula. Such a method allows us to approximate the non-Lipschitzian SDEs with iterative exponential methods. Further, we could apply symmetries with respect to decomposition of the related matrix-operators to reduce the computational time. We discuss the different operator splitting approaches for a nonlinear SDE with multiplicative noise and compare this to standard numerical methods.
Collapse
|