Addressing metastability in interfacial phenomena across multiple time and length scales
- Simone Meloni (Sapienza University of Rome, Italy)
- Alberto Giacomello (Sapienza University of Rome, Italy)
- Halim Kusumaatmaja (Durham University, United Kingdom)
Phenomena occurring at the solid/liquid/gas interface are of great fundamental interest and play a crucial role in engineering and industrial applications. For example, superhydrophobic surfaces for drag reduction rely on the existence, as well as thermodynamic and/or kinetic stability of the Cassie-Baxter state , in which water is suspended over a gas layer entrapped in the texture of hydrophobic surfaces; Limiting nucleation of vapor bubbles is important, e.g., for marine applications, because the implosion of cavitation bubbles can produce damages on propellers and other submerged parts .
These interfacial problems are intrinsically characterized by multiple time and length scales. The timescales range from the microscopic time of the molecular system determining the properties of fluids and their fluctuations to the macroscopic time of nucleation or wetting dynamics. A number of rare event techniques exists to cope with multiple timescales, and several quasi-static methods (umbrella sampling, nudged elastic band, string method) have been used in conjunction with micro and macroscopic models of interface systems [3-5]. However, there is crucial need for systematic comparisons among these methods, for assessing their suitability for interface phenomena and evaluating the importance of kinetics and dynamics that are neglected in quasi-static methods. Rare event methods accounting for these latter effects, e.g., forward flux sampling and minimum action method, have been used in a limited number of applications [6-7]. Moreover, a major open problem is how to consolidate results from rare event techniques against macroscopic simulations of interfacial dynamics, e.g., using fluctuating hydrodynamics methods [8-9].
Interfacial problems are also often characterized by multiple length scales, ranging from the thickness of the liquid-gas interface, the hierarchical roughness of bio-inspired surfaces, to the macroscopic fluid body. In this context, models with different levels of detail have been developed. For example, to study vapor nucleation in confined systems, the macroscopic sharp interface model , classical density functional theory , and atomistic models  have been used. An open question in computations of actual interfacial systems is how to find a compromise between expensive microscopic descriptions and simpler but fast models; spatial multiscale methods would guarantee the advantages of both approaches but are still being developed.
An additional difficulty in the study of the interface problems considered in this workshop is the limited number of experimental results available. Well-designed, quantitative experiments might serve as a benchmark for computational techniques and theoretical models of nucleation and wetting, but the measured observables are not always accessible in simulations and vice versa. Recent experiments [12-13] have contributed to shed some light on these phenomena but more experiments, especially if designed in collaboration with theoreticians and computational scientists, will help to clarify many aspects of the subject of this workshop.
We identify three interrelated categories of topics to be discussed: (i) concepts and methods, (ii) software development, and (iii) applications. To stimulate the discussions we envisage a balanced mix of participants: scientists who develop methods, simulators and experimentalists.
Concepts and Methods
* Modeling of processes involving fluid interfaces (e.g. liquid/gas) in contact with textured surfaces often involves multiple length scales. Several recent articles have highlighted the crucial roles of nanoscopic effects such as line tension, thermal fluctuations, curvature dependent surface tension and pinning due to multiscale roughness. What is the minimal model to capture these nanoscopic effects? How important are they for macroscopic dynamics? How do we ‘stitch’the macroscopic and nanoscopic pictures?
* There is strong interest to combine macroscopic interfacial dynamics with stochastic rare events methods, but to date no one has derived a coherent scheme. What is the most promising interfacial dynamics/rare event method combinations? How do we develop a strong theoretical foundation for such methods?
* There is a number of rare event methods, with varying degree of computational costs and level of information. Nudged elastic band and string methods provide equilibrium, quasi-static path and free energy profile. Forward flux sampling is better suited if we want to include non-equilibrium effects, but it still requires the problem to be stationary. There are also methods, such as the minimum action method, where we can account for the finite duration of the transition. Which kind of information is relevant for interfacial dynamics? Can we still learn anything meaningful from ‘relatively cheap’ methods such as nudged elastic band and string methods, which only provide an equilibrium free energy profile?
* Multiscale modeling has developed a major impact in the biophysics/chemistry community, where we are now able to combine quantum mechanical, classical mechanics, and continuum (typically polarizable dielectrics) models. What can we learn from this area? Can we adopt a similar approach? Do we simply combine existing software, or do we need a truly integrated approach?
* How do we implement these methods to make them available to the larger community of researchers focusing on applications, who understand the principles of the methods, and how to tune the various parameters, but won’t be able to implement these methods themselves? What is the best avenue to organise and fund such software project?
* An emblematic application is that of superhydrophobicity, which at the same time is strongly metastable, encompassing multiple timescales, and possessing roughness with length scales from nanometres to microns. Other examples of similar nature which have garnered strong interests in the scientific community include contact angle hysteresis and heterogeneous nucleation. Can we exploit metastabilities and the multiscale nature of interfacial systems for smart materials and technological applications?
* This wealth of scales is in many cases inextricable, a challenge which is also faced by experimentalists. Can we come up with benchmark experiments that
accentuate this multiscale nature? Can we then use them to build quantitatively reliable theories and simulation methods?
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