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The Liquid-Vapor Interfacial Region: A Nanoscale Perspective
Published in Van P. Carey, Liquid-Vapor Phase-Change Phenomena, 2020
The characteristics of the interfacial region can be explored in a more quantitative way by extending classical thermodynamic analysis to the interfacial region with the idealization that properties vary continuously across the region and that local thermodynamic equilibrium applies in a time averaged sense within small control volumes within the interfacial region. This approach was pioneered by van der Waals [1.6] and is usually referred to as the van der Waals theory of capillarity or the molecular theory of capillarity. It is also sometimes referred to as a mean field theory because it is based on the idealization that the behavior of each molecule in a localized region is dictated by the mean field associated with the surrounding molecules.
The Liquid-Vapor Interfacial Region – A Nanoscale Perspective
Published in Van P. Carey, Liquid-Vapor Phase-Change Phenomena, 2018
The characteristics of the interfacial region can be explored in a more quantitative way by extending classical thermodynamic analysis to the interfacial region with the idealization that properties vary continuously across the region and that local thermodynamic equilibrium applies in a time averaged sense within small control volumes within the interfacial region. This approach was pioneered by van der Waals [1.6] and is usually referred to as the van der Waals theory of capillarity or the molecular theory of capillarity. It is also sometimes referred to as a mean field theory because it is based on the idealization that the behavior of each molecule in a localized region is dictated by the mean field associated with the surrounding molecules.
From the vapour–liquid coexistence region to the supercritical fluid: the van der Waals fluid
Published in Molecular Physics, 2023
In the mean field theory [1] the effect of many-body interactions is approximated by an average effect and thus a many-body problem is reduced to a one-body problem. The celebrated van der Waals (vdW) equation of state (EoS) [2] is a typical example of the application of the mean-field theory in dealing with a stable vapor–liquid system. With the vdW EoS the net molecular interaction is a result of the competition between the repulsive and attractive forces. The vdW EoS sets up the foundation for the vapor–liquid equilibrium (VLE) calculation as subjected to the Maxwell construction (the equal-area rule) [3]. Based on the vdW EoS, several cubic EoS’s have been proposed successfully for solving VLE problems for various systems [4]. Here a VLE problem refers to calculations of the saturated pressure, vapor and liquid volumes (densities) and other related properties in the vapor–liquid existence region. With a cubic EoS and majority more complex EoS [5], there are three solutions (roots) to a VLE problem, one as the vapor volume, another, the liquid volume and third one, an ‘unphysical’ solution. The last one has been considered as an artefact of the mean-field theory and thus discarded.
Filament-motor protein system under loading: instability and limit cycle oscillations
Published in Soft Materials, 2021
Amir Shee, Subhadip Ghosh, Debasish Chaudhuri
Using mean field theory and stochastic simulations, we consider the motion of a filament in a gliding assay of MPs, in the presence of an external force. As has been shown recently, the depletion potential in filament bundles can change from a linear to harmonic form with increase in filament number .[7] We consider an external force that could be constant or be a function of filament position. Under a constant load, the filament on MP assay shows a dynamical crossover from stable to unstable phase. Whereas, in the presence of an elastic loading, the filament shows stable limit cycle oscillations when the number of MPs is larger than a critical value .[12,18] We show how the onset of spontaneous oscillations depends on the MP activity in terms of its extension rate and detachment force, which can be tuned, e.g., by changing ATP concentration .[21–23]
Dynamic magnetic and hysteretic properties of the different type core/shell nanostructures: the effect of geometry of wire shape
Published in Philosophical Magazine, 2018
Behiye Boyarbay Kantar, Mehmet Ertaş
In this paper, we have investigated the dynamic magnetic and hysteretic properties of a different type of core/shell nanostructures by using the framework mean-field theory based on Glauber-type stochastic dynamics. First, we have obtained the phase transition behaviours for each of the other wire systems. Then, we have studied the hysteresis properties, namely, loops, coercivity and remanent magnetisations. Finally, we have composed the dynamic magnetic and hysteretic properties of the wire systems. The transition temperature is comparable with the presented study, which exhibits close values for the cylindrical and cubic systems. We have found that the core/shell-structured wire systems exhibit qualitatively similar results on the coercive field and remanent magnetisations with the effect of temperature and crystal field.