Moving contact lines in a pure-vapor atmosphere: a singularity-free description in the sole framework of classical physics

We here show that, even in the absence of "regularizing" microscopic effects (viz. slip at the wall or the disjoining pressure/precursor films), no singularities in fact arise for a moving contact line surrounded by the pure vapor of the liquid considered. There are no evaporation-related singularities either even should the substrate be superheated. We consider, within the lubrication approximation and a classical one-sided model, a contact line advancing/receding at a constant velocity, or immobile, and starting abruptly at a (formally) bare solid surface with a zero or finite contact angle.Comment: To be submitted to Phys. Rev. Let

Asymptotic analysis of the evaporation dynamics of partially wetting droplets

We consider the dynamics of an axisymmetric, partially wetting droplet of a one-component volatile liquid. The droplet is supported on a smooth superheated substrate and evaporates into a pure vapour atmosphere. In this process, we take the liquid properties to be constant and assume that the vapour phase has poor thermal conductivity and small dynamic viscosity so that we may decouple its dynamics from the dynamics of the liquid phase. This leads to a so-called ‘one-sided’ lubrication-type model for the evolution of the droplet thickness, which accounts for the effects of evaporation, capillarity, gravity, slip and kinetic resistance to evaporation. By asymptotically matching the flow near the contact line region and the bulk of the droplet in the limit of a small slip length and commensurably small evaporation and kinetic resistance effects, we obtain coupled evolution equations for the droplet radius and volume. The predictions of our asymptotic analysis, which also include an estimate of the evaporation time, are found to be in excellent agreement with numerical simulations of the governing lubrication model for a broad range of parameter regimes

Asymptotic analysis of evaporating droplets

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.We consider the evaporation dynamics of a two-dimensional, partially-wetting sessile droplet of a volatile liquid in its pure vapour, which is supported on a smooth horizontal superheated substrate. Assuming that the liquid properties remain unchanged, we utilise a one-sided lubrication-type model for the evolution of the droplet thickness, which accounts for the effects of evaporation, capillarity, slip and the kinetic resistance to evaporation. We follow an asymptotic approach, which yields a set of coupled evolution equations for the droplet radius and area, estimating analytically the evaporation-modified apparent angle when evaporation effects are weak. The validity of our matching procedure is verified by numerical experiments, obtaining also an estimate for the evaporation time

Leidenfrost drops on a heated liquid pool

We show that a volatile liquid drop placed at the surface of a non-volatile liquid pool warmer than the boiling point of the drop can experience a Leidenfrost effect even for vanishingly small superheats. Such an observation points to the importance of the substrate roughness, negligible in the case considered here, in determining the threshold Leidenfrost temperature. A theoretical model based on the one proposed by Sobac et al. [Phys. Rev. E 90, 053011 (2014)] is developed in order to rationalize the experimental data. The shapes of the drop and of the substrate are analyzed. The model notably provides scalings for the vapor film thickness. For small drops, these scalings appear to be identical to the case of a Leidenfrost drop on a solid substrate. For large drops, in contrast, they are different and no evidence of chimney formation has been observed either experimentally or theoretically in the range of drop sizes considered in this study. Concerning the evaporation dynamics, the radius is shown to decrease linearly with time whatever the drop size, which differs from the case of a Leidenfrost drop on a solid substrate. For high superheats, the characteristic lifetime of the drops versus the superheat follows a scaling law that is derived from the model but, at low superheats, it deviates from this scaling by rather saturating

Solutal Marangoni instability of binary mixtures evaporating into air: an analytical model describing highly unstable cases

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Asymptotic theory for a Leidenfrost drop on a liquid pool

Droplets can be levitated by their own vapour when placed onto a superheated plate (the Leidenfrost effect). It is less known that the Leidenfrost effect can likewise be observed over a liquid pool (superheated with respect to the drop), which is the study case here. Emphasis is placed on an asymptotic analysis in the limit of small evaporation numbers, which proves to be a realistic one indeed for not so small drops. The global shapes are found to resemble "superhydrophobic drops" that follow from the equilibrium between capillarity and gravity. However, the morphology of the thin vapour layer between the drop and the pool is very different from that of classical Leidenfrost drops over a flat rigid substrate, and exhibits different scaling laws. We determine analytical expressions for the vapour thickness as a function of temperature and material properties, which are confirmed by numerical solutions. Surprisingly, we show that deformability of the pool suppresses the chimney instability of Leidenfrost drops

The relation of steady evaporating drops fed by an influx and freely evaporating drops

We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and capillarity play a major role. The model is first employed to study steady evaporating drops that are fed locally through the substrate. An asymptotic analysis focuses on the precursor film and the transition region towards the bulk drop and a numerical continuation of steady drops determines their fully non-linear profiles. Following this, we study the time evolution of freely evaporating drops without influx for several initial drop shapes. As a result we find that drops initially spread if their initial contact angle is larger than the apparent contact angle of large steady evaporating drops with influx. Otherwise they recede right from the beginning

Non-Equilibrium Gibbs' Criterion for Completely Wetting Volatile Liquids

During the spreading of a liquid over a solid substrate, the contact line can stay pinned at sharp edges until the contact angle exceeds a critical value. At (or sufficiently near) equilibrium, this is known as Gibbs' criterion. Here, we show both experimentally and theoretically that for completely wetting volatile liquids there also exists a dynamically-produced critical angle for depinning, which increases with the evaporation rate. This suggests that one may introduce a simple modification of the Gibbs' criterion for (de)pinning, that accounts for the non-equilibrium effect of evaporation

Cоциокультурные и психологические факторы критики идеи права

The juridical structure involves the choice of a legal model formed by abstraction, or idealization, of the legislative project. The goal of this paper is to identify the cultural and psychological factors of the many-sided criticism of the idea of the rule of law, which is fundamental for constitutional state. Methodology: a concrete historical method was used to analyze the variety of criticism of the idea of the rule of law from Karl Marx to the present, excluding the concept of denial of law. Results: unlike criticism by Marx and Mannheim of law in terms of ideology, contemporary theorists criticize the idea of the rule of law from their own psychological and cultural positions such as ignoring the role of specific socio-cultural conditions that generate special legal norms and relations, is often exploited to position these norms and relations as natural and universal. In the opposite case, the existence of universal legal knowledge (epistemic relativism associated with the relativity of the existence of legal facts) and universally valid legal norms (moral and legal relativism associated with the relativity of the meanings of legal ideas, concepts and norms) is denied, since ideas and values always depend on the views of cognitive or moral subject. Conclusion: while modern law and society need multidimensional criticism from different perspectives, then the idea of the rule of law requires protection in the framework of the theory and philosophy of law.La construcción legal implica la elección de un modelo legal que se forma por abstracción, es decir, la idealización del proyecto legislativo. El observatorio de este estudio es identificar los factores culturales y psicológicos de la crítica versátil de la idea de la primacía de la ley, que es la base del estado de derecho. Metodología: con la ayuda del método específico e histórico, se analizaron las opciones para criticar la idea de la primacía de la ley desde Marx hasta la actualidad, excluyendo los conceptos de negación de ley. Resultados: a diferencia de la crítica de Marx y Mannheim de la ley desde el punto de vista de la ideología, el principal factor espiritual de la crítica de la ley en la sociedad moderna es ignorar el papel de las condiciones socioculturales específicas que generan normas y relaciones jurídicas especiales, lo que permite posicionar estas normas y relaciones como naturales y universales. En la opción opuesta se niega la existencia de un conocimiento jurídico universal (relativismo epistémico relacionado con la relativa de la existencia de hechos jurídicos) y normas jurídicas de carácter general (relativismo moral y jurídico relacionado con la relativa de los valores de las ideas, conceptos y normas jurídicas), ya que las ideas y valores siempre dependen del punto de vista del sujeto cognitivo o moral.Юридическая конструкция предполагает выбор правовой модели, которая формируется путем абстракции, то есть идеализации законодательного проекта. Цель данного исследования – выявить культурные и психологические факторы разносторонней критики идеи верховенства закона, являющейся основой правового государства. Методология: при помощи конкретно-исторического метода проанализированы варианты критики идеи верховенства закона от Карла Маркса до современности, исключая концепции отрицания права. Результаты: в отличие от критики Марксом и Мангеймом права с точки зрения идеологичности, основным духовным фактором критики права в современном обществе является игнорирование роли конкретных социокультурных условий, порождающих особые правовые нормы и отношения, которое позволяет позиционировать эти нормы и отношения как естественные и универсальные. В противоположном варианте отрицается существование универсального правового знания (эпистемический релятивизм, связанный с относительностью существования юридических фактов) и общезначимых правовых норм (морально-правовой релятивизм, связанный с относительностью значений правовых идей, понятий и норм), поскольку идеи и ценности всегда зависят от точки зрения познающего или морального субъекта. Вывод: если современное право и общество нуждаются в многомерной критике с различных позиций, то идея верховенства закона требует защиты в рамках теории и философии права

Linear stability analysis of an evaporating binary liquid layer with fully transient reference profiles

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