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By solving a long-wave evolution model numerically for power-law fluids, the authors aim to investigate the hydrodynamic and thermal characteristics of thermocapillary flow in an evaporating thin liquid film of pseudoplastic fluid.

The flow reversal attributed to the thermocapillary action is manifestly discernible through the streamline plots.

The thermocapillary strength is closely related to the viscosity of the fluid, besides its surface tension. The thermocapillary flow prevails in both Newtonian and pseudoplastic fluids at a large Marangoni number and the thermocapillary effect is more significant in the former. The overestimate in the Newtonian fluid is larger than that in the pseudoplastic fluid, owing to the shear-thinning characteristics of the latter.

This study provides insights into the essential attributes of the underlying flow characteristics in affecting the thermal behavior of thermocapillary convection in an evaporating thin liquid film of the shear-thinning fluids.

The present study aims to investigate the inverse-thermocapillary effect in an evaporating thin liquid film of self-rewetting fluid, which is a dilute aqueous solution (DAS) of long-chain alcohol.

A long-wave evolution model modified for self-rewetting fluids is used to study the inverse thermocapillary characteristics of an evaporating thin liquid film. The flow attributed to the inverse thermocapillary action is manifested through the streamline plots and the evaporative heat transfer characteristics are quantified and analyzed.

The thermocapillary flow induced by the negative surface tension gradient drives the liquid from a low-surface-tension (high temperature) region to a high-surface-tension (low temperature) region, retarding the liquid circulation and the evaporation strength. The positive surface tension gradients of self-rewetting fluids induce inverse-thermocapillary flow. The results of different working fluids, namely, water, heptanol and DAS of heptanol, are examined and compared. The thermocapillary characteristic of a working fluid is significantly affected by the sign of the surface tension gradient and the inverse effect is profound at a high excess temperature. The inverse thermocapillary effect significantly enhances evaporation rates.

The current investigation on the inverse thermocapillary effect in a self-rewetting evaporating thin film liquid has not been attempted previously. This study provides insights on the hydrodynamic and thermal characteristics of thermocapillary evaporation of self-rewetting liquid, which give rise to significant thermal enhancement of the microscale phase-change heat transfer devices.

There exist long-term fluctuations in the process of capital accumulation. The economic long wave is an essential part of research into non-mainstream western economics. After the Second World War, the capitalist world experienced the fourth long wave of expansion and then entered into a downward phase of the long wave in the 1970s. Regarding to whether a new long wave of expansion took place in the 1980s, left-wing scholars hold different viewpoints. The purpose of this paper is to focus on this issue.

First, based on the review of the long wave history, this paper discusses three kinds of long wave theories with significant influence and puts forward the theoretical framework of analyzing the long wave of capitalist economy. Next, under the guidance of this theoretical framework and in combination with the actual development and evolution of the capitalist economy, the issue of whether the fifth long wave of the capitalist economy began to emerge in the 1980s is discussed deeply.

This paper argues that, from the early 1980s to 2007, the US-dominated developed countries experienced a new long wave of expansion driven by the information technology revolution, the adjustment of the neoliberalism system and the economic globalization. However, the financial-economic crisis of 2008–2009 led to a new phase of long wave downswing.

This paper does not agree with the single-factor analysis of the intrinsic formation mechanism of economic long wave and sticks to the multi-factor analysis centering on the fluctuation of accumulation rate. It is pointed out that the evolution of the long wave of capitalist economy depends on the combined influence of technology, institutions and market. The study of the long wave of the economy will help us to correctly understand the historical stage and characteristics of the current world capitalist economy in the long-term fluctuations, so that we can make an appropriate and positive response.

In this paper, we consider the fundamental characteristics of motion in the universe in terms of the whole and local evolutionary forms of fluids, based on the theory of blown‐ups and the experiment of spinning disc of currents. It is pointed out that the practical meaning of “the invisible Tao”, see Lao Tsu for more details, is that of currents, and the central theory of fluid dynamics is the vortex flow dynamics, and the practicability of the nonlinear evolutions of mathematical models is getting away from the assumption of continuity.

While still arguing whether a quasi‐linear equation has a “stability” problem in integration, comparative analyses are made by numerical experimentations using conservation with smoothing and non‐conservation schemes as well as a time‐moving treatment scheme proposed by the first author respectively. The results show that the solution seeking method of the quasi‐linear model should not be considered as a “stability” problem. The traditional well‐posed computational model needs to be improved. The Lorenz’s “butterfly effect” should be in nature a Richardson’s explosive increase in time evolution of moving fluid.

The purpose of this paper is to obtain analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations by the homotopy analysis and the homotopy Padé methods.

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series.

The approximation solutions by [m,m] homotopy Padé technique is often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

In this paper, analytic solutions of the (1+1) and (2+1)‐dimensional dispersive long wave equations are obtained by the homotopy analysis and the homotopy Padé methods. The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] homotopy Padé technique are often independent of auxiliary parameter ℏ and this technique accelerates the convergence of the related series.

In this paper, mathematical properties of nonlinearity of the equations in Navier‐Stokes model of currents are studied based on the reasoning logic of systems evolutions, combined with methods of analysis and synthesis. It is discovered that the derivative terms are the same as the nonlinear forcing term, in that they all evolve with time and contain discontinuous reversing changes. Consequently, a theoretical and application system is proposed. The concept of blown‐ups constitutes a key step toward the understanding of whole evolution of non‐linear models. The range of applications of this concept is not only limited to research of almost 240‐years‐old mystery of the nonlinearity of currents, but also encompasses the reconsideration of many important principled issues in various theoretical disciplines and related applications.

This chapter enquires into the contribution of two British writers, Herbert Somerton Foxwell and Henry Riverdale Grenfell, who elaborated upon the hints provided by Jevons towards a description of long waves in the oscillations of prices. Writing two decades after Jevons, they witnessed the era of high prices turning into the great depression of the last quarter of the nineteenth century, the causes of which they saw in the end of bimetallism. Not only did they take up Jevons’s specific explanation of the long fluctuations, but they also based their discussion upon graphical representation of data and incorporated in their treatment a specific trait (the superposition principle) of the ‘waves’ metaphor emphasized by the Manchester statisticians in the 1850s and 1860s. Their contribution is also interesting for their understanding of crises versus depressions at the time of the emergence of the interpretation of oscillations as a cycle, which they have only partially grasped – as distinct from the approach of later long wave theorists.

Based on the summary and analysis of the particle dynamics, developed in the past 300 years, and of fundamental properties of unevenness of natural materials, we propose the opinion of the second stir. We analyze the gains and loses of employing the non‐dimensionalization method developed in the quantitative analysis system of the first push. Combined with some theoretical models, we also consider the epistemological failures of pure quantification, linearization, and formal logic analysis.

The purpose of this study is to use a weak light source with spatial distribution to realize light-driven fluid by adding high-absorbing nanoparticles to the droplets, thereby replacing a highly focused strong linear light source acting on pure droplets.

First, Fe₃O₄ nanoparticles with high light response characteristics were added to the droplets to prepare nanofluid droplets, and through the Gaussian light-driven flow experiment, the Marangoni effect inside a nanofluid droplet was studied, which can produce the surface tension gradient on the air/liquid interface and induce the vortex motion inside a droplet. Then, the numerical simulation method of multiphysics field coupling was used to study the effects of droplet height and Gaussian light distribution on the flow characteristics inside a droplet.

Nanoparticles can significantly enhance the light absorption, so that the Gaussian light is enough to drive the flow, and the formation of vortex can be regulated by light distribution. The multiphysics field coupling model can accurately describe this problem.

This study is helpful to understand the flow behavior and heat transfer phenomenon in optical microfluidic systems, and provides a feasible way to construct the rapid flow inside a tiny droplet by light.