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11.
Karin Schwarzenberger Thomas Köllner Hartmut Linde Thomas Boeck Stefan Odenbach Kerstin Eckert 《Advances in colloid and interface science》2014
According to the seminal theory by Sternling and Scriven [1], solutal Marangoni convection during mass transfer of surface-active solutes may occur as either oscillatory or stationary instability. With strong support of Manuel G. Velarde, a combined initiative of experimental works, in particular to mention those of Linde, Wierschem and coworkers, and theory has enabled a classification of dominant wave types of the oscillatory mode and their interactions. In this way a rather comprehensive understanding of the nonlinear evolution of the oscillatory instability could be achieved. A comparably advanced state-of-the-art with respect to the stationary counterpart seemed to be out of reach a short time ago. Recent developments on both the numerical and experimental side, in combination with assessing an extensive number of older experiments, now allow one to draw a more unified picture. By reviewing these works, we show that three main building blocks exist during the nonlinear evolution: roll cells, relaxation oscillations and relaxation oscillations waves. What is frequently called interfacial turbulence results from the interaction between these partly coexisting basic patterns which may additionally occur in different hierarchy levels. The second focus of this review lies on the practical importance of such convection patterns concerning their influence on mass transfer characteristics. Particular attention is paid here to the interaction between Marangoni and buoyancy effects which frequently complicates the pattern formation even more. To shed more light on these dependencies, new simulations regarding the limiting case of stabilizing density stratification and vanishing buoyancy are incorporated. 相似文献
12.
Karin Schwarzenberger Thomas Köllner Hartmut Linde Stefan Odenbach Thomas Boeck Kerstin Eckert 《The European physical journal. Special topics》2013,219(1):121-130
We study characteristic convection patterns emerging during the mass transfer of acetic acid from a glycerol-water layer to a superposed acetone layer by means of experiments and numerical simulations. The patterns form as a result of the stationary Marangoni instability. The initial phase of the pattern evolution is studied using high-resolution simulations. They show hierarchically ordered cellular structures which closely resemble experimental observations. In the later stages presently accessible to the experiments, the cells are locally replaced by relaxation oscillation waves. The emergence of these structures is favored when the experiment is performed in narrow cuvettes. 相似文献
13.
In this paper we consider bounded operators on infinite graphs, in particular Cayley graphs of amenable groups. The operators
satisfy an equivariance condition which is formulated in terms of a colouring of the vertex set of the underlying graph. In
this setting it is natural to expect that the integrated density of states (IDS), or spectral distribution function, exists.
We show that it can be defined as the uniform limit of approximants associated to finite matrices. The proof is based on a
Banach space valued ergodic theorem which even allows explicit convergence estimates. Our result applies to a variety of group
structures and colouring types, in particular to periodic operators and percolation-type Hamiltonians. 相似文献