Linde instability

Wassmuth et al. (1990) modelled this type of surface instabilities, denoted as Linde instability. The resulting hair needle-like flow pattern in the surface is shown in Fig. 3C.6. The condition of two dimensional continuity of flow is fulfilled in the surface. 

Reichenbach, J. and Linde, H., Linear perturbation analysis of surface-tension-driven convection at a plane interface (Marangoni instability), J. Colloid Interface Sci., 84, 433 143, 1981. Nepomnyashchy, A.A., Velarde, M.G., and Colinet, R, Interfacial Phenomena and Convection, CRC Press/Chapman Hall, London, 2002. 

Linde, H. et al.. Interfacial wave motions due to Marangoni instability. I. Traveling periodic wave trains in square and annular containers, J. Colloid Interface Sci., 188, 16-26, 1997. 

It is generally agreed that thermally induced vibrations of atoms in solids play a major role in melting [2.144]. The simple vibrational model of Linde-mann predicts a lattice instability when the root-mean-square amplitude of the thermal vibrations reaches a certain fraction / of the next neighbor distances. However, the Lindemann constant/varies considerably for different substances because lattice anharmonicity and soft modes are not considered, thus limiting the predictive power of such a law. Furthermore, Born proposed the collapse of the crystal lattice to occur when one of the effective elastic shear moduli vanishes [2.138], Experimentally, it is found instead that the shear modulus as a function of dilatation is not reduced to zero at Tm and would vanish at temperatures far above Tm for a wide range of different substances [2.145]... 

Firstly, several of the higher metallated compounds are inherently less stable than their monovalent counterparts, presumably because the accumulation of negative charge from the highly polar carbon-magnesium bond imparts instability to the molecule, so that the compound has to be handled at low temperature and/or converted as fast as possible. Secondly, even if the stability is suflt-eieni. derailments often occur during the preparation. and it may be tricky to lind the proper pathways anti conditions. However, the increasing number of such compounds testifies to the skill and perseverance of chemists and does make us optimistic lor the future. 

Linde, H., Schwartz, P. and Wilke, H., "Dynamics and Instability of Fluid Interfaces", Lecture Notes in Physics, 105, Springer, Berlin, (1979)... 

Example of autowaves of first-order roll-cells of Marangoni instability (left pictures) and of BZR (right pictures), a) concentric rings, b) spirals, according to Linde and co-workers... 

Another complicated interfacial dynamic instability is observed when the surfactant covers the liquid surface in a frame, for example on a Langmuir trough. If the surface is subjected to a shear stress either produced by a one-dimensional flow in the liquid bulk or by an air flow the surface instability observed looks like a hair-needle-like flow (Linde Shuleva 1970, Linde Friese 1971, Schwartz et al. 1985). 

Velarde, M. G., Rednikov, A. Ye., and Linde, H. (1999) Waves generated by surface tension gradients and Instability, in Fluid Dynamics at Interfaces, edited by W. Shyy, University Press, Cambridge, 43-56. 

H. Linde, in Convective Transport and Instability Phenomena, (J. Zierep and H. Oertel,... 

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