THEORY OF VISCOUS BUCKLING AND GRAVITY INSTABILITY OF MULTILAYERS WITH LARGE DEFORMATION
An exact treatment of the stability of multilayered viscous fluids in slow motion with large deformations leads to an analog model which includes the effect of gravity. A distinction can be made between true mechanical instability and an apparent instability of purely kinematic nature. A mechanism for concentric folding is derived, leading to predictions in good agreement with experimental results (De Sitter, 1939). Exact equations are obtained for the time history of viscous buckling of multilayered fluids for small deflections superimposed upon a large variable compressible strain. A numerical application to the single embedded layer checks the practical validity of the simplified thin-layer theory with interfacial slip. For gravity instability, the analog model provides a method of analysis applicable to very large deformations in salt structures.
ON THE FOLDING OF A VISCOELASTIC MEDIUM WITH ADHERING LAYER UNDER COMPRESSIVE INITIAL STRESS
The exact solution is given for the folding by compression of a visco- elastic layer embedded in a viscoelastic medium, under the assumption that there is perfect adherence between layer and medium. This solution agrees closely with the earlier result obtained by Biot which was based on the assumption that layer and medium could slip over each other. In a previous publication, Biot (l) has discussed the case of folding a layered visco- elastic medium under initial stress. An exact solution was presented for the folding, due to instability, of a viscoelastic layer of thickness h embedded in a viscoelastic medium extending infinitely far in both directions perpendicular to the layer; the assumption was made that layer and medium did not adhere and could slip over one another as if perfectly lubricated. An approximate solution for the case of perfect adherence was developed in a second publication of the same year by Biot (2). The influence of the adherence was found to be small. The purpose of this note is to check this conclusion by an exact solution for the case when perfect adherence exists between layer and medium. The method is the same as that in Ref. (l) and it combines two distinct developments contained in earlier work by the same author. One of these developments is the theory of elasticity of a medium under initial stress (1934-1941). The other was introduced as a correspondence principle (1954-56) by which elastic moduli are replaced by corre- sponding operators (3, 4, 51. Results are therefore applicable to either elastic or visco- elastic media of a very general nature. It was shown at the same time that the corre- spondence extends to problems which involve anisotropy, dynamics, wave propagation, and variational procedures. The mathematical restrictions on the operators were also derived from thermodynamics (3). The horizontal and vertical displacements u and v, in the layer representing the departure of the displacement from an initial steady state, satisfy the equations
Evaluation of CuAl2O4 as an Oxygen Carrier in Chemical-Looping Combustion
The chemical-looping combustion (CLC) process is a novel solution for efficient combustion with intrinsic separation of carbon dioxide. The process uses a metal oxide as an oxygen carrier to transfer oxygen from an air to a fuel reactor where the fuel, or gasification products of the fuel, reacts with the solid oxygen carrier. In this work, copper(II) aluminate (CuAl2O4) was assessed as a potential oxygen carrier using methane as fuel. The carrier particles were produced by freeze–granulation and calcined at 1050 °C for a duration of 6 h. The chemical-looping characteristics were evaluated in a laboratory-scale fluidized-bed reactor in the temperature range of 900–950 °C during 45 alternating redox cycles. The oxygen carrier exhibited reproducible and stable reactivity behavior in this temperature range. Neither agglomeration nor defluidization was noticed in any of the cycles carried out at 900–925 °C. However, after reactivity tests at 950 °C, soft agglomeration and particle fragmentation were observed. Systematic phase analysis of the Cu–Al–O system during the redox cycle was carried out as a function of duration of reduction and oxygen concentration during the oxidation period. It was found that the CuAl2O4 is reduced to copper(I) aluminate (CuAlO2; delafossite), Cu2O, and elemental Cu. The CuAlO2 phase is characterized by slow kinetics for oxidation into CuO and CuAl2O4. Despite this kinetic limitation, complete conversion of methane with reproducible reactivity of the oxygen carrier is achieved. Thus, CuAl2O4 could be a potential oxygen carrier for chemical-looping combustion.