REACTOR DYNAMICS Fronts Spontaneous Oscillations and Patterns :

Luss et al (1991) Above: mult. of homogeneous and front solutions in controlled wire Below: A back-and-forth travelling pulse

Left: A hot pulse rotating around Ni ring during H 2 oxidation Right: A travelling pulse during CO oxidation in a bed (feed from left; Hlavacek et al)

Spatiotemporal patterns in CO oxidation on Pd/GFC (Sheintuch et al, 2003)

CO oxidation over a disk (1.4 % CO;Tg= 225; Ts= º)

1 2 3

Figure 2: Propagating reaction waves on catalytic surfaces. (A) Temperature wave observed in CO oxidation on the surface of a supported Pd catalyst. The wave arises from coupling of the autocatalytic heat generation to heat conduction. (B) Spirals and target patterns in the isothermal NO reduction on Rh single crystal. The wave is arises from to coupling of the autocatalytic generation of empty

The Phenomenology of the Belousov-Zhabotinsky Reaction

Anodic oxidation of Nickel

Anodic oxidation of aluminum

Fig. 1Schematic drawing showing the difference between the morphogen gradient model and Turing model. (A) A morphogen molecule produced at one end of an embryo forms a gradient by diffusion. Cells “know” their position from the concentration of the molecule. The gradient is totally dependent on the prepattern of the morphogen source (boundary condition). (B) Adding a second morphogen produces a relatively complex pattern; but with no interactions between the morphogens, the system is not self- regulating. (C) With addition of the interactions between the morphogens, the system becomes self-regulating and can form a variety of patterns independent of the prepattern. [Art work by S. Miyazawa]

Fig. 2Schematic drawing showing the mathematical analysis of the RD system and the patterns generated by the simulation. (A) Six stable states toward which the two-factor RD system can converge. (B) Two-dimensional patterns generated by the Turing model. These patterns were made by an identical equation with slightly different parameter values. These simulations were calculated by the software provided as supporting online material. (C) Reproduction of biological patterns created by modified RD mechanisms. With modification, the RD mechanism can generate more complex patterns such as those seen in the real organism. Simulation images are courtesy of H. Meinhardt [sea shell pattern (5)] and A. R. Sandersen [fish pattern (13)]. Photos of actual seashells are from Bishougai-HP ( Images of popper fish are courtesy of Massimo Boyer (

Flow reversal operation  Direct heat exchange  The bed acts as regenerative heat exchanger  Accumulation of the heat generated  Simple design and small dimensions  High temperatures for low concentrations

ספיקה : 15 ליטר לדקה, ריכוז בכניסה : 0.5% תוצאות ניסוייות זרימה מחזורית – זרימה חד- כיוונית

Flow rate of 15 l/min and feed concentration of 0.5% Reverse-flow operation

Maximal temperature vs. Flow rate Simulation Experimental

Maximal temperature vs. Concentration Flow rate of 10 l/min

Inner-recirculation Flow rate of 5.7 l/min and feed concentration of 0.5% ToTo TnTn T n (Exp.) T o (Exp.)

Conclusions Reverse flow and inner recirculation operations exhibit higher temperatures than the once-through operation. No difference was seen between the homogeneous and heterogeneous models. Reverse flow operation is favorable at high flow rates, and inner-recirculation operation at low flow rates. Parameter analysis showed that heat transfer coefficient and bed conductivity affect the most.