Oscillation theory

Applied Catalysis A: General 294 (2005) 22–33 www.elsevier.com/locate/apcata

Oscillation theory Part 4. Some dynamic peculiarities of motion in catalyst pores Leonid B. Datsevich * LS CVT, University of Bayreuth, Universitaetsstr. 30, D-95447 Bayreuth, Germany Received 18 March 2005; received in revised form 18 May 2005; accepted 2 June 2005 Available online 30 August 2005

Abstract The present paper continues the series of articles devoted to the oscillatory behaviour in gas–liquid/liquid reactions on a porous catalyst. Based on the theoretical predictions given earlier, some phenomena (e.g. pressure pulsations in pores caused by the liquid oscillations, leading in some cases to the catalyst destruction) and some approaches to the reaction enhancement (e.g. the preparation of special pores leading to the liquid pumping through the catalyst particle in the demanded direction) are discussed in detail. Several deductive, illustrative experiments demonstrating the oscillatory behaviour and some possible investigation methods have been described. # 2005 Elsevier B.V. All rights reserved. Keywords: Multiphase catalysis; Oscillation model; Catalyst engineering; Pore optimisation; Liquid pumping; Cavitation; Catalyst destruction; Sound spectrum; Reacting boiling

1. Introduction A theoretical analysis of multiphase reactions on a porous catalyst with gas and/or heat evolution given in [1–3] has shown that the conventional Thiele/Zeldovich model [4,5] is not always appropriate for the description of such processes since under some conditions, the oscillatory motion of liquid can occur in pores of a catalyst particle. The occurrence of such behaviour is dependent on the criterion number Dapore (Eqs. (1) and (2)) that is equal to the ratio of the rate of heat (or gas) generation in the pore to the maximum possible rate of the heat (or gas) removal by molecular heat conductivity (or molecular diffusion) Dapore;heat ¼

Dapore;gas ¼

rvapor rvapor ðDHÞ Qgenerated ¼ y2pore rs lliquid sTM Qremoved max Qreaction Qdiffusion max

¼ y2pore rs

nRT DDl sH

(1)

(2)

Oscillations of liquid will take place in catalyst pores if Dapore > 1. * Tel.: +49 921 55 74 32/+49 1511 161 4019; fax: +49 921 55 74 35. E-mail addresses: [email protected], [email protected]. 0926-860X/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apcata.2005.06.024

The cause of the oscillations is the appearance of gas– vapor (or gas) bubbles inside the pores due to the failure of the conventional molecular mechanism (thermo conductivity and diffusion) to remove the produced heat (or gas) from the pore. When the bubble appears, it starts pushing the liquid out of the pore. On the part of the pore occupied by the bubble, the reaction ceases, and because of the dissipation processes, the pressure inside the bubble becomes equal to the initial value (the pressure in the reactor) so that a new portion of liquid with saturated gas comes into the pore again, driven by the capillary effect and the process of the bubble formation repeats. Oscillatory behaviour can be discovered in many industrial and special applications such as these: (i) Reactions with gas production: decomposition of H2O2, hydrazine and its derivatives; destruction of furfurol and derived compounds; preparation of Ni–Raney catalyst (the leaching of Al by NaOH in H2O); dissolution of some sparking and bubbling medicines in water (e.g. aspirin tablets). (ii) Reactions with heat production: hydrogenation of unsaturated compounds such as nitrocompounds, aldehydes, ketones and olefins, as well as other exothermic reactions.

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Nomenclature concentration of hydrogen peroxide (mol/m3) diameter of the catalyst particle (m) diameter of the catalyst pore (m) diameter of the bubble leaving the pore mouth (m) Da criterion number based on y (see [1–3]) Dapore criterion number Da related to the reaction with gas or heat production and based on ypore Dapore,gas criterion number Da related to the reaction with gas production and based on ypore Dapore,heat criterion number Da related to the reaction with heat production and based on ypore DDl diffusion coefficient of the gas compound in the liquid phase (m2/s) f frequency (Hz) FArchim buoyancy force defined by the Archimedean principle (N) F Stock drag force defined by Stock’s law (N) F tension surface tension force holding the bubble in the pore mouth (N) g acceleration due to gravity (m/s2) H Henry coefficient DH heat of the reaction (J/mol) M molar mass of the evaporated compound (kg/ mol) Dpcapillary capillary pressure (N/m2) Pbubble pressure inside the bubble (N/m2) Pgas partial pressure of gas (N/m2) Pmax maximum possible pressure inside the pore (Pmax = Pbubble) (N/m2) PO 2 partial pressure of generated oxygen (N/m2) Ppore pressure inside the pore (N/m2) Preactor pressure in the system (N/m2) Pvapor partial pressure of vapor (N/m2) Qdiffusion max maximal possible diffusion flux through pore (mol/s) Qgenerated heat generated in the pore per unit time (W) Qreaction molar rate of gas formation (mol/s) Qremoved max maximal possible heat removed from the pore per unit time (W) rs reaction rate related to pore surface (mol/ (m2 s)) rvapor heat of vaporization per mol (J/mol) R gas constant (8.314 J/(mol K)) T current temperature in the pore (K) DT temperature difference (K) Ts temperature on outer surface of the particle (K) Udisplace velocity of displacement motion (m/s) Ufill velocity of filling motion (m/s) ¯ flow U mean velocity of the surrounding flow passing over the pore mouth (m/s) CH2 O2 dparticle dpore D

y ycr ydisplace ypore

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lengthofporefromoutersurfacetothecentre(m) length of pore at which oscillation appears (m) distance of displacement (m) length of the pore (m)

Greek letters lliquid thermal conductivity of liquid (W/(m K)) m viscosity of liquid (N s/m2) n stoichiometric coefficient in the reaction with gas production A (liquid) ! B (liquid) + nD (gas) (e.g. H2O2 decomposition) Dr density difference between liquid and gas (kg/ m3) rliquid density of liquid (kg/m3) s liquid surface tension (N/m) t current time (s) tp tortuosity factor of catalyst

Some reactions can be considered as the simultaneous processes with both gas and heat production, for instance, hydrogenation of furfurol, as well as almost all the reactions listed in (i) at high concentrations of the reacting compounds. Some major consequences that have been predicted by the oscillation model and partly approved experimentally are given in Table 1. It is necessary to point out that the conventional theories and models are not suitable for all the enumerated phenomena and fail to forecast them. Despite the fact that the theory definitely postulates the existence of the oscillatory mechanism and that some consequences predicted by the oscillation model have already been proved experimentally [6,7,10,12], similar questions are often posed in discussions: Do the oscillations in catalyst particles really exist? Is the oscillatory behaviour possibly only the fruit of the cunning calculations? In this paper, some experiments demonstrating the distinctive oscillatory behaviour are described. As an admirable show underlining some extreme features of the oscillatory performance, the experiment, in the course of which the catalyst particle is destroyed, is presented. The harmonic analysis of ‘‘voices’’ of different catalyst particles is considered as a possible tool for the investigation of some reactions under oscillations. In addition to [12] where the unsophisticated modification of the pore structure results in the process intensification, in the present paper the design of the special pores inducing the motion of liquid in the demanded direction is theoretically considered.

2. Qualitative description of the elementary steps of an oscillation A bubble consisting of gas (reactions with gas production) or of gas and vapor (exothermic reactions) must appear

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Table 1 Major features and consequences predicted by the oscillation model NN

Consequences coming from the oscillation model

Short description

References and comments

1

Alternating motion of liquid in pores

[1–3]

2

Absolutely different macrokinetic dependence in comparison to the Thiele/Zeldovich model

3

The distinct temperature difference between the centre of the catalyst particle and its surface in exothermic reactions Initial loss of catalyst activity in reactions with non-evaporated substances (often encountered in hydrogenation of some nitrocompounds) Significant enhancement of effective internal mass transfer in the oscillating part of the catalyst pore

The oscillatory motion of liquid can be characterized by extremely high velocities up to 10–100 m/s with frequencies more than 1 Hz The physicochemical parameters such as liquid surface tension, specific heat of vaporization, etc. have an impact on the reaction rate, resulting in other macrokinetic dependences The temperature difference can be tremendously higher than the difference evaluated by the Thiele/Zeldovich model The initial loss of catalyst activity may be explained by the deposition of non-evaporated species dissolved in liquid on the pore wall during the bubble presence, which results in deactivation of this part of the pore The oscillatory behaviour results in more than a 30-fold increase of the internal effective mass transfer coefficient compared to molecular effective diffusion There is an extremely intensive mass exchange between the particle environment and the pores More than a 10-fold increase of external mass transfer in comparison to the values evaluated by the conventional mass transfer correlations is observed in reactors. (Note: As supposed in the conventional mass transfer correlations, only the hydrodynamic parameters influence mass transfer coefficients. According to the oscillation model, the disturbances induced by oscillations can have an overwhelming impact on external mass transfer compared to ‘‘disturbances’’ caused by the flow around the particle.) In the ideal catalyst particle, which can be thought of as a structure consisting of the parallel pores, two zones inside can exist: the zone near the catalyst shell where the oscillations mainly take place, and the stagnation zone into which the oscillations do not penetrate The oscillation model shows that the oscillation phenomenon can occur easier if a solvent has less surface tension or a critical temperature closer to the temperature in the reactor Oscillatory behaviour can be initiated by heat generation in the particle by means of electrical disturbance (e.g. an electrical current or electromagnetic field) The development of bubbles inside the pores and, as a result, an increase in internal mass transfer can be provided by the pressure modulation in the reactor By changing the ratio between large (macro) and small (micro) pores oscillations can be intensified resulting in an increase in the reaction rate The pressure inside the single pore Ppore (especially if ydisplace > ycr) varies at least in the range Preactor  Dpcapillary < Ppore < Preactor + Dpcapillary The diapason of the pressure pulsation should be still higher if the dynamic characteristics of liquid flow with velocities of 10–100 m/s are taken into account

5

6

Significant enhancement of external mass transfer

7

Possible existence of two zones inside the catalyst particle

8

Intensification of the process by choice of an appropriate solvent

9

Intensification of the process by heat or pressure modulationa

10

Process enhancement by modification of the pore structure Pressure pulsation inside the particle

11

[6] [2]

[1–3]

[1–3,8,9]; external mass transfer in the reaction of H2O2 decomposition and in some hydrogenation reactions has been studied in [10,11] in detail; analogy between the nucleate boiling theory and the oscillation theory in the light of external mass transfer is given in [1]

[1]; probably, such behaviour can also be encountered in real catalysts where there should be zones with different frequencies of oscillations and even stagnation zones [1–3]

[1]

[12] Discussed in the present paper

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[1–3]; more details in the future publications

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a

Possibility of ‘‘liquid pumping’’ between different pores. Creation of specially designed pores in order to make the liquid move in the demanded direction Sound generation 14

The possibility of the process intensification by pressure pulsation in the reactor was considered by several excellent research groups [13–17] long before the oscillation model was developed.

Discussed in the present paper

Process intensification by some additives (if chemistry and economics permit the use of such substances) 13

The formation of the bubbles inside the pores should be accompanied by sound generation that can be recorded and analyzed

Discussed in the present paper

[1,2]

Destruction of the particle 12

The destruction of the catalyst particle can be observed in some reacting systems. The phenomenon is caused by strong pressure pulsations resulting apparently in cavitations inside the pores If a reaction on the porous catalyst has no oscillations, the process of oscillations can be induced if certain reagents are added in the reaction mixture so that heat or gas is produced resulting in the oscillatory motion in pores There is a possibility of creating such a pore structure that the despotic, forced pumping of the liquid through the catalyst particle can be organized

Discussed in the present paper

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Fig. 1. Representation of the major oscillation steps in the ideal pore (see [1–3]). (a) At the beginning, the pore is empty and then is filled with the liquid from the particle surroundings. The pressure in the pore is equal to Preactor. (b) The new bubble at the distance of the oscillation penetration ycr begins to grow because of the transition of the oversaturated vapor and/or gas from the liquid alongside the bubble. (In reality, the micropores branching off the macropore also contribute vapor and/or gas to the bubble just born.) The pressure in the nucleus is Pbubble = Preactor + Dpcapillary. (c) The growing bubble’s complete displacement of the liquid out of the pore can be ‘‘observed’’ on the catalyst surface. (The form of the real bubble outside the pore does not look like that shown here and is defined by the flow around the particle (see Fig. 6b).) When the outer part of the bubble is swept away by the surrounding flow, at every instance, the pressure in the pore returns to the initial value Preactor.

in the pore at the distance from the pore mouth equal to ycr (Fig. 1b) if Dapore > 1 [1–3]. As a result of the gas and/or vapor oversaturation, this new bubble starts growing, pushing the liquid out of the pore. There are two possible mechanisms of the liquid displacement out of the single pore: Either the liquid cannot entirely be expelled by the growing bubble, or the growing bubble can completely displace the liquid out of the part of the pore (see Fig. 1c). All stages of the oscillatory motion and estimations of their temporary characteristics are analyzed in [1–3]. For the

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following consideration, let us regard the case when the liquid is totally displaced out of the pore fragment and the part of the bubble which has just appeared in the pore mouth is swept away by the surrounding flow, so that the pressure in the pore occupied by the rest of the bubble becomes equal to the pressure in the reactor at that very instant when the outer part of the bubble is torn away by the flow. Fig. 1 shows the major stages of an oscillation in the single pore in the case when the liquid is completely expelled out of the pore. Fig. 1a represents the process of pore filling when the particle that is initially empty is then submerged in the liquid. The same situation can be observed when the growing bubble has pushed the liquid out of the pore, so that the outer part of this bubble is then washed off by the surrounding flow or is driven off by the Archimedean force. Since the pressure inside the pore at that every moment becomes equal to the pressure in the reactor, the liquid begins to occupy the pore under the capillary force, filling it during a very short time, 106 to 102 s at velocities of about 10 m/s or more [1–3]. Because the time of pore filling is far less than the characteristic time of the reaction, the concentrations of both the reacting compounds and the saturated gas are equal to those in the surrounding flow at the first moment, so that the reaction rate related to the pore surface is the same throughout the whole pore length. The schematic development of pressure before the appearance of the bubble in the pore is shown in Figs. 2 and 3. The bubble embryo at the distance ycr appears at the time t6, since the pressure becomes equal to the maximum possible pressure that can ever be achieved in the pore Pbubble ¼ Preactor þ D pcapillary

(3)

That happens because either the generated gas in reactions with gas production cannot be removed by molecular diffusion or the temperature gradient in exothermic reactions cannot be smoothed by molecular thermo conductivity. (Note: The process of the bubble nucleation in exothermic reactions and in reactions with gas production has the same physical features. The gas (reactions with gas production) or gas–vapor (exothermic reactions) nuclei come into existence when the total pressure of the saturated gas and generated vapor exceeds the maximum possible pressure in the pore. In opposition to the reaction with gas production, where the source of the oversaturated gas is the reaction itself, in the exothermic reactions, the source of the ‘‘oversaturated gas and vapor’’ is an increase in temperature.) The transition of the ‘‘oversaturated gas and/or vapor’’ from the surrounding liquid into the bubble leads to its growth and, as a result, to the displacement of the liquid out of the pore (Fig. 1b and c). If the distance of the liquid displacement ydisplace is more than the distance of oscillation penetration ycr, the bubbles appearing in the pore mouths should be observed on the outer surface of the catalyst particle.

Fig. 2. Reaction with gas production: hydrogen peroxide decomposition. Concentration profile of H2O2 and pressure inside the pore just after the pore filling, and before the bubble starts displacing the liquid out of the pore. The maximum possible pressure in the pore corresponds to the pressure in the bubble (the pressure in the reactor plus the capillary pressure 4s/dpore) (see [3]).

In the real catalyst particle, the oscillatory mechanism is much more complex than can be imagined. The porous structure, consisting of pores differing in diameters and branching off one another, induces extremely chaotic behaviour that cannot be modelled by the exact deterministic equations because there is a very strong mutual interaction between pores: therefore, it is impossible to formulate and then to resolve all equations for the whole assembly of the pores. Nevertheless, the qualitative analysis of the oscillatory processes can be considered a helpful tool for practical use in order to understand the phenomenon, to develop catalysts, and to intensify processes.

3. Visualisation and simulation of oscillations 3.1. Reactions with gas production As discussed in [1–3] and in the previous section, if the displacement distance ydisplace is more than the distance of oscillation penetration ycr, the appearance of the bubbles should be observed on the outer surface of the catalyst particle in the pore mouths (see Fig. 1c). The size of the bubble and the duration of its ‘‘life’’ in the pore mouth depend on the flow velocity around the particle. The higher

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Fig. 4. Film frame from Movie 1 [18]. Reaction of hydrogen peroxide decomposition on a Ni catalyst (30% H2O2, catalyst: NISAT 6 mm  6 mm, Su¨ d-Chemie). Small bubbles can be seen around the particle. The ‘‘mist’’ of small bubbles torn off from the catalyst surface can also be observed over the particle. The movie distinctly shows the bubbles periodically appearing in pores. Fig. 3. Reaction with heat production. Temperature and pressure profiles just after the pore filling, and before the bubble starts displacing the liquid out the pore. The maximum possible pressure in the pore corresponds to the pressure in the bubble (the pressure in the reactor plus the capillary pressure 4s/dpore) (see [1,2]).

the velocity of the liquid, the smaller the bubble and the less the time during which the bubble remains attached to the pore mouth (see Appendix A). In real processes, the velocities of the liquid flow around the particle and the pressure are comparatively high, so they hinder the observation of bubbles on the outer surface of the catalyst. Nevertheless, there are some reactions that allow the oscillatory performance to be beheld by the naked eye without any devices. Hydrogen peroxide decomposition can be chosen as the best example for demonstrative purposes, because the reaction can be carried out under room temperature and atmospheric pressure in a simple laboratory glass. (It is necessary to emphasize that the same mechanism of oscillations can be observed and demonstrated by other very simple reactions, during which the gaseous products are formed in the porous medium: the leaching of Al from Ni–Al alloy by a NaOH solution in preparation of Ni–Raney catalyst (H2 formation) and CO2 production during the solution of some sparkling medicines and vitamin tablets in water (e.g. aspirin produced by Bayer AG). Despite the fact that these reactions do not exactly represent traditional catalytic processes, they have the same features of the

oscillatory phenomenon: the production of a gaseous compound in pores.) In Fig. 4, a film frame taken from the supplementary Movie 1 [18] is presented. In the movie and in Fig. 4, the small bubbles appearing periodically can be observed in the mouths of such pores in which ydisplace > ycr. However, if the velocity of liquid around the particle is increased, it will be impossible to register the bubbles without special instruments, because their size will become considerably less and the time of the bubble existence will be very short. 3.2. Exothermic reactions To observe by the naked eye the appearance of bubbles in the pore mouths in exothermic reactions (e.g. in hydrogenation reactions) is rather a difficult task because high pressure handicaps any surveillance inside the reactor. For didactic purposes, nevertheless, the oscillatory behaviour similar to that in exothermic reactions can be simulated with the help of a very simple device presented in Fig. 5. It consists of two reservoirs filled with water and connected to each other by a capillary. (Note: The water that is used in experiments is always saturated with air so that the partial pressure of air Pgas in the water corresponds to the atmospheric pressure (1 bar).) By means of an electric current running through the capillary, heat is produced, increasing the partial pressure of water vapor. The gas–vapor bubble does not appear in the

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Fig. 5. Simulation of exothermic reactions. (a) A schematic representation of the simulating device. (b) A film frame from Movie 2 [19], ‘‘Simulation of the oscillatory behaviour in a capillary by electrical current’’. The bubble that has just appeared can be seen in the circle.

capillary until the sum of the partial pressure of saturated air Pgas (1 bar) and water vapor Pvapor is less than the maximum possible pressure Pbubble for this capillary (see Eq. (3)). In order that the total pressure Pgas + Pvapor can exceed the maximum pressure Pbubble, the increment of the vapor pressure in the device should have comparatively small values (e.g. for the capillary of 0.5 mm, it is equal to 5.0  103 bar). It is notable that such an increase in the partial pressure of water vapor is produced by an insignificant temperature increase DT (e.g. for 0.5 mm, DT 0.1 8C). Thus, if the total pressure of the saturated air and water vapor becomes equal to the maximum possible pressure for this capillary, the bubble consisting of air and water vapor comes into existence, displacing part of the liquid out of the capillary. In the wake of the bubble in the capillary, there is no further heat production, and because of the heat dissipation, the pressure inside the bubble returns to the initial value Pgas. The new portion of the water with the saturated air comes into the capillary again and, therefore, the process of the oscillation repeats (see the supplementary Movie 2 [19]). In exothermic reactions, the same processes take place in the catalyst pores filled initially with a reacting mixture

and saturated gas. In the course of the reaction, there is heat evolution and an appearance of the bubble. On the part of the pore where the bubble is located, the reaction ceases: there is no further heat production. As a result of the heat dispersion (ydisplace < ycr) or the removal of the part of the bubble from the pore mouth by the flow around the particle (ydisplace > ycr), the pressure inside the bubble recurs to the initial value: the pressure in the reactor, and the new portion of the reacting mixture with the saturated gas comes into the pore again, repeating the oscillations. As shown in [1,2] (see also Eq. (1)), the characteristics of the oscillations depend on the rate of heat production (reaction rate) and on the physical properties of liquid. By changing both the rate of heat evolution and the liquid properties, it is possible to control the oscillations in pores. The experiments that can be carried out in the simulating device can show how temporal characteristics and the intensity of oscillations can be ruled by heat production or by liquid surface tension. (The rate of heat production can be controlled by the current strength (addition of NaCl) or voltage. The water surface tension can be changed by addition of a surface active agent, e.g. a wash additive. It is recommended that NaCl be added if the water conductivity is not sufficient to demonstrate the experiment.) Because the main point is didactic, the author does not include a detailed description of all simulation experiments. By means of a very simple device, we have the possibility of demonstrating oscillatory behaviour and understanding some fundamental issues. It is noteworthy that recently worked out NMR methods [20] allow the visualisation of oscillations in the catalyst particle in the course of an exothermic reaction. Despite the fact that in these experiments the image acquisition time (34 s) is much more than the characteristic time of oscillations (less 1 s), the NMR images reveal the oscillatory behaviour predicted exactly by the oscillation theory [1,2,21] long before it occurs.

4. Pressure pulsation and cavitation effects in catalyst pores According to the conventional theories, if the pore is wetted with liquid, there are only two possible values of the pressure inside it. If the pore is completely occupied by the single phase gas or liquid, the pressure inside the pore is equal to the pressure outside in the reactor. If the pore is partly occupied by liquid so that inside the pore there are bubbles, the pressure inside the bubbles is more than the pressure in the reactor because of the capillary pressure. In compliance with the oscillation model, the pressure in pores Ppore should vary at least in the diapason Preactor  D pcapillary < Ppore < Preactor þ D pcapillary

(4)

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of liquid or at the rapid movement of impeller blades [22,23]. The theoretical analysis given in [1–3] shows that the processes of the liquid displacement and the pore filling can be characterized by a very small time about 105 s, and by velocities of magnitude 10 m/s or more. We can expect that the dynamics of such violent motions of liquid should generate much higher pressure variation some kind of hydraulic impact. As is well known, the cavitation in many technical applications can lead to the destruction of materials caused by very powerful forces during the birth of the bubble and then its collapse. The direct experiment during which the catalyst particle is destroyed in the course of the reaction proves the hypothesis about the possible cavitations in the catalyst pores. In Movie 3 [24] (several film frames are presented in Fig. 7), we can see and hear how mightily the catalyst particle can be crashed.

5. Sound generation in reactions with oscillations

Fig. 6. Variation of pressure in the pore in the course of the oscillation. (a) The pressure distribution as the bubble is situated inside the pore. (b) The pressure inside the bubble before the outer part of the bubble leaves the pore mouth. (c) The pressure distribution just as the bubble is torn off. The meniscus stretches the rest of the liquid, decreasing the pressure in it.

The character of the pressure variation is explained in Fig. 6. As the bubble created during the reaction is inside the pore, the pressure in the bubble is by Dpcapillary more than the pressure in the liquid alongside it (Fig. 6a and b). However, if the displacement distance is more than the distance of oscillation penetration ydisplace > ycr, then just as the bubble leaves the pore mouth, the pressure in the rest of the liquid becomes by Dpcapillary less than the pressure in the reactor, because the meniscus stretches this residual liquid (Fig. 6c). Such a liquid extension can result in the appearance of the gas (or gas–vapor) bubbles because of the far less pressure. It is worth pointing out that such behaviour has similar features to the well-known physical phenomenon of cavitation: the creation of bubbles due to the ‘‘elongation’’ of liquid, e.g. during the suction

The formation and disappearance of the gaseous phase in liquid should be accompanied by the sound generation [25]. The nature of the noise is a fluctuation of pressure connected with oscillations, during which the bubbles appear and move in pores, leaving the catalyst surface if ydisplace > ycr. The sound generated in the course of the reaction can be considered some kind of acoustic signature bearing the identity inherent in the oscillation process. With the help of the experimental setup shown in Fig. 8, ‘‘voices’’ of different catalysts have been recorded in the reaction of 30% hydrogen peroxide decomposition. The sound produced by the catalyst particle is directed to a microphone through the plastic tube. The sound waves are detected by the microphone and recorded electronically in a personal computer. (The spot of the sound pickup should be situated under the catalyst particle in order to avoid the noises that can be generated by the gas bubbles passing or coming into the microphone tube. The liquid level should be high enough to prevent the recording of the strange sounds derived from bubble outbursts on the liquid surface.) In Fig. 9, the harmonic analyses of several catalyst particles made by Spectrum Lab [26] are given. One of the catalysts ‘‘voices’’ is available online [27]. Regarding the spectrums, the following conclusions can be made: (i) as expected [1–3,6,12], the oscillatory performance has the distinctive features of chaotic behaviour. There are no dominant harmonics. (ii) Each catalyst particle has its own inimitable ‘‘speech pattern’’. (iii) The ‘‘speech pattern’’ depends not only on the catalyst material, but also on the pore structure. We can see that the NISAT particle after the pore modification (see [12]) has another spectrum because of a new network of macropores created on the particle shell. We can notice a change in harmonics and, in the case of the modified particle, even an

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Fig. 7. Destruction of the catalyst particle due to cavitations caused by oscillations. Film frames from Movie 3, ‘‘Destruction of a catalyst particle in the reaction of hydrogen peroxide decomposition’’ [24]; 30% H2O2, catalyst: NISAT 1.5 mm Extr.RS, Su¨ d-Chemie.

exhaustion of some of them. (The change in a sound spectrum is also an additional proof that the reaction enhancement in [12] is a result of the more intense oscillations.) The experiments described above can be considered not only a didactic illustration of oscillations, but as a possible tool for investigation of oscillatory phenomenon: however, it should be taken into account that many reactions are

Fig. 8. The experimental setup for sound recording. Hydrogen peroxide decomposition (30% H2O2, catalyst: NISAT 6 mm  6 mm). (1) Microphone; (2) tube; (3) catalyst particle.

carried out under conditions of intense stirring and liquid– gas flowing, so that detecting and distinguishing noises generated by oscillations can be an extremely difficult task.

Fig. 9. Sound spectrums of several catalysts.

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Fig. 10. Scenarios of oscillations in two pores of different diameters situated near each other. (a) Direction of the heat and concentration (arrow) dissipation: from the small pore to the large one. In exothermic reactions, dissipation also runs through the solid structure. (b) Liquid fluxes (arrows) during the displacement motion in the large pore.

6. Catalyst engineering: is it possible to pump the liquid inside the particle in the demanded direction? Since catalysts have extremely complex pore structures, the deterministic description of all processes in pores is not possible. This conclusion can be illustrated by two pores situated near each other (Fig. 10a). Despite the fact that for both pores Dapore > 1, the oscillations in pore 1 can have a very weak feature or cannot happen at all. The explanation of such behaviour is in the dissipation processes directed from the smaller pore to the larger one, evening out the difference in the gas concentration (reactions with gas production) or the difference in the temperature (exothermic reactions). More specifically, because of the capillary pressure Dpcapillary = 4s/dpore, the pressure inside the smaller bubble and, as a consequence, the concentration of the generated gas (reactions with gas production) are higher than in the larger one. As a result of the diffusion flux from bubble 1 to bubble 2 through the network of fine pores (see Fig. 10a), the smaller bubble becomes less and less, while the larger one increases in size. In exothermic reactions, the higher pressure in the smaller bubble is provided by the excessive temperature. The heat flux from this pore to the larger one through the catalyst bulk wetted with liquid annihilates the smaller bubble, so that the bigger bubble becomes larger at the expense of the smaller pore. Thus, we can see that in the oscillatory mechanism, the smaller pores play roles of gas or heat donors, while the

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larger pores accept the generated gas or heat. The redistribution of gas and heat between pores of different diameters results in much more violent behaviour in big pores, while it weakens or suppresses oscillations in the smaller ones. The divergence of oscillations in different pores can lead to chaotic liquid pumping inside the catalyst porous structure. In Fig. 10b, the scenario of such behaviour is presented when there are no oscillations in the smaller pore 1, while in the neighbouring pore 2, oscillations take place and ydisplace > ycr. During the liquid displacement in pore 2, as the part of the bubble outside is being swept away by the surrounding flow (see also Fig. 6b and c), the meniscus of the rest liquid begins to move, pumping the liquid from pore 1 into pore 2. The pumping of liquid inside the particle should have an irregular character because of fluctuations in temperatures, concentrations, and external flow. The design of the catalyst particle facilitating oscillations can be of great importance for practical applications. One direction of catalyst engineering is to create an optimum in the pore distribution between macro and micropores. As shown in [12], the formation of extremely big macropores can substantially increase the reaction rate in an exothermic process. The most exciting challenge is the creation of special pores that can provide the pumping of liquid through the bulk of the catalyst particle in the demanded direction. Fig. 11 introduces the geometry of pores, in which the directional motion of liquid can be carried out by oscillations. If a conical pore filled with liquid that possesses a wetting ability has a gas bubble, then this bubble should move in the widening direction since the pressure in the gas phase over the meniscus with a smaller diameter is higher than over the greater meniscus. That results in the dislodgement of liquid situated behind the greater meniscus out of the conical pore,

Fig. 11. Direction of the forced pumping (bold arrows) in conical pores: (a) open pore; (b) closed pore.

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while the liquid behind the smaller meniscus is pulled into the pore. In Fig. 11a, the direction of liquid pumping in the open conical pore is shown just after the bubble comes into existence. By choosing parameters of the pore, it is possible to create such conditions under which the liquid will be forced to move mainly from one side of the catalyst particle to another. Fig. 11b represents the closed conical pore, in which the liquid can be forced to move through the catalyst bulk to the pore mouth. Naturally, theoretical approaches to catalyst engineering demand scrupulous study and careful experimental examination in order to put the latent capabilities of catalysts into practice.

bubble outside the pore can be torn off from the pore mouth by the liquid flow or by the buoyancy force as shown, for instance, in Fig. 6b. The approximate size of the bubble that leaves the pore mouth can be determined from the balance between the surface tension force F tension and the drag force F Stock if there is a surrounding flow, or between the surface tension force F tension and the buoyancy force FArchim if the flow around the particle is absent. All the enumerated forces can be expressed as Ftension spdpore

(A1)

FStock 3pmDU¯ flow

(A2)

FArchim ¼ 7. Conclusion The author hopes that the information presented in this paper helps a reader to find the answers to the questions posed above. It is necessary to point out that all consequences and phenomena enumerated in Table 1 have first been predicted theoretically and only then have been confirmed by the experiments described in [6,7,10,12,20] and in this paper. The oscillation model can be helpful not only for the intensification of the reactions where oscillations already exist, but also for intensification of other liquid reactions without any gas or heat evolution in which there are strong intraparticle or external mass transfer limitations. It also reveals new opportunities for scientific purposes and for practical applications: however, a lot of experimental work is still demanded in order to realize the whole potential of the oscillatory phenomenon.

Acknowledgements

pD3 Drg 6

(A3)

The diameter of the bubble torn off by the flow can be estimated as D¼

s ¯ flow dpore 3mU

(A4)

¯ flow is the mean velocity of the surrounding flow where U passing over the pore mouth. The diameter of the bubble that departs the pore due to the ¯ flow ¼ 0) can be evaluated as Archimedean force (U sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 6sdpore (A5) D¼ Drg The characteristic sizes of bubbles leaving the single pore as a function of the pore diameter are shown in Fig. A1. For the real catalyst, even if there is no flow around the ¯ flow ¼ 0), the diameter of the departing bubble particle (i.e. U cannot be estimated with high accuracy by Eq. (A5), because the oscillations produced in other pores cause a lot of microvortexes that can forcedly tear off the bubble of smaller sizes.

The author would like to express his appreciation to Prof. Agar, Dr. Gru¨ newald, Mr. Kahnis (University of Dortmund, Germany), Prof. Jess and Mr. Oehmichen (University of Bayreuth, Germany) for the fruitful discussions. The author thanks Mr. Schmidtner (Media Center, University of Bayreuth) for taking movies and Mr. Gerchau (CVT, University of Bayreuth, Germany) for technical support. The author also gratefully acknowledges the help of MPCP for hosting the supplementary files to this paper and Su¨ dChemie AG (Germany) for the catalyst samples.

Appendix A. The sizes of the bubbles leaving the outer surface of the catalyst particles If the displacement distance is more than the distance of the oscillation penetration ydisplace > ycr, the bubble formed in the pore should appear in the pore mouth. The part of the

Fig. A1. Diameter of the outer bubble torn off from the pore mouth vs. ¯ flow ¼ 0 m/s; (2) the pore diameter. Hydrogen peroxide decomposition. (1) U ¯ flow ¼ 0:01 m/s; (3) U ¯ flow ¼ 0:1 m/s; (4) U ¯ flow ¼ 0:5 m/s; (5) U ¯ flow ¼ U 1:0 m/s.

L.B. Datsevich / Applied Catalysis A: General 294 (2005) 22–33

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[18] Supplementary Movie 1 ‘‘Oscillatory behaviour in the reaction of hydrogen peroxide decomposition’’, available on http://www.mpcp. de/movies//Movie2.mpg. [19] Supplementary Movie 2 ‘‘Simulation of the oscillatory behaviour in a capillary by electrical current’’, available on http://www.mpcp.de/ movies//Movie2.mpg. [20] I.V. Koptyug, A.A. Lysova, A.V. Kulikov, V.A. Kirillov, V.N. Parmon, R.Z. Sagdeev, Appl. Catal. A 267 (2004) 143–148. [21] L.B. Datsevich, in: Proceedings of the Symposium on CAMURE-4, Lausanne, October 22–25, 2002, pp. 83–84. [22] J.M. Smith, Z. Gao, J.C. Middleton, Chem. Eng. J. 84 (2001) 15– 21. [23] O. Coutier-Delgosha, R. Fortes-Patella, J.L. Reboud, N. Hakimi, C. Hirsch, Comput. Fluids 34 (2005) 319–349. [24] Supplementary Movie 3 ‘‘Destruction of a catalyst particle in the reaction of hydrogen peroxide decomposition’’, available on http://www.mpcp.de/movies/Movie3.mpg. [25] G.F. Zebende, M.V.S. da Silva, A.C.P. Rosa Jr., A.S. Alves, J.C.O. de Jesus, M.A. Moret, Physica A: Statist. Mech. Appl. 342 (2004) 322– 328. [26] W. Bu¨ scher, Software ‘‘Spectrum Lab’’, available on http://www. qsl.net/dl4yhf/spectra1.html or http://people.freenet.de/dl4yhf/ spectra1.html. [27] Supplementary sound file ‘‘Voice of a NISAT catalyst in the reaction of hydrogen peroxide decomposition’’, available on http://www.mpcp. de/movies/h2o2-nisat6.wav.