A numerical and experimental investigation of the interactions between a non‐uniform planar array of incompressible free jets

The interaction between multiple incompressible air jets has been studied numerically and experimentally. The numerical predictions have been first validated using experimental data for a single jet configuration. The spreading features of five unequal jets in the configuration of one larger central jet surrounded by four smaller equi‐distant jets, have been studied, for different lateral spacing ratios of 1.5, 2.0 and 2.5 and a central jet Reynolds number of 1.24×105 (corresponding to a Mach number of 0.16). Flow of five equal jets has also been simulated, for the sake of comparison. The jet interactions commence at an axial distance of about 3–4 diameters and complete by an axial distance of about 10 diameters for the lowest spacing ratio of 1.5. For larger spacing ratios, the length required for the start and completion of jet interaction increase. Peripheral jets bend more towards the central jet and merge at a smaller distance, when their sizes are smaller than that of the central jet. The entrainment ratio for multiple jets is higher than that for a single jet. Excellent agreement is observed between the experimental data and theoretical predictions for both mean flow field and turbulent quantities, at regions away from the jet inlet. The potential core length and initial jet development, however, are not predicted very accurately due to differences in the assumed and actual velocity profiles at the jet inlet. Copyright © 2004 John Wiley & Sons, Ltd.     

Coboundaries of irreducible markov operators onC(K)

LetK be a compact Hausdorff space, and letT be an irreducible Markov operator onC(K). We show that ifgεC(K) satisfies sup _N ‖Σ _j ^=0N T ^j g‖<∞, then (and only then) there existsfεC(K) with (I − T)f=g. Generalizing the result to irreducible Markov operator representations of certain semi-groups, we obtain that bounded cocycles are (continuous) coboundaries. For minimal semi-group actions inC(K), no restriction on the semi-group is needed.     

Analysis of nonlinear sliding structures by modified stochastic linearization methods

Probabilistic characteristics of a sliding structure is investigated by using new versions of stochastic linearization technique. The structure is composed of base part and upper part, which are connected to each other in a spring-damping system. Coulomb friction between the base structure and earth ground is considered. Two alternative versions of stochastic linearization approach, suggested by X. Zhang and I. Elishakoff, respectively, are applied to such a sliding structure to evaluate its statistical properties. Compared with the results of Monte Carlo simulation, the two new approaches are performing much better than the conventional one in their applications to the sliding structure. Moreover, numerical results indicate that the criterion proposed by Elishakoff turns out to be superior to all other versions in the problem under study. Numerical results also suggest that the entire structure may be replaced by the rigid body in the sliding problem as long as the difference of velocity responses are considered less important than those of displacement responses.     

Detection of toluene diisocyanate in air with a coated piezoelectric crystal: Part 2. Development of an Instrumental Method For Personal Monitoring

Gases in the atmosphere are monitored with chemically-coated quartz piezoelectric crystals; the method is demonstrated in the use of polyethylene glycol for toluene diisocyanate determination. A microprocessor is used to control the gas sample flow through the detector head as well as the data acquisition. A computer-based procedure for data treatment permits signal integration and background drift correction, resulting in a theoretical detection limit of about 0.006 ppm. The design of a basic portable instrument for piezoelectric crystal monitoring of toxic gas is described with a view to future modification and microprocessor control.     

Crystalline calmagite and a study of sulphonation effects on azo dye metal-ion indicators

Calmagite was introduced in 1960 as a stable substitute for Eriochrome Black T in EDTA titrations of calcium plus magnesium. The colour changes were the same but somewhat sharper. Indicator stock solutions were stable indefinitely. The new indicator was designed as an indicator and not as a wool dye. Azo dye impurities which may be present in some commercial supplies tend to lengthen the end-points. A simple means of removing these impurities to yield crystalline indicator has been developed. The effects of sulphonation on the performance of azo dyes as indicators have been studied.     

Co-monotone allocations,Bickel-Lehmann dispersion and the Arrow-Pratt measure of risk aversion

For every integrable allocation (X ₁,X ₂, ...,X _n ) of a random endowmentY= _i ^=1/n X _i amongn agents, there is another allocation (X ₁*,X ₂*, ...,X _n *) such that for every 1in,X _i * is a nondecreasing function ofY (or, (X ₁*,X ₂*, ...,X _n *) areco-monotone) andX _i * dominatesX _i by Second Degree Dominance.If (X ₁*,X ₂*, ...,X _n *) is a co-monotone allocation ofY= _i ^=1/n X _i *, then for every 1in, Y is more dispersed thanX _i * in the sense of the Bickel and Lehmann stochastic order.To illustrate the potential use of this concept in economics, consider insurance markets. It follows that unless the uninsured position is Bickel and Lehmann more dispersed than the insured position, the existing contract can be improved so as to raise the expected utility of both parties, regardless of their (concave) utility functions.     

Study of the chromonic liquid-crystalline phases of bis-(N,N-diethylaminoethyl)perylene-3,4,9,10-tetracarboxylic diimide dihydrochloride by polarized optical microscopy and 2H NMR spectroscopy

The chromonic liquid-crystalline properties of bis-(N,N-diethylaminoethyl)perylene-3,4,9,10-tetracarboxylic diimide dihydrochloride in an aqueous solution were investigated by polarized light microscopy and 2H NMR spectroscopy. Both techniques indicate a narrow I + N biphasic region and a broad N phase region at concentrations ranging from approximately 6.9 to approximately 30 wt % at room temperature. Optical microscopy indicates that a hexagonal M phase exists at higher concentrations. The variation of the I --> N + I and N + I --> N transition temperatures with concentration was studied by 2H NMR spectroscopy. Finally, the effects of temperature and concentration on the order parameter of the N phase were investigated by 2H NMR using a tetra-deuterated derivative. A value of 0.97 was obtained for the N phase at its upper concentration limit.     

Adsorption kinetics and electrode processes

Prof. H. A. Laitinen (Urbana):We have used double layer capacity measurements to measure adsorption as a function of time during the life of slowly forming mercury drops. For many substances that are not extremely surface active, so that the solution concentration is 1 to 10 mM, the double layer capacity per unit area is essentially constant during the time interval of 5 to 15 sec of drop life. It appears, therefore, that adsorption equilibrium has essentially been attained during the later portions of drop life.Prof. P. Delahay:We have also used a similar method of following the differential capacity during drop life. I would agree that one can achieve conditions for which adsorption equilibrium with respect to bulk concentration is practically reached (high enough concentration and long drop time). But this is quite often not the case (drop time of 3–4 sec in polarography).Mr. G.C. Whitnack (China Lake, U.S.A.);In determination of nitrate esters in presence of phthalate esters we have observed considerable dropping of current height of nitrate ester wave before start of phthalate ester wave. Is this due to an adsorption process occurring at the DME?Prof. P. Delahay:It might well be, but I would hesitate to comment any further on this point because more information would be required. You probably have quite a complicated situation. Perhaps we can discuss the matter later?Prof. Dr. H. Fischer (Ettingen):Ich möchte hinzufügen, class es Fälle geben kann, in denen mcht allem der Blockierungseffekt don Grenzstrom verringert, sondern eine Veränderung des Diffusionsfilmes durch Sekundärreaktion des Inhibitors. Dies ist z.B. bei der Abscheidung von Wasserstoff an einer festen Elektrode (Fe) der Fall, wenn der Inhibitor sich spaltet in eine schwerlösliche Verbindung und ein Proton (RNH⁺ → [RN] + H⁺). Dies beobachtet man z.B, bei den Kationen von heterozyklischen Aminen (Acridin). Offentlich bildet sich eine diffusionshindernde Barriere aus.Prof. P. Delahay:The case of the hydrogen electrode is complicated, and I shall attempt to answer your question only in the case of an ideally smooth electrode. Then, diffusion toward the electrode (partially covered with an adsorbed substance) is little affected by adsorption because the size of “the holes” in the film is very small in comparison with the diffusion layer thickness. Of course, there is no diffusion where there is complete blocking.Prof. B. Breyer (Sydney):The importance of the chemical nature of the film adsorbed at the interface, which has been mentioned by Prof. delahay, seems to me to play a major part in the type of processes discussed. Thus it must be kept in mind that complex formation between the diachargeable ion and the adsorbed film might occur (cf. e.g. heyrovsky? and matyas, 1941). The fact that T1+ ion is little influenced by the presence of an adsorbed film at the electrode solution interface could then be partly explained by the notoriously low co-ordination tendency of that ion.Prof. P. Delahay:The difficulty involved in the “blocking” of the limiting current for thallium is due, I think, to the small size of this ion (large diffusion coefficient of Tl+ in comparison with other ions). Of course, complex ions can be relatively very bulky and this enhances “blocking”.Prof. E. Lange (Erlangen):I agree with prof. delahay that it is very important to investigate the connections between the adsorption and electrode reaction.This is easy for a steady state, e.g., each heterogeneous reaction between two phases that is accompanied by a transfer of ions or electrons, i.e. of electrical charges, from one phase to the other. In such a case, the Galvani tension does not change and the transfer between the two phases must be compensated by a corresponding transfer of charges within the phases.But in the non-steady state, also, an adsorption process may behave as an “electrode reaction” for instance, even an adsorption of a dipole molecule may cause a “transfer of charge” accompanied by a corresponding change of the Galvani tension. In this manner, it seems to me that for the non-steady state it is necessary to define precisely what one means by “electrode reaction”.Prof. P. Delahay:I entirely agree with Prof. i.ange about the necessity of clear definitions. I think that the fact that a steady state with respect to diffusion of the reductible or oxidizable substance has not been reached is not too serious because this scarcely affects the Galvani potential (large excess of supporting electrolyte).Variations in the amount of adsorbed organic substances indeed affect the Galvani potential (dipole orientation), but this effect is included in the dependence of the rate constant ks (at the standard potential) on the electrode coverage.Prof. N. Tanaka (Sendai, Japan).I am very grateful to Prof. delahay for his beautiful work on adsorption kinetics. I should like to make one comment in connection with the rotated dropping mercury electrode. The relation between log i and log t on the current — time curve was found to be 0.5 only in the absence of the surface-active substance. In the presence of surface-active substance, the slope of log i vs. log t changed at a certain point of the current — time curve. This can be explained when the slow adsorption of the surface-active substance on the surface of the electrode is taken into consideration.Prof. P. Delahay:Even for stirred solutions, adsorption equilibrium is not reached very rapidly. A simple calculation based on a model of the Nernst diffusion layer shows that perhaps 1–5 sec are required. Your conclusion is, therefore, quite correct.Prof. W. Kemula (Warsaw):We have recently published that, in several cases, the addition of extremely small concentrations of organic surface-active substances provokes at first a rise of the diffusion current, this current then being suppressed by additional quantities of the substance.