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Efficiency of an aerator driven by fluidic oscillation. Part I: Laboratory bench scale studies. William B. Zimmerman1, Václav Tesa�2, H.C. Hemaka Bandulasena1 1Department of Chemical and Process Engineering; University of Sheffield, Sheffield S10 2TN 2Institute of Thermomechanics of the Academy of Sciences of the Czech Republic v.v.i., 182 00 Prague, Czech Republic. Abstract Recently, a new microbubble generation technique involving fluidic oscillation has been developed. Conventional bubble generation with steady gas flow relies on buoyant forces to overcome the wetting force on the aperture from which the gas is injected. Typically, the bubble must grow to an order of magnitude larger than the size of the aperture diameter before buoyancy is sufficient to overcome the wetting anchor force. Using fluidic oscillation, several approaches are demonstrated to dislodge the nascent bubble at a much earlier stage. One of the most promising is simply to oscillate the inlet stream sufficiently fast that the inertial acceleration force of the pulse of air overcomes the wetting force directly. In laboratory bench trials, this high frequency oscillation mode with greater than 10Hz frequency was observed to generate a fine mist of microbubbles from custom drilled nozzle bank. The nozzle bank has 600µ apertures with a significant horizontal component to their orientation (45º to the vertical). From this nozzle bank, the mean bubble size was estimated as 700µ with fluidic oscillation, and nearly 10mm with steady flow. §1 Introduction Zimmerman et al. (2008) reviewed recent patents in microbubble generation, including the fluidic oscillator technique of Tesar and Zimmerman (2006). This technique aims to produce small bubbles on the same scale as the aperture diameter from which the bubble emerges by using fluidic oscillation to drive the bubble separation mechanism. The aim of this paper is to explain several approaches to how fluidic oscillation can separate the bubble at a minimum size from the aperture. Typically, the bubble must grow to an order of magnitude larger than the size of the aperture diameter before buoyancy is sufficient to overcome the wetting anchor force. The fluidic oscillator approach introduces a third force – the acceleration inertia of the pulsed air – as well as a strong transient which could drive other motions or instabilities. This paper has two major components. In §2, the theory and development of the fluidic oscillator driven microbubble generation is presented in the context of bubble generation processes. Laboratory trials of bubble generation are presented. In §3, experiments measuring dissolved oxygen profile histories are collated and analysed to assess the aeration efficiency of the fluidic oscillator by comparison to a control of steady flow. In §4, discussion and conclusions are made. §2 Design of a microbubble generation mechanism The usual method of breaking down the major pollutants in waste water - organic matter, nitrates and phosphates (Stevenson, 1997) – is their aerobic biological decomposition. Efficiency of this process is limited by availability of oxygen needed by the aerobic microorganisms for their growth and activity. The air is usually provided by aeration with the most direct approach being injection of bubbles into the water through orifices located near the bottom of the water treatment tank. This is a relatively expensive process. Hänel (1988) estimates that its requirements represent more than 80 % of total energetic consumption in typical municipal installations. Unfortunately, the effect is often disproportionately poor. In fact, the authoritative monographs on the subject, e.g. (Hänel 1988), say that “…majority of current [waste water treatment] plants suffer from oxygen deficiency …”. At the core of the problem is the relatively large size of the air bubbles, usually between 8 and 10 mm in diameter, and their fast motion towards the surface, since the rising speed increases with size.

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Figure 1. Percolation of air into water through pores, which are often made (e.g. as voids in sintered material) much more irregular than shown here. Disappointingly, the size of the generated bubbles does not decrease in proportion to the smaller size. The process in unstable: bubble formation tends to concentrate into several pores while others remain inoperative. The pressure instability is similar to channelling by viscous fingers in porous media (Zimmerman and Homsy, 1991). It has been always recognized that the oxygen transfer would be much higher if the bubbles could be made small. The smaller they are, the longer they stay in the water and the larger is their ratio of total surface area across which the transfer takes place to the total air volume. §2.1 Transport properties The above argument for the benefit in transfer efficiency is typified by the common chemical engineering phenomenological description of interphase mass transfer flux J (moles per second):

( )L g lJ K a c c= − (1)

where LK is the mass transfer coefficient (units of velocity), a is the interfacial area per unit volume, and cg and cl are molar concentrations of oxygen in the gas and liquid phases. Mass flux J, all things being equal, increases proportionate to S, and therefore inversely proportionate to the diameter d of the microbubble. Bredwell and Worden (1997) inferred KL in an oxygen microbubble column from a plug flow concentration model for the dissolved oxygen. A laser diffraction technique was used to compute the interfacial area S. Worden and Bredwell (1997) demonstrate that the very high mass transfer rates of microbubbles require modeling of an intrinsically transient nature. They found that the presence of non-transferred gas in the microbubble limited the mass transfer rates. But one might argue that this flux enhancement effect is balanced by the cost of producing microbubbles. As we pointed out in the beginning of this section, one would think that to produce smaller bubbles requires smaller holes or pores. Therefore, with continuous flow through these smaller openings, the friction force would be expected to be proportionately larger. As friction increases with surface area of pores or channels, one would expect the head loss on the pump due to hydraulic resistance to rise inversely proportionate to the

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opening diameter. So the transfer performance increase is offset by the energetic decrease, and no expected overall efficiency is likely. This argument, however, argues against seeking to produce smaller bubbles by miniaturizing the hole. The “win” can only occur if the friction loss remains about the same, but the bubble size is reduced. A different mechanism for bubble production is required. In an attempt to make the bubbles small, aerator designers choose very small size of the air injection orifices, in the final stages this trend leading to air percolation through submillimetre pores (Fig. 1) in sintered porous materials. Unfortunately, the small size does not help much. Quite common is the agonising experience of the bubble size remaining nearly the same no matter how small are the pores, so that the net outcome is essentially just an unwelcome increase of required supply pressure and operational problems due to pores clogging by various debris and particles carried with the air. The bubble formation is found to concentrate into just a few locations, no matter how large is the area of the sintered surfaces. According to (Hänel 1988), usually less than 60% of the sintered aerator surface area actually produces the bubbles. This is sometimes due to the clogging, but a more fundamental reason for the poor uneven distribution is hydrodynamic instability of bubble formation process. A remedy has been sought in moving the aerators – such as e.g. by placing them on a rotating arm, (Diaz et al. 1997). The shear stress on the flow past the aerator surface limits the bubble growth. An additional benefit is the stirring. The advantage claimed in Diaz et al. (1997) of a single row of orifices on the arm being able to cover quite large volume is hardly convincing, the bubbles being simply more diluted in the larger volume. Serious disadvantage of this approach is the cost of the driving motor and gearbox (held on expensive stiff struts above the surface), bearings, and rotating seals (which tend to become worn and need maintenance. Of course, the consumed power for the driving motor increases the operation cost. This paper presents a novel solution to the problem, capable of producing bubbles practically an order of magnitude smaller – and at the same time using no moving components. The aim is to describe the qualitative aspects: the reasons for the failure of the aerators used so far, the new idea which circumvent the existing limitations as well as experience obtained in laboratory feasibility study of the new approach. As an aside, the argument given above for mass and heat transfer enhancement by smaller bubbles with equivalent volume of dispersed phase holds for momentum transport too, with some modification. The classical Stokes law serves as a guide for the residence time of a microbubble in a viscous liquid:

229stokes

l

g dU

ρµ

∆= (2)

Due to the second power of diameter in (2), it is clear that the residence times of small bubbles is markedly longer for the same height of liquid than for larger bubbles. Thus smaller bubbles have much longer to transfer their momentum from the bubble to the liquid dragged along with them, even though they have less momentum to transfer. These two effects would balance, but for the surface area to volume ratio – momentum is also transferred, by shear stress, across the surface area of the bubble. Therefore the flux of momentum is markedly increased by the decrease in bubble size. It follows that microbubbles have a higher “dragging ability” when rising or flotation capability with the

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same volume of fluid holdup. This effect is potentially very important for improved mixing in a riser region of the aeration tank, provided the bubbles can be produced energetically

Figure 2. The extreme shape of a vertically elongated air bubble made by careful expulsion of air from a syringe. Note that if vertically inverted, this shape corresponds to that of a “pendant” drop. efficiently, i.e. the cost of the microbubble production per unit volume does not rise due to rising friction factor. For design purposes, if the goal is to achieve the same mixing level with microbubbles, then potentially this can be achieved by a lower volumetric flow rate, since the longer residence time in the height of liquid permits higher holdup at lower volumetric flow rates. Deep aeration tanks have been investigated for this purpose with conventional steady flow aeration, with less than satisfactory results because the high pressure of the head of liquid opposes bubble formation. §2.2 Basics of bubble theory §2.2.1 Bubble shape The property of the liquid which governs the bubble formation is the surface tension σ [N/m] – the proportionality constant between the force exerted when the air/water phase boundary surface is increased and the circumference length of the enlarged boundary. For clean, distilled water on one side and air on the other side, the value of the surface tension at T = 25ºC is σ = 72.3 mN / m. A useful working idea is to imagine a thin elastically deformed “skin” on the surface, though physically more appropriate picture is that of the energy required for moving additional liquid molecules from inside of the liquid volume to the newly formed surface, where they are exposed to one-sided pull of the attractive forces of the internal molecules. The basic law governing the behaviour of the liquid/gas interfaces is the Young-Laplace relation (Yong, 1805; Laplace 1806) between the surface tension force and the force due to the pressure difference across the boundary. The shape of stationary bubbles, especially if they are attached to a solid wall, is visibly influenced by gravitational forces. Classical solutions were derived for the two cases: the shape elongated by the lift force (Fig. 2) acting on a bubble which is held at its bottom (this case corresponds, with inverted sign, to the shape of “pendant” liquid drops), and the shape in which the hydrostatic lift tends to press the bubble upwards against the solid wall at which it is held by its upper pert (the classical solution of the “sessile” drops). Essential length parameter in problems associated with surface tension in balance with gravitation forces is the capillary length scale

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(3)

Fig. 3 Shapes of top part of bubbles computed for a range of bubble sizes and hence a range of the corresponding values of the pressure parameter p, eq. (5). Also shown are the osculation circles passing through the apex points (their radius is equal to the apex radius rA ). with the specific volume of air va [m3/kg] = r T / P (where T – temperature, P – pressure, and the gas constant r for humid air taken r = 288 J/kgK), specific volume of water vw = 10-3m3/kg and g = 9.81 m2/s gravity acceleration. For the water/air interface the capillary length is lcap = 2.72 mm. The problem with bubbles influenced by the gravity forces is their aspherical shape. Instead of the radius r, a more complex form of the Young-Laplace equation with two principal radii r1 and r2 in two mutually orthogonal planes is to be used. Only at the apex does the shape possess a single curvature; it is the apex radius rA for which from the Laplace-Young equation follows the pressure difference

2apex

A

Prσ∆ = (4)

across the top of the elongated bubble as shown in Fig. 2 (or across the bottom of the compressed, “sessile” drop, bubble). Elsewhere, the pressure varies over the bubble height with the changing hydrostatic pressure dependent on vertical position. The resultant non-linear differential equation for the bubble shape contains a parameter which may be usefully non-dimensionalised to

2 cap

A

lp

r= (5)

called the pressure parameter, since it is through eq.(4) determined by the apex pressure. Several numerical solutions of the bubble shapes for different values of the pressure parameter are plotted in Fig. 3. It is evident that stationary air bubbles in water of diameter ~ 1.2 mm or smaller are practically spherical. If the bubble size is increased, the shape in this “pendant drop” case becomes significantly deformed by the hydrostatic pressure difference so that it is more and more elongated – with the extreme of realisable stationary shapes corresponding to Fig. 2 of diameter ~ 8 mm.

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Figure 4. Simultaneous generation of two bubbles in parallel in an aerator corresponding to the state of the-art conventional device (Hänel 1988) with a row of parallel holes connected to the single-large-diameter hole manifold. The balance between the two bubbles is unstable. §2.2.2 Instability of parallel bubble growth Let us now consider the formation of two bubbles according to Fig. 4. This is a reasonable representation of a section of the currently developed aerator (Diaz et al. 1997), but may also represent two neighbouring pores of a sintered aerator. In the initial stages of their formation the two bubbles are small, of submillimetre size, so that their shape (cf. Fig. 3) is practically spherical, fully determined by the radius r, in Fig. 4, which is equal to the apex radius r = rA.

The air pressure inside the bubble is equal to the apex pressure given by eq. (4). The fact of paramount importance is that eq. (4) shows this pressure difference decreases gradually as the bubble radius r grows. This pressure decrease during the growth, or the negative slope of the pressure-radius dependence eq. (4), is at the core of the problems. Suppose some small external disturbance (or even the small hydraulic resistance of the part of the manifold between the two exits) causes the downstream bubble D in Fig. 4 to be slightly retarded in its growth. Its internal pressure becomes higher than that the pressure in the in the upstream bubble U. This, of course, will make the pressure may drive air away. Indeed, even the hydraulic pressure loss in the manifold will make air entry into the upstream bubble U more favourable, i.e. the air flow incurring less resistance. The bubble U will grow at the expense of the downstream neighbouring exits, which may produce enough imbalance to destabilise the growth. In the line of parallel air injection nozzles it usually the first upstream bubble which starts growing uncontrollably until it separates. Strictly speaking – as will be shown below – this instability mechanism takes place only for bubbles beyond a certain critical, hemispherical shape. However, with steady air flow into the bubble there is no mechanism that can produce bubbles and stop them growing before the unstable regime is reached. Due to the instability, it is impossible to produce many small bubbles in parallel. Instead, the general tendency is to concentrate the air flow into a single injection port, the bubble at which grows unstoppably to a large size.

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§2.2.3 Separation instability If a growing bubble is supplied by a steady air flow, its growth passes through the progression of shapes shown in Fig. 3. Pressure parameter p gradually decreases towards the limiting value p = 2. The solutions in Fig. 3 were not computed especially close to the approach of the parameter p → 2 and should be avoided, as the bottom part of the bubbles occur there. This is because the numerical procedure experiences difficulties in this regime. The solution loses uniqueness and becomes numerically unstable. The non-uniqueness is associated with bifurcation: the appearance of two solution branches. These represent the “necking” of the bubble, local contraction at its bottom region. The numerical instability, which makes it progressively difficult to perform the computations of the “neck” shape as p → 2, reflects, in fact, a mechanical instability of the bubble shape. The shape becomes unstable as the diameter of the “neck” decreases rapidly to zero. The result is separation of the bubble from its orifice through which it is supplied. Exact details of the process, due to the instability and extreme sensitivity, are easily influenced even by small perturbations. In theory, the separation takes place at the bubble size exactly proscribed by p = 2 . In practice the bubbles may continue growing slightly beyond this limit, if supplied by a powerful air flow. On the other hand, if the bubble is generated by a single exit orifice, it is possible to obtain a smaller bubble size by using a small air flow rate. This leads to slow bubble growth and a (quite reliably occurring) chance that some disturbances will cause the bubble to form the “neck” and then separate even while its pressure parameter is still at p > 2. This, however, is not usable as a practical way of generating small bubbles, since a single orifice would be uneconomic and multiple orifices would switch the flow into a large bubble due to the bubble growth instability. §2. 3 Fluidic aerator The present paper presents a solution to the problem of improving the aeration efficiency by generation of much smaller bubbles. Essentially, bubbles are kept small by operating the aerator in periodic oscillatory regime. The bubble size, instead being governed by the surface tension “necking” mechanism, is limited by terminating the growth at the end of each oscillation half-cycle. This solution is based on utilising a combination of several ideas. 1) In the first half of the cycle, bubbles are not left to grow (or, at least, not substantially) beyond the initial stable stage of their formation. This makes it possible to produce simultaneously a large number of small bubbles of practically the same size. 2) In the second half of the oscillation cycle the shear-flow induced separation mechanism is applied to remove the bubbles from their injection nozzles. 3) The oscillation is generated by using quite simple fluidic oscillation generator in the air supply. This device has no moving components and consists essentially of just a specially shaped bifurcation cavity. As shown schematically in Fig. 5, the fluidic oscillator is of the diverting type, with the output flow alternating between the two exit branches, A and B. The air flow in A reaches up to the aeration orifices at the bottom of the water treatment tank. Due to the bleeding exit, water is left to fill the branch B. the alternating air pressure there acts on surface of water, generating water jets issuing from the second set of parallel orifices. These water jets act on the small bubbles and separate them from the air orifices in the second half of each oscillation cycle, while the bubbles are still too small and normally would not separate.

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§2.3.1 The fluidic oscillator The last item in the above the list, availability of a suitable oscillator is the key factor for the new approach. Without a no-moving-part generator the operation in sustained oscillation would be impractical, due to inevitable wear of mechanical components. This is no problem in the device based on employing purely aerodynamic phenomena in a cavity with fixed

Figure 5. Schematic representation of the investigated model of the pulsating flow aerator. The no-moving-part fluidic oscillator in the air supply operates in diverter mode. During the first half of the cycle, it directs the air flow into A and to the air orifices producing the bubbles. In the next part of the cycle, the air acts on the water in the vertical pipe B and generates water jets that separate the bubbles from their air nozzles. walls. The fluidic oscillator is so simple and easy to manufacture that it does not cause any significant increase to aerator complexity or price. The actually tested version consists of two components: a fluidic no-moving-part jet-deflection amplifier (Fig. 6) and a single feedback loop tube. The principle of the amplification in the first component, the fluidic diverter valve, is based on the sensitivity of a jet deflecting actions of flows admitted into the perpendicularly oriented control nozzles. The deflection changes the proportion of the jet fluid captured in two collectors opposing the nozzle from which issues a jet of supplied air. Geometry of the model used in the present tests was based upon successful early valve design (Tesa�, 1975) later used by Perera and Syred (1983). The flow amplification gain of this model in steady state is approximately 14.5. This means that to terminate into the other it is sufficient to apply a control flow rate equal to approximately 7% of the supplied flow. In actual operation, the

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flow in the amplifying valve is switched by control pulses which – owing to their sudden shock character – may be even weaker. The version of the amplifier used in the tests, as shown in Fig. 6, was originally a laboratory model designed for a different purpose (Tesa� et al. 2006), where all the details of its geometry and full description of experimentally found behaviour are described. This valve operates in a bistable regime: without any acting control signal it remains in one of two alternative full jet deflection stable states. This is achieved by using

Figure 6. Laboratory fluidic amplifier model of 1.4 mm main nozzle width used in the tests. It consists of a stack of five Perspex sheets, each 1.2 mm thin, with laser-cut cavities, covered by 10 mm thick top and bottom Perspex cover plates. The bottom plate contains the ferrules for the feedback loop and output tubing. the Coanda effect of jet attachment to walls. The model was made by laser cutting of the cavities in plastic material (transparent polymethylmetacrylate). In fact, this inexpensive and fast manufacturing method may be suitable even for the operational version of the device. The second component, which converts the amplifier into an oscillator, is a de-stabilising fluidic feedback loop. Instead of the classical connecting of the output and control terminals, a simpler version of feedback actually used (Fig. 5) uses a single feedback loop connecting the two control terminals. This, together with experimental data, is also described by Tesa� et al. (2006). This oscillator has been used for the study of jet transfer mechanisms (Tesa� et al., 2007) as well. The mechanism of the feedback utilises the fact that pressure levels in the control terminals are unequal. There is much lower pressure on the side to which the jet is deflected. In fact the Coanda attachment to the wall is associated with the low pressure on the concave side of the deflected jet. The pressure difference gives rise to a fluid flow in the loop towards the lower-pressure control nozzle. This flow gradually gains a sufficient momentum for producing a substantial outflow from this nozzle, sufficient to switch the jet to the opposite attachment wall when it reaches the 7% limit. The pressure difference then changes sign, leading to reversal of the flow direction in the loop. Essential for the oscillation generation is a delay of the flow in the loop. Because of fluid inertia, it takes some time for the fluid to stop and then begin flowing back. The jet remains for a certain short time attached to the opposite attachment wall, sufficiently long to produce the inverted pressure levels in the control nozzles. The delay depends on the length of the feedback loop tube. As a result, the oscillation frequency may be adjusted by the feedback tube length. To give some idea about the length and frequency range, experimental data are given in Fig. 7 for the amplifier from Fig. 6. §2.3.2 Utilizing the stable regime

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The instability of parallel bubble formation, described above in association with Fig. 4, does not affect the initial stage of bubble formation -- before the bubble assumes the hemispherical shape. In these initial stages the bubble radius r actually decreases with growing bubble size so that the pressure inside the bubble increases, making the conditions stable. This initial regime is utilized in the novel aerator, with stable formation of bubbles in a large number of parallel air exit orifices during the first half-period (upstroke) of the oscillation generated by the fluidic oscillator. The growth is terminated -- since the air flow pulse comes to an end – before the bubble shape reaches the hemispherical limit. Of course, the bubbles below this limit are too small for their separation from the air exit orifice to occur naturally, at least in steady states. At high oscillation frequency, a dynamic separation regime was observed,

Figure 7 Dependence of the oscillation frequency f=f(Q,l) on the length l of the feedback loop. Results of experimental investigations of the oscillator (Tesa� et al. 2006). Fig. 6, with the 10 mm i.d. plastic tube loop and air supply flow rate Q=10 l/min held constant. Very low oscillation frequency is obtainable, though with an inconveniently long feedback loop. which occurs due to the discrepancy between the accelerated water around the bubble on one hand, tending to move away from the orifice, while the air flow changes sign on the other hand and tends to return the air flow back into the exit. Operationally, this high frequency operation mode has the advantage that all the momentum of the gas stream is used to create microbubbles and all the gas stream is available for phase transfer processes. At low operating frequencies, this dynamic separation mechanism is insufficient and has to be assisted by another, flow shear mechanism – which, of course, may become the dominant mechanism in some frequency range. §2.3.3 Bubble release by water jet Removing of the small, sub-hemispherical bubbles from their air exit orifices according to the present solution uses the principle of interaction of perpendicular flows, analogous to the interaction of perpendicular flows utilised in the fluidic amplifying valve. The system of parallel air orifices is connected to the exit branch A of the fluidic oscillator, Fig. 5. There is yet another system of orifices, connected to the water filled branch B. A water and an air exit orifices form a pair, with their axes mutually perpendicular, as shown in Fig. 10. Fig. 11 presents a cross section passing through the two orifices of the pair. The mutual position of the two nozzles in the pair is such that the water jets formed by the water flow from the water nozzles act form aside on the bubbles formed at the exit of the air nozzle. For ease of manufacture of the test model by the simple drilling, the holes are made to exit into in a 90º groove.

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The filling of the water into the water nozzles is made possible by the bleeding exit, as shown in Fig. 7, which enables the air flow into the branch B to escape into the atmosphere. It should be noted that there is a restrictor in the bleeding exit. The pressure drop on the restrictor, varying with the magnitude of the instantaneous air flow from the oscillator, produces a pressure action on the top of the water column in the branch B. In fact, the restrictor used in the investigated model had a character of small cross section capillary, which may have contributed by yet another effect – the inertance (see e.g. Tesa� , 2007) of the flow accelerated in the capillary. This makes possible easy escape of the time mean air

Figure 8 Initial stage of bubble formation are stable, the pressure difference across the water/air interface increasing with bubble size – until the hemispherical shape is obtained. From then on, the slope of the dependence changes sign and the instability of Fig. 4 takes place.

Figure 9. Dependence of the pressure difference across the bubble water/air interface, computed for 0.6 mm and 1 mm exit hole diameters, on the volume V of the spherical cap in Fig. 8, which is roughly commensurable with the bubble volume. Note that the hemispherical shape divides the growth into two regimes – the initial stable growth with decreasing r and the later unstable one.

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Figure 10. The groove with the mutually perpendicular nozzle pairs in the aerator model. The layout was chosen for ease of manufacturing of the holes (e.g. drilling at right angle to the local surface) in the model. A different manufacturing technique - and resultant shape – is envisaged for the operational version.

Figure 11. Geometry of the groove and the pair of water and air nozzles. Note the asymmetry: the air nozzle is smaller, water nozzle larger and located so that its exit reaches to the bottom of the groove. This helps the water jet to sweep away the air bubble held at the air nozzle exit. flow component (and thus ingress of water into the branch B) while the unsteady air pulsation cannot leave easily and acts quite strongly on the water column. In the second half of the oscillation cycle (downstroke), while the bubbles are still held outside it air nozzle exit by the accelerated surrounding water, the air pressure pulse in the branch B expulses water from the water nozzles, forming water jets. Note that the geometry of the water nozzles causes the jet to follow the grove wall with the air nozzle exit. The water jet impinges upon the bubbles.

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Figure 12. Drilling of the 0.6 mm air nozzle holes – the groove in Fig. 10 makes the drilling at right angle to the local surface easier. §2.4 Experimental results The model of the new aerator was made from two parts, made from the transparent PMMA acrylic glass and mutually connected by transparent flexible tubes. One of the parts, the oscillator (Fig. 6), was outside the test tank filled with water. Immersed at the bottom of the tank was aerator component (Fig. 14). This was of rectangular shape, with water and air connection ferrules leading from opposing sides to the water and air nozzles, drilled in the groove on the top of this component.

Figure 13. The first half of the oscillation cycle. While the bubbles formed by the air flow admitted to the air nozzles.are still small, of the sub-hemispherical size, the distribution of the air flows is stable. All bubbles grow simultaneously to the same size.

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Figure 14. The water jets issuing from the water nozzles in the second half of the oscillation cycle separate the air bubbles and move them away from the aerator surface. In the oscillatory regime, the length of the feedback loop tube was adjusted so that the oscillation frequency was initially low, f = 2 Hz. Because the oscillator was originally made for a different purpose, its size was too large for the mere 38 water nozzles and 38 air nozzles and some generated pulsatile flow was bled not only on the water side, as shown in Fig. 5, but in a similar layout (with an adjustable restrictor) also on the airs side, branch A. This, of course, was only a temporary measure. If the oscillation was interrupted, for instance by blocking of the feedback loop, the steady air flow admitted into the row of the air nozzles resulted in a stream of air bubbles issuing, as documented by the photograph Fig. 15, from the first air nozzle immediately downstream from the inlet ferrule bringing the air into the immersed aerator component. This provided a graphic demonstration of the bubble formation instability: all air flow concentrated into just a single orifice – the one offering the least hydraulic resistance. The generated bubbles were

Figure 15. Photograph of standard sized ~8 mm diameter bubbles produced by steady airflow into the branch A.

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Figure 16. Photograph of the small ~ 0.8 mm diameter bubbles leaving the air holes of the aerator during the downstroke of the cycle. irregular, their size was measured from the photographs and was evaluate to correspond to 8.2 mm spheres. With the oscillation, the character of the generated bubbles changed essentially. The process of bubble generation takes place in two stages, Figs. 13 and 14, which at the originally set low oscillation frequency were clearly discernible. The bubble size decreased by a decimal order of magnitude, to the mean diameter 0.86 mm (again evaluated from the photographs). As the example in Fig. 16 shows, the bubbles were released progressively along the length of the air nozzle row, in a pattern resembling a result of an acting travelling wave. A striking difference was observed in the rising speed of the bubbles. While the large bubbles in Fig. 15 shoot towards the surface, characteristically forming bubble clusters which move together, the motion of the small bubbles in Fig. 16 was slow. This slow rising speed is an advantage, providing more time for the oxygen transport between the bubble and the water. In a later experiment, the length of the feedback loop tube was decreased considerably, which resulted at oscillation frequency measured to be f = 90 Hz. The mechanism of bubble formation changed towards the dynamic release of the bubbles, which remained in operation – albeit with immediately apparent irregularity – even when the oscillation of the water tube B (which decreased so as to be practically unrecognisable anyway) was eliminated completely. The obvious advantage of this high-frequency operation mode was the visibly increased production rate of the bubbles from the same number of nozzles. The rising bubbles with the surrounding water formed a clearly visible column, decreasing in cross section in the vertical direction. This “fine mist” of microbubbles is demonstrated in the design of an airlift loop bioreactor (Zimmerman et al. 2009). §2.5 Preliminary conclusions The main contribution of this section is qualitatively new approach to the aeration problem. By pulsating the supply air flow – preferably using the cheap and reliable fluidic oscillator -: it demonstrates the feasibility of a new method of producing air bubbles in liquids. The size of the bubbles may be demonstrably decreased by an order of magnitude. This change of the size, together with the accompanying decrease in the bubble rising speed, provides a substantially increased opportunity for mass transfer between the injected gas (air) and liquid (water). The next section tests this hypothesis using transient studies of dissolved oxygen

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levels to assess the enhancement to oxygen transfer efficiency due to the fine mist of microbubbles generated in the high frequency dynamic mode identified here. §3 Aeration efficiency study In §2, we introduced several methodologies for producing bubbles on the scale of the diameter of the aperture from the active principle of fluidic oscillation. It is expected that, given the surface area to volume ratio of smaller bubbles, it should be possible to achieve an order of magnitude higher mass transfer rates according to equation (1) than with steady flow with the same volumetric flow rate. This is important, as it relieves the standard trade-off that to achieve smaller bubbles, smaller apertures are used. As discussed in §2.1, there are reasons that still lead to much larger bubbles from smaller apertures, but even if aperture reduction led to proportionately smaller bubbles, one would expect that the cost of such smaller bubbles would rise inversely proportionate to the aperture diameter, as the smallest restriction leads to an increased friction factor. Thus better aeration performance is traded-off with higher cost. By achieving an order of magnitude increase in mass transfer for roughly the same cost given the same volumetric flow rate, this trade-off is relieved substantially. However well accepted the mass transfer coefficient theory underlying equation (1), it is the case that the mass transfer coefficient is a holistic quantity from the cooperative motion of all the bubbles rising and the resultant, complicated, velocity field. As smaller bubbles rise more slowly, there is a greater time for mass transfer, but nevertheless the accompanying maximum rise velocity is lower, creating the possibility that the global mixing effect is decreased even if the local phase transfer is more rapid, the potential for lower mesoscale convective mixing could lead to a curbing of the expected increase in mass transfer. Thus, in this section, a set of experiments is presented that assess the level of enhancement of mass transfer for oscillatory flow over the control of steady flow, which just replaces the fluidic oscillator with a flow splitter. For convenience, the 90Hz dynamic mode with both sides of the nozzle bank of Figures 13 and 14 are feed with an air stream, was tested. This seems the operationally most attractive of the configurations observed in §2.

Figure 17 Experimental set up. A clear acrylic glass tank of water was arranged with flexible tubing feeding both nozzle banks from the outlets of the fluidic oscillator. The air bleeds were used to find a regime of regular bubble formation for both the oscillatory flow and steady flow. A dissolved oxygen

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probe was held at various positions horizontally removed from the symmetry plane and at different vertical levels. §3.1 Experimental procedure A clean glass tank with dimensions of 30cm X 20cm X 20cm was filled with 12 liters of clean tap water. The aerator body was placed in the middle of the tank connected with compressed air supply through novel fluidic oscillator (see Figure 17). The procedure followed an internal protocol proscribed by Yorkshire Water, in agreement with the ASCE standard measurement of oxygen transfer in clean water. Cobalt Chloride was added to the tank and mixed well for four hours. Sodium sulphite was then added in to the water to remove any dissolved oxygen. A dissolved oxygen (DO) probe was positioned at a desired location to measure variations of DO. After 20 minutes, aeration was started and flow rate was fine tuned to give a stream of small air bubbles. The size of the small bubbles was estimated to be less than 1 mm. The bubble size distribution from a similar experiment (Zimmerman et al. 2009) shows a mean bubble size of 700µ. It was not possible to measure the very low levels of air flow required to produce the small bubbles using standard flow meters. Therefore an alternative method was implemented to measure average air flow rates. A vessel was inverted over the bubble stream and air was collected from the aerator body for 20 minutes. The collected air was transferred to a measuring cylinder which had a small cross sectional area. Air pressure was adjusted to atmospheric pressure by changing the cylinder vertical position. Calculations were done to determine the air flow rate at correct pressure and temperature. See Figure 18 for a schematic of the flow rate determinations. It should be noted that this technique ignores the accumulation of air in the tank (gas holdup) since it is presumed to have reached a steady level during the capture period. The DO probe was positioned at various points in the tank to determine the OTE at these points. The positions in the tank are summarized in Figure 19. Hypothetically, we are only interested in the dissolved oxygen levels and oxygen transfer efficiency (OTE) exactly in the plane of the microbubble generation. The characteristic operation of an aeration system

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Figure 18. Average flow measurements using an inverted collection vessel.

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Figure 19. Dissolved oxygen sensor positions used in the experiments. Front Elevation shows the height variations of DO probe in cm with fixed lateral position (5 cm away from bubble stream). Plan shows the change in lateral positions in cm of DO probe with constant height (height fixed at 10cm). End Elevation shows the water height in cm. envisaged is for full coverage of the tank with microbubble generation. In practise, the DO probe cannot survive direct contact with the bubble plume. So the elaborate placements in Figure 19 were selected so that these multiple positions permit the extrapolation of DO levels and OTEs to near and within the plume, presuming that the DO profile is continuous. The OTE of small bubbles was determined in 8 positions; one position was repeated with large bubbles. Large bubbles of approximately 10 mm in diameter were formed by by-passing the fluidic oscillator and allowing the air to directly enter the aerator body. The OTE of the large bubbles was determined 2 cm from the bubble stream at a fixed height of 10 cm from the bottom of the tank. Details of the positions of the DO probe can be seen in Figure 20.

Figure 20. A summary of the positions of the DO probe within the tank.

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The air flow rate required to generate small bubbles was measured in the range of 9 – 11 ml/min. It was not possible to generate the large bubbles using such low air flow rates. The large bubbles were generated using an air flow rate of 25 ml/min. At lower air flow rates using the steady flow configuration, the rise of bubbles was intermittent. At this flow rate, there was a regular production of large bubbles. At higher flow rates for the oscillatory flow configuration, the bubble production is too rapid and coalescence is a dominant feature. Thus the comparison is about flow regimes – regular bubble production in both oscillatory flow and steady flow, where the latter has the advantage of 2.5-fold larger volumetric flow.

Dissolved oxygen concentration and temperature was continuously recorded every half an hour after addition of sodium sulphite until DO reached saturation level at that temperature. This procedure was repeated with different DO sensor positions desired (as outlined in Figures 19 and 20). On average, each experiment took around 24 hours and during that period ±2oC temperature differences were observed. Barometric pressure was taken at the beginning and end of each experiment. §3.2 Oxygen transfer efficiency analysis Calculations were carried out according to the methodology used by Yorkshire Water which adapts the ASCE standard (1992) for measurement of oxygen transfer in clean water. Similar calculations are presented by Tchobanoglous and Burton (1991). The calculation of oxygen transfer efficiency occurs in three stages: 1. Fitting of a log-linear curve for

( )expsi l Lc c K a t− = − (6) to find the negative of the slope, LK a , where sic is the saturation dissolved oxygen level at the temperature of the liquid,

lc is the dissolved oxygen level at time t, a is the specific area of gas-liquid interface per unit volume, and LK is the mass transfer coefficient. “The linear portion of the log deficit versus time plot is usually found between 20% and 80% of the saturation value and this is the standard editing of data. The slope may be found by linear regression analysis with at least square line-fit” according to the ASCE standard. The italics are to draw attention to the inherent assumption that the log-linear regime are the most important dynamics. Bredwell

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Figure 21. A photograph of the aeration tank and flow configuration.

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2

4

6

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1 0

D is s o lve d o x yg e n V s T im e

2 c m fro m bu b b le s tre a m 4 c m fro m bu b b le s tre a m 8 c m fro m bu b b le s tre a m 6 c m fro m bu b b le s tre a m

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Figure 22. Dissolved Oxygen concentration Vs time. Height of the DO sensor is kept constant, 10 cm above the bottom of water tank. and Worden (1997) inferred KL in an oxygen microbubble column from a plug flow concentration model for the dissolved oxygen, specifically because the finite capacity of oxygen within the microbubble is a limiting feature to mass transfer with sufficiently long residence time or with sufficiently high dissolved oxygen levels. There are two driving forces for mass transfer: equation (6) emphases the difference between current DO level lc and the saturated DO level sic . Equation (1) shows a different driver for mass transfer, the difference between liquid and gas concentration levels. At equilibrium, there is a partition coefficient which relates the two. But as mass transfer is a non-equilibrium process, there is no general relationship and both driving forces in equations (1) and (6) must be non-zero for mass transfer to proceed. With microbubbles, the finite capacity of the microbubble can decrease the difference in (1) to zero before the difference in (6) reaches zero. Bredwell and Worden cater for this in their model. In these experiments, it is presumed that the residence time is sufficiently short that the ASCE standard model is appropriate to infer LK a . Should

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OTE vs distance from bubble stream

0

2

4

6

8

10

12

0 2 4 6 8 10

Distance from bubble stream (cm)

OTE Small Bubbles

Large Bubbles

Figure 23. Oxygen Transfer Efficiency vs. distance from the bubble stream. Height of the DO sensor is kept constant, 10 cm above the bottom of water tank.

Figure 24. Maximum dissolved oxygen concentrations achieved for different lateral positions (16 hours after aeration starts). Height of the DO sensor is set to 10 cm from the bottom of water tank. the finite capacity be important, then the log-linear regime will not be observable – a changing slope curve with decreasing apparent LK a with time. It should also be noted that most wastewater aeration plants operate between 10-30% of saturation DO level, so the LK a inferred by this technique is of ambiguous value if the log-linear regime is largely higher than this range -- the ASCE standard throws out at least half of the industrially important range, and the other half can be greatly influenced by practically unimportant behaviour. 2. Calculation of the oxygen capacity of the tank.

C L siO K aV c= (7) Where LK a and sic are “corrected” to 20ºC by standard correlations. 3. Calculation of the oxygen transfer efficiency.

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COOTE

Qρ χ= (8)

Q is the air volumetric flow rate; ρ is the gas density, and χ is the mole fraction of oxygen in the gaseous phase, presumed constant and corrected for relative humidity of the gaseous stream. §3.3 Aeration efficiency results and discussion This section reports on two separate studies, each with a comparison to the control of steady flow. §3.3.1 presents a horizontal variation study. The DO probe is held at a constant height of 10 cm from the bottom of the tank while the distance from bubble stream is adjusted. §3.3.2 presents a vertical variation study. The DO probe is held at a constant 5 cm from the bubble stream while the height is adjusted.

§3.3.1 Aeration study with horizontal variation Measurements taken from the experiments were analyzed to check the efficiencies of transferring oxygen at different spatial positions. Monitored DO concentration against time is presented in Figure 22. During the initial period, DO concentration rises rapidly due to high oxygen concentration difference inside the bubbles and surrounding water. After some time, water starts to saturate with oxygen and mass transfer rates begin to reduce. DO concentration then tends to become constant with time after full saturation corresponding to the temperature. In our water tank, DO concentrations at 2, 4 and 6 cm away from the bubble stream at a fixed height of 10 cm follow this trend but further away, oxygen transfer becomes more inefficient. Oxygen Transfer Efficiencies were calculated for each lateral position. Figure 23 shows the OTE data generated as the probe was moved from 8 cm to 2 cm away from the bubble stream at a fixed height of 10 cm from the bottom of the tank. There is a linear increase in OTE the closer the probe is positioned to the bubble stream. At the closest measurement point, 2cm away from the bubble stream, records a high efficiency of above 10%. By extrapolation, OTE very close to bubble plume could be high as 13.5%. A control experiment was done with large bubbles to compare OTE at a point 2 cm away from the bubble stream and 10 cm above the bottom of the water tank (Fig. 23). Large bubbles were produced by bypassing the oscillator in supping air to the aerator. Bubble diameters were estimated to be approximately ten times the smaller bubbles. A very low OTE of 1.4 % was recorded with large bubbles compared to approximately 10.2% with small bubbles at the same position. This means that the small bubbles generated by the novel aerator system are more than seven times more efficient at oxygen transfer than the large bubbles. The main reason for the dramatic reduction in OTE with the large bubbles is the low surface area to volume ratio of these large bubbles. It is also due in part to the inferior mixing observed with the large bubbles. When the air was delivered to the tank as small bubbles many hundreds of bubbles were observed in the tank at one time. These bubbles produced some limited mixing of the air with the water. When the air was introduced into the tank as large bubbles only 5 large bubbles were observed in the tank at any one time which would

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(a) Large bubbles (approximately 10 mm) (b) Small bubbles (approximately 700µ)

Figure 25. Photographs of aeration system contribute to inefficient mixing. If a larger air flow was used to produce the large bubbles and more large bubbles were produced more efficient mixing would result which could lead to a higher OTE. However, this could also have been true for the small bubbles if the aerator had been designed to produce small bubbles at a higher air flow rate. The small bubbles will promote less mixing throughout the tank than the equivalent large bubbles; in a real system we may have to investigate the use of a separate mixing system to improve the efficiency of the small bubbles throughout the tank. In industrial aeration systems, rising large bubbles cause considerable mixing of fluids in the tank. This helps to keep a nearly uniform dissolved oxygen level throughout the tank. Mass transfer due to concentration gradients is much weaker compared to mass transfer due to convection currents. In our lab scale aeration system, small bubbles at the low air flow rates used caused less mixing in the tank and diffusion became the main form of mass transfer. This leads to a reduced OTE away from the bubble stream. Figure 24 shows the effect of saturation DO, presumed to be the final steady value, against the position of the DO probe. The slope of the graph (Fig. 24) gives an indication of the oxygen diffusion rate. The oxygen transfer process in our system could be further enhanced by the addition of mixing. In general, a mechanical propeller is more energy intensive to employ in industry for long periods. Therefore occasional large bubbles could be encouraged to help good mixing. Running the aeration system with the oscillator at optimum air flow rate could cause intermittent large bubbles due to fluctuating flows. Experiments were performed slightly below this flow rate to avoid large bubbles in order to compare OTEs with small bubbles with oscillation vs. large bubbles without oscillation. But in practice, intermittent large bubbles rising at random locations could be used as an efficient way of transferring oxygen within water.

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Figure 26. Oxygen Transfer Efficiency vs. vertical position of the DO sensor. The distance between DO sensor and bubble stream is fixed to 5cm. Vertical distance is measured in cm.

Figure 27. Maximum dissolved oxygen concentrations achieved for different vertical positions. The distance between DO sensor and bubble stream is fixed to 5cm. Figure 25 shows a pictoral comparison of the microbubbles (right) produced by fluidic oscillation to the control experiment (left) with this high frequency dynamic regime where microbubbles need no additional “knock-off” mechanism. This should be compared with Figure 15 and 16 which only generate microbubbles during the liquid jet during the down stroke that knocks off microbubbles formed, but not detached, during the upstroke. Similar bubble formation experiments are reported in Zimmerman et al. (2009) for the design of an airlift loop bioreactor and showed the microbubble mean bubble size was 700µ with a fairly narrow bubble size distribution from this nozzle bank of 600µ apertures. Note that the “fine mist” of microbubbles in Figure 25 is apparently uniformly spaced and relatively free of coalescence. Crabtree and Bridgwater (1969) show experimentally that chains of small bubbles rising in Stokes flow are hydrodynamically stabilizing and non-coalescent. This feature is particularly important to avoid the problem of “smaller holes but

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still large bubbles” that has plagued attempts to mass produce microbubbles with both energy efficiency and fidelity. §3.3.2 Aeration study with vertical variation The OTE was measured with the DO probe at different heights while keeping the planar position constant. The results are shown in Figures 26 and 27. Clearly, oxygen transfer efficiency is a weak function of vertical position, as is the long-time unvarying level of DO. These effects are likely considering that the rising velocity most likely decreases from its ejection from the aperture to its terminal Stokes rise velocity since it ejects with substantial momentum from the oscillator driven pulse. If the overall pressure drop is roughly constant between the oscillatory outlets and the steady flow control experiment to achieve comparable flow rates, then the pressure drop during the upstroke in one outlet must be double that of steady flow. Taking into account the acceleration effects due to the high frequency oscillation, the bubble emerges with substantial inertia from the oscillatory flow by comparison with the steam flow emergence, which occurs just super-critically as buoyancy eventually overcomes the wetting anchor. Thus near the bottom of the tank, as the bubbles decelerate to their terminal velocity, effective residence time in a fluid element increases with height. This translates into increasing mass transfer rates with height, but the effect is offset by the decrease of oxygen content in the microbubble with rising time, which Worden and Bredwell (1997) identified as a major feature of microbubble mass transfer. The saturated values of DO with position (Fig. 27) reflect this interpretation of the mass transfer mechanisms as well. §4 Discussion and Conclusions In this paper, the development of several mechanisms for microbubble detachment from customized nozzle banks are presented, with the intention of exploiting fluidic oscillation to result in substantially smaller bubbles. These mechanisms were analyzed theoretically and studied visually to demonstrate that the practically most useful mechanism is a high frequency oscillation which feeds both outlets of the oscillator into adjacent banks of nozzles. With oscillatory flow of 90Hz, the microbubbles produced regularly were nearly uniform in size, spatially separated and non-coalescent, with an estimated average diameter of 700µ from 600µ apertures. With steady flow, the bubbles were approximately 10mm diameter. Although the expectation of theory is that, if the mass transfer coefficient remains roughly constant with decreasing average bubble diameter, the rapidly growing surface area per unit volume will result in much higher mass transfer rates of approximately an order of magnitude higher. Furthermore, smaller bubbles have a much longer residence time, so the oxygen transfer efficiency should be enhanced by this effect as well. However, the critical assumption that the mass transfer coefficient does not vary significantly should be assessed experimentally. The experiment to test mass transfer coefficients and oxygen transfer efficiencies is presented. The measured oxygen transfer efficiencies for the experiment with oscillation gave an OTE of 10.2% 2cm from the plume and without oscillation, 1.4% at the same position. This confirms the intuition that smaller bubbles that are non-coalescent should maintain high transfer rates. The target application, however, is wastewater aeration, which does not used fixed nozzle banks of the custom design employed here. Typically, diffusers with flexible membranes and slits that open and close with the detachment of small bubbles, typically of 1mm

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diameter size. Whether fluidic oscillation can enhance aeration rates in such circumstances is an open question addressed in the accompanying article (Part 2). Nevertheless, gas-liquid transport dynamics are central to many chemical engineering processes that could incorporate a custom designed nozzle bank, as has been recently demonstrated in the design of an airlift loop bioreactor (Zimmerman et al. 2009), and could be useful in biochemical oscillation (Zimmerman, 2005). Many chemical reactors are mixed phase and are mass transfer controlled (Deshpande and Zimmerman (2005a,b), including bubble columns (Heijnen and Van’t Riet, 1984). Generalized flotation mechanisms are much more important as the bubble size decreases, and microhydrodynamics dominates (Grammatika and Zimmerman, 2001). The fundamental principle of superceding the buoyant detachment with inertial/accelerative detachment of a pulse of air can lead to microbubble generation with substantially higher mass transfer rates and therefore potentially energy efficient operation of gas-liquid dynamics. Whether there is an energy cost to pay for the introduction of the fluidic oscillator so that the optimum operating efficiency can be determined for microbubble generation and performance is a question that also arises, and is assessed in Part 2. Acknowledgements WZ would like to thank support from the EPSRC for the development of the acoustic actuated fluidic oscillator (Grant No. GR/S67845) and for financial support from the Food Processing Faraday Partnership, Yorkshire Water, and Sheffield University Enterprises Ltd. WZ would like to thank the Royal Academy of Engineering / Leverhulme Trust Senior Research Fellow programme. The authors wish to acknowledge the support of Simon Butler and Hu Shi and the assistance of Olu Omotowa, Amar Varma, Shu-Chen Kuo, and Xingyan Zhang, as well as helpful discussions with Ilyas Dawood, Andrew Calvert, and Martin Tillotson of Yorkshire Water, Brenda Franklin of AECOM Design Build and Ted Heindel. VT acknowledges the financial support obtained through the research project AV0Z20760514 at the Institute of Thermodynamics of the Academy of Sciences of the Czech Republic. Technical support from Adrian Lumby, Clifton Wray, Mark O’Meara, Andy Patrick, and Oz McFarlane is much appreciated. References ASCE standard, “Measurement of oxygen transfer in clean water,” ACSE Publications, ABSI/ASCE 2-91, 1992. Bredwell, M.D. and Worden, R.M., "Mass-Transfer Properties of Microbubbles. 1. Experimental Studies," Biotechnology Progress, 14(1): 31-38 (1998) Crabtree JR and Bridgwater J, “Chain bubbling in viscous liquids” Chemical Engineering Science, 24: 1755-1768, 1969. Deshpande K.B. and W.B. Zimmerman, ``Experimental study of mass transfer limited reaction. Part I: A novel approach to infer asymmetric mass transfer coefficients’’ Chemical Engineering Science 60(11)2879-2893, 2005a. Deshpande K.B. and W.B. Zimmerman, ``Experimental study of mass transfer limited reaction. Part II: Existence of crossover phenomenon.’’ Chemical Engineering Science 60(15) 4147-4156, 2005b. Diaz M., Komarov S.V., Sano M,: "Bubble Behaviour and Adsorption Rate in Gas Injection through Rotary Lances", ISIJ International, Vol. 37(1), p. 1, 1997 Grammatika M, Zimmerman WB,`` Microhydrodynamics of flotation processes in the sea surface layer,’’ Dynamics of Oceans and Atmospheres, 34:327-348 (2001). Hänel K. Biological treatment of sewage by the activated sludge process, Chichester (Ellis Horwood books in water and wastewater technology): Ellis Horwood, 1988 Heijnen JJ and Van’t Riet K., “Mass transfer, mixing and heat transfer phenomena in low viscosity bubble column reactors.” Chemical Engineering Journal and the Biochemical Engineering Journal 28(2):21-42, 1984. Laplace de (Marquis) P. S.: "Traité de Mécanique Céleste", 4th volume, 1st section (Teéorie de l'action capillaire) of the supplement to Book 10 (Sur divers points relatifs au systéme du monde), publ. by Cez Courier, Paris, 1806.

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Perera P.C., Syred N., “A Coanda Switch for High Temperature Gas Control”, Paper 83-WA/DSC- 26, American Society of Mechanical Engineers, Winter Annual Meeting, Boston 1983. Stevenson D. G.: “Water Treatment Unit Processes” London, Imperial College Press, 1997. Tchobanoglous G., Burton F.L., (Metcalfe & Eddy), Wastewater Engineering: treatment, disposal, and reuse, McGraw-Hill, New York, 1991. Tesa� V.: „A Mosaic of Experiences and Results from Development of High-Performance Bistable Flow-Control Elements”, Proceedings of the Conference 'Process Control by Power Fluidics', Sheffield, United Kingdom 1975. Tesa� V, Pressure Driven Microfluidics, Artech House, Boston, 2007. Tesa� V, Hung C-H., and Zimmerman WB, “No moving part hybrid synthetic jet mixer.” Sensors and Actuators A 125(2):159—169, 2006. Tesar V Travnicek Z Kordik J Randa Z, Experimental investigation of a fluidic actuator generating hybrid-synthetic jets, Sensors and Actuators A 138(1): 213—220, 2007. Tesa� V, Zimmerman WBJ, “Aerator with fluidic oscillator,” UK0621561, 2006. Worden, R.M. and Bredwell, M.D., "Mass-Transfer Properties of Microbubbles. 2. Analysis Using a Dynamic Model," Biotechnology Progress, 14(1): 39-46 (1998). Young T., Philosophical Transactions of the Royal Society (London), 95:65, 1805 Zimmerman W.B. and G.M. Homsy, ``Nonlinear viscous fingering in miscible displacement with anisotropic dispersion.'' Physics of Fluids A 3(8) 1859 (1991). Zimmerman W.B., “Metabolic pathways reconstruction by frequency and amplitude response to forced gylcolytic oscillations in yeast. “Biotech. Bioeng., 92(1): 91-116, 2005a. Zimmerman W.B, Tesa� V, Butler SL, Bandulasena HCH, “Microbubble Generation”, Recent Patents in Engineering, 2:1-8, 2008. Zimmerman W.B, Hewakandamby B.N.,Tesa� V., Bandulasena HCH, Omotowa OA, “On the design and simulation of an airlift loop bioreactor with microbubble generation by fluidic oscillation”. Chemical Engineering Research and Design, IChemE Roadmap to the 21st Century, Special Edition on Biorefineries: New Technologies, in press, 2009.