Bubble formation/detachment

Janssen and Hoogland (J3, J4a) made an extensive study of mass transfer during gas evolution at vertical and horizontal electrodes. Hydrogen, oxygen, and chlorine evolution were visually recorded and mass-transfer rates measured. The mass-transfer rate and its dependence on the current density, that is, the gas evolution rate, were found to depend strongly on the nature of the gas evolved and the pH of the electrolytic solution, and only slightly on the position of the electrode. It was concluded that the rate of flow of solution in a thin layer near the electrode, much smaller than the bubble diameter, determines the mass-transfer rate. This flow is affected in turn by the incidence and frequency of bubble formation and detachment. However, in this study the mass-transfer rates could not be correlated with the square root of the free-bubble diameter as in the surface renewal theory proposed by Ibl (18). 

Steep temperature gradients inside the catalyst layer will enhance the bubble formation and bring about efficient product desorption and effective regeneration of vacant active sites consequently. There irreversible processes are followed by another irreversible act of bubble detachment from the surface. 

Fig. 5 shows the simulated air-bubble formation and rising behavior in water. For the first three bubbles, the formation process is characterized by three distinct stages of expansion, detachment, and deformation. In comparison with the bubble formation in the air-hydrocarbon fluid (Paratherm) system, the coalescence of the first two bubbles occurs much earlier in the air-water system. Note that the physical properties of the Paratherm are p — 870kg/m3, Pi — 0.032 Pa - s, and a — 0.029 N/m at 25 °C and 0.1 MPa. This is due to the fact that, compared to that in the air-Paratherm system, the first bubble in the air-water system is much larger in size and hence higher in rise velocity leading... 

The bubble is now assumed to detach when its center has covered a distance equal to the sum of the radius of the final bubble arid the radius of the orifice. If the radius of the orifice is R and if it is assumed that V0 = (4tt/ 03/3), then the time of bubble formation can be obtained by plotting on the same axes Eq. (9) and (r + K) as a function of time from Eq. (8). 

The above equation is applicable when the bubble detaches at s = rF. But if the orifice diameter is large, the authors recommend the use of the relation s = (rF + 2 ) to obtain a better value of the time of bubble formation. Then Eq. (39) is modified to... 

There exists the maximum amount of contradiction regarding the role of viscosity in bubble formation. The present model indicates that for both the stages of expansion and of detachment—... 

In the absence of surface tension influences, the drop formation at vertical orifices is expressed by the equation given for bubble formation. The force due to kinetic energy of the liquid is neglected as its component is zero in the vertical direction. The drop ascends right from the beginning according to the equation of motion and detaches when it has covered a distance equal to the diameter of the nozzle. 

The drop formation is considered to proceed exactly in the same fashion as the bubble formation under constant flow conditions, viz. the two step (the expansion and detachment) mechanism. The tensile force does not arise in the expansion stage because there is no neck formation. 

In the bubble formation from a horizontal surface, the bubble development and the bubble detachment are coupled. When the buoyancy of a developing bubble overcomes the bubble attachment force due to the interfacial tension, the bubble detaches from the surface and completes the process of the bubble formation. A higher flow rate of air in the low flow rate regime (e.g., 0.2-30 seem) simply increases the frequency of the bubble formation but does not change the volume of bubble [1]. 

In the bubble formation from an inclined surface, however, the bubble development and the bubble detachment processes are decoupled because a developing bubble could drift out of the orifice due to the component of the buoyancy parallel to the inclined surface. Once a sessile bubble drift out of the orifice, the bubble development ceases because no air is fed into a sliding bubble. Since the bubble development and detachment are decoupled, the flow rate of air becomes an important factor, which controls the frequency of sliding bubble... 

The flow rate of air simply inereases the frequeney of bubble formation and detachment, and has no effect on the size of bubble as depicted in Figure 34.25 for a... 

The mechanism of bubble formation by nucleation requires supersaturation of the dissolved gas [11-13] and a nucleus radius greater than the critical [7], The main sources of heterogeneous nucleation are usually surface irregularities capable of containing entrapped gas, e.g. pits and scratches. The bubbles typically develop over the electrode surface, grow in size until they reach a break-off diameter and subsequently detach into the electrolyte. After detachment, some residual gas remains at the nucleation site and another bubble will form at the same place [2,13,14], In most two-phase flow simulations [15-19], it is assumed that bubbles detach with a constant diameter, although from experiments [20,21] it is know that electrochemically formed bubbles show a size distribution. 

The probability of formation of stable particle-bubble aggregates is determined by the probabilities of its attachment and retention on the bubble. The detachment is affected either by gravity or by inertia. These forces are proportional to the volume of particles, i.e. as the cube of the linear dimension of a particle hence, they are very big for large particles and very small for fine particles. This trivial fact results in radical consequences when analysing the role played by the size of particles in the mechanism of the elementary act of flotation (Derjaguin Dukhin 1960, 1979). 

In the standard version of the MPTl measuring cell the dead time is of the order of 70-80 ms. To decrease down to 10 ms it is necessary the decrease the length of the capillary 1 and the volume of detaching bubbles. The bubble volume can be controlled by the distance between the capillary tip and the electrode located opposite to it (cf Fig. 5.12). For different lengths of the capillary reproducible and accurate bubble formation was possible under the conditions summarised in Table 5F.1. 

FIGURE 15.31 Stages in subcooled pool boiling as the surface heat flux is increased, (a) no bubble formation (natural convection heat transfer) (6) bubbles grow but do not detach (c) bubbles increase in number and some detach to condense in the bulk liquid (d) bubbles become so numerous that they coalesce to form a continuous vapor layer on the heated surface (from Hewitt et al. [13], with permission. Copyright CRC Press, Boca Raton, FL). 

The subject of diffusion-controlled bubble growth is, of course, a rather small part of the large subject of bubble dynamics, whose scope is too broad to be included in this review. Specifically excluded are cavitation bubbles, whose collapse is inertia rather than diffusion controlled, the formation and detachment of bubbles from orifices, oscillations of bubbles in a pressure field, and the challenging subject of the mechanism of nucleate boiling heat transfer, in which bubble formation and detachment must certainly play a dominant role. 

Electrolytic gas evolution is a complicated and important problem in many industrial processes. The details of bubble formation and the effects of the bubbles presented in this review are but the microscopic aspects of a phenomenon that affects the macroscopic behavior of electrochemical cells. The knowledge summarized here applies in part to the even larger world of boiling liquids in which bubbles also nucleate, grow, coalesce with each other, and detach. In general, the sudden appearance of a phase much less dense than its parent phase will always be an important phenomenon for research because that phase will profoundly affect the process in which it appears. 

Ppg is the radius of the detached bubble and <7 is the surface tension of the liquid used. During bubble formation, the bubble is moving along the impeller at a velocity of 2nNR( -K). The physical process of bubble detachment has been described by Rielly et al. (1992). Accordingly, the detached babble radius was calculated from... 

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