Bubbles detachment

Zeng et al. (1993) proposed that the dominant forces leading to bubble detachment could be the unsteady growth force and buoyancy force. In order to derive an accurate detachment criterion from a force balance, all forces should be accurately known. If a mechanism is not known precisely, then approximate expressions, one or two fitted parameters and comparison with experiments might offer a solution. Such fitting procedures have indeed been applied (Klausner et al. 1993 Mei et al. 1995a Helden et al.l995). 

The bubble layer is assumed to have constant void fraction along the length before DNB, with a balanced rate of bubble detachment and bubble condensation in the layer. Hence, the average properties p, p, and c of the bubble layer are assumed to be independent of position. 

Bowring, R. W., 1962, Physical Model, Based on Bubble Detachment and Calculation of Steam Voi-dage in the Subcooled Region of a Heated Channel, Inst, for Atomenergie Rep. HRP-10, Oslo, Norway. (3)... 

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. 4.8 Schematic illustration of the working principle of the dynamic bubble pressure method. If the bubble radius equals the capillary radius, maximum pressure is detected. The pressure minimum occurs on bubble detachment.

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... 

Depending on its subtraction from or addition to the buoyancy force, the continuous phase velocity can either increase or decrease the bubble volume. Normally, this velocity is such that the bubble detaches prematurely from the nozzle tip. Maier (M2) has shown that the shear force experienced by the bubble, which causes its premature detachment, is a maximum when the continuous phase flows at right angles to the nozzle axis. 

The process begins with an air bubble inside the liquid phase. At the surface, the bubble detaches and moves up under gravity. The detergent molecule forms a bilayer in the bubble film. The water in between is the same as the bulk solution. This may be depicted as follows a surface layer of detergent is applied, a bubble forms with air and a layer of detergent, and the bubble at the surface forms a double layer of detergent with some water in between TLF varying from 10 pm to 100 pm). 

This process can be nuclear or film type. In nuclear boiling, bubbles detach themselves quickly from the heat transfer surface. In film boiling the rate of heat transfer is retarded by an adherent vapor film through which heat supply must be by conduction. Either mode... 

Unlike formation in a liquid the boundary of a fluidised bed bubble can only expand by gas flowing across it to produce the drag force that will cause the particles to move appropriately. During the time that a bubble grows to the size shown in Figure 9 the gas that produced it has advanced to fill the volume indicated by the outer broken line. The annular region above and around the bubble now contains an excess of gas and so the powder void-age must increase. This is unstable and as the bubble detaches and rises through the expanded dense phase the powder relaxes and and returns the excess gas to the bubble. This appears to be completed by the time it has risen about one diameter (of order 1/10 second) and thereafter is of constant volume until it coalesces. 

In Grahame (1957), the presence at a liquid surface of a quasi-ice structure was hypothesised. Moreover, study of droplets on inclined planes, and of bubbles clinging to vertical surfaces, reveals behaviour (contact angle hysteresis) which cannot be accounted for without such an ice film. On a vertical wall, a bubble experiences an upward buoyancy force, but in the absence of an ice film, a zero restraining force. The restraining force is made evident by the phenomenon of contact angle hysteresis, followed by film rupture as bubble growth occurs, and leads to bubble detachment. 

The critical conditions for contact base expansion and bubble detachment can be seen as... 

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... 

Zeng, L.Z., Klausner, J.F. and Mei, R. (1993) A unified model for the prediction of bubble detachment diameters in boiling systems-1. Pool boiling, International Journal of Heat and Mass Transfer, Vol. 36, pp. 2261-2270. 

Typical flow pattern for flow boiling are shown in Fig. 5. For subcooled boiling and high liquid flow rate, the observed bubble detachment size is smaller than the gap size. The treatment of the data showed that correlation [26] obtained for a large tube flow boiling can be applied to predict subcooled flow boiling heat transfer in a confined space. For saturated flow, the vapor bubbles have a tendency to merge and produce the... 

Because of gas evolving in the gravity field, the industrial two-phase electrolysis processes generally use vertical electrodes to promote bubble detachment and avoid gas accumulation. This is the reason why the present work focuses upon vertical electrodes. 

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. 

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