Bubble, dead time

The most suitable technique for studying adsorption kinetics and dynamic surface tension is the maximum bubble pressure method, which allows measurements to be obtained in the millisecond range, particularly if correction for the so-called dead time, t. The dead time is simply the time required to detach the bubble after it has reached its hemispherical shape. A schematic representation of the principle of maximum bubble pressure is shown in Figure 18.14, which describes the evolution of a bubble at the tip of a capillary. The figure also shows the variation of pressure p in the bubble with time. 

The idea of a maximum bubble pressure instrument is that the pressure inside a growing bubble passes through a maximum. The pressure maximum is reached at a hemispherical bubble size. After the maximum has passed the bubble grows fast and finally detaches. For quantitative interpretation of bubble pressure experiments details are required on the time scale of the bubble growth (cf Fig. 5.8). First of all, the dead time, needed by a bubble to detach after it has... 

The time for bubble growth to a hemisphere t, is the difference between the total bubble time Tb and the dead time x, p and L are pressure and gas flow rate and p and are the respective values at a critical point. From considerations discussed above about adsorption processes at the surface of growing drops it is concluded that the situation with the growing bubble is comparable, at least until the state of the hemisphere. Then, the process runs without specific control and leads to an almost bare residual bubble after detachment due to the very fast bubble growth. 

To separate the surface lifetime from the total time interval between subsequent bubbles an approximation of the dead time according to geometric parameters of capillary and bubble volume was derived Fainerman Lylyk (1982) and Fainerman (1990). A substantial improvement for the exact determination of surface lifetime and its calculation was carried out by Fainerman (1992) who defined a critical point in the experimental curve in co-ordinates "pressure-gas flow rate". This point corresponds to a change in the flow regime from individual bubble formation to a gas jet regime. The calculation of the so-called effective age the surface (effective adsorption time) from the bubble surface lifetime was discussed by different authors ... 

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. 

The coefficient takes values between = 2 / 3 (ideal sphere) and = 1 (conditions in the MPTl (Fainerman et al. 1994a). In the moment of bubble detachment this coefficient can reach values > 1. Hence, the effective life time of the bubble during this second stage of its growth (effective dead time) results to... 

Liquid line from the condenser to the accumulator. This location is only feasible when the line is continually filled with condensate. This location gives a good dynamic response (unobstructed by the accumulator lag), and a representative sample (some vapor bubbles may be present, but because vapor density is much smaller than liquid, this has little effect on the analysis). Drawbacks of this location include an inaccurate correlation with product composition when the reflux drum is vented fairly long sample lines additional dead time in the sample line (because liquid and not vapor is sampled). This method evades the major drawbacks to the other two, and is frequently recommended (258, 301, 309, 332) whenever feasible. The author shares this view. 

The results of Fig. 16 illustrate for water and a C BMPO solution how the bubble time tb = td + ti and dead time td can be determined via the gas flow oscillation method with measurement systems of different gas volume. For a given liquid, the td vs tb dependence is almost independent of Vg. 

Figure 16. The dependence of the dead time td on the bubble time tb = td + ti for water (2) and C12DMPO solution (1) for the capillary radius 0.85 mm and system volumes Vg = 1.5 ( ), 3.7 ( ), 4.5 (A) and 20.5 ml (A) lines 1 (C12DMPO solution) and 2 (water) are calculated from Eq. (49).

This fact is in agreement with the maximum bubble pressure theory (Fainerman and Miller 1998), and indicates that the use of a bubble deflector is important. The deflector is employed to ensure a stable bubble size irrespective of the formation frequency, and, therefore, the dead time remains approximately constant for a fixed pressure in the system. This can be seen from the data for water as shown in Fig. 16. The variation of the system pressure is taken into account via the Poiseuille equation. The lines 1 and 2 were calculated from the system pressure according to the procedure ... 

The asterisks refer to the corresponding parameters in the critical point. Therefore, the dead time in the critical point L (shown by an arrow in Fig. 16) for the capillary employed is 11.0 and 11.5 ms for water and the C12DMPO solution, respectively. The lines calculated from Eq. (49) agree quite well with the measured values. At the same time, the results indicate that the minimum dead time determined from gas flow oscillations is about 1 ms lower than the calculated value. This difference results from the hydrodynamic effects which occur at high bubble formation frequencies and are considered so far only in the software of the BPA. At a fixed bubble volume, any increase of the capillary radius results in a decrease of the dead time, and vice versa. 

The calculation of dead time can be simplified when taking into account the existence of two gas flow regimes for the gas flow leaving the capillary bubble flow regime when t > 0 and jet regime when t = 0 and hence tt = ta- Figure 11.25 shows a typical dependence of p on L. 

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