Maximum bubble pressure experiment

The kinetics of the adsorption process taking place at the surface of a growing drop or bubble is important for the interpretation of data from drop volume or maximum bubble pressure experiments. The same problem has to be solved in any other experiment based on growing drops or bubbles, such as bubble and drop pressure measurements with continuous, harmonic or transient area changes (for example Passerone et al. 1991, Liggieri et al. 1991, Horozov et al. 1993, Miller at al. 1993, MacLeod Radke 1993, Ravera et al. 1993, Nagarajan Wasan 1993). 

The diagram in Fig. 5.26 shows schematically the ratio between the experimental time t, which is the life time of a drop or bubble in the respective experiment, and the effective adsorption time Tg. It becomes clear that each experimental method works under specific conditions and, therefore, different relations between a specific experimental time and the effective adsorption time or surface age exist. While the effective age igina maximum bubble pressure experiment... 

There is one point important to note here, the experimental data plotted as y( - 1) must cross the ordinate at a value identical to the surface tension of the surfactant-free system, i.e. the surface tension of water for a water/air interface. This is often not the case, in particular for drop volume or maximum bubble pressure experiments where due to the peculiarities of the measurement an initial surfactant load of the interface exists. It has been demonstrated in the book by Joos [16] that even in these cases, assumed it is the initial period of the adsorption time, the slope of the plot y( /t) yields the diffusion relaxation time defined by Eq. (4.26) and hence information about the diffusion coefficient. For small deviation from equilibrium we have the relationship... 

A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. 

Fundamental knowledge about the behavior of charged surfaces comes from experiments with mercury. How can an electrocapillarity curve of mercury be measured A usual arrangement, the so-called dropping mercury electrode, is shown in Fig. 5.2 [70], A capillary filled with mercury and a counter electrode are placed into an electrolyte solution. A voltage is applied between both. The surface tension of mercury is determined by the maximum bubble pressure method. Mercury is thereby pressed into the electrolyte solution under constant pressure P. The number of drops per unit time is measured as a function of the applied voltage. 

Methods. All experiments were performed at 25°C. Critical micelle concentrations were determined using the maximum bubble pressure method on a SensaDyne 6000 surface tensiometer. Dry nitrogen was used as the gas source for the process and was bubbled through the solution at a rate of 1 bubble/sec. Cmc s measured using the Wilhemy plate method were in agreement with those obtained from the bubble tensiometer however, the bubble pressure method was used since it is less susceptible to error due to impurities and the nitrogen environment makes pH control easier. 

In fig. 1.30 the surface tension of a sodium dodecylsulfate (NaDS) solution, as measured by the maximum bubble pressure is given. The maximum age of the bubble replaces the time axis. Very fast processes cannot be obtained, so the range of y 72 mN m for t - 0 is not attainable. This experiment illustrates the well-known complication of the hydrolysis of NaDS to produce the strongly surface... 

Fig. 8.3 Schematic diagram of a maximum bubble pressure apparatus used to study the mercury electrolyte solution interface. The pressure applied to the mercury in reservoir R is measured as a function of the shape of the emerging mercury bubble at the capillary tip T. The pressure is a maximum when this shape is hemispherical. The experiment is carried out for different voltages V applied between the reference electrode and the mercury reservoir.

Under certain circumstances, the contact angle between Hg and the solution can change with applied potential. For this reason, the maximum bubble pressure method which is independent of contact angle is preferred (see section 8.2). This technique is easily adapted to computer-controlled experiments. 

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 maximum bubble pressure technique is a classical method in interfacial science. Due to the fast development of new technique and the great interest in experiments at very small adsorption times in recent years, commercial set-ups were built to make the method available for a large number of researchers. Rehbinder (1924, 1927) was apparently the first who applied the maximum bubble pressure method for measurement of dynamic surface tension of surfactant solutions. Further developments of this method were described by several authors (Sugden 1924, Adam Shute 1935, 1938, Kuffiier 1961, Austin et al. 1967, Bendure 1971,... 

In a recent paper Miller et al. (1994d) discussed parallel experiments with a maximum bubble pressure apparatus and a drop volume method (MPTl and TVTl from LAUDA, respectively), and oscillating jet and inclined plate instruments, performed with the same surfactant solutions. As shown in Fig. 5.27, these methods have different time windows. While the drop volume and bubble pressure methods show only a small overlap, the time windows of the inclined plate and oscillating jet methods are localised completely within that of the bubble pressure instrument. 

Experiments with a maximum bubble pressure and a drop volume set-up were performed with aqueous solutions of an oxyethylated para-tertiary butyl phenol with 10 EO-groups, pt-BPh-EOIO (synthesised and purified by Dr. G. Czichocki, Max-Planck-Institut fur Kolloid- und Grenzflachenforschung Berlin). The dynamic surface tension of a 0.025 mol/1 solution of pt-BPh-EOlO is shown in Fig. 5.30. 

One of the reasons of the insufficient reliability of micellisation kinetics data determined from dynamic surface tensions, consists in the insufficient precision of the calculation methods for the adsorption kinetics from micellar solutions. It has been already noted that the assumption of a small deviation from equilibrium used at the derivation of Eq. (5.248) is not fulfilled by experiments. The assumptions of aggregation equilibrium or equal diffusion rates of micelles and monomers allow to obtain only rough estimates of the dynamic surface tension. An additional cause of these difficulties consists in the lack of reliable methods for surface tension measurements at small surface ages. The recent hydrodynamic analysis of the theoretical foundations of the oscillating jet and maximum bubble pressure methods has shown that using these techniques for measurements in the millisecond time scale requires to account for numerous hydrodynamic effects [105, 158, 159]. These effects are usually not taken into account by experimentalists, in particular in studies of micellar solutions. A detailed analysis of... 

For data obtained by the maximum bubble pressure method, such a correction is needed as the bubble grows during the experiment. 

Actually, the maximum bubble pressure technique is not suitable for long time experiments. Due to the small size of a single bubble, the experiment is very sensitive to smallest temperature changes. However, for relatively large system volumes, a self-generation of bubbles with longer lifetimes is possible. This method as known as the so-called stopped flow method (Fainerman and Miller 1998). 

The two methods maximum bubble pressure and profile analysis tensiometry complement each other experimentally and cover a total time range of nine orders of magnitude from about lO" seconds up to 10 seconds (many hours). The example given in Fig. 33 shows the dynamic surface tension of two Triton X-100 solutions measured with the instruments BPA and PAT (SINTERFACE Technologies) over the time interval of 7 orders of magnitude. As one can see, the experiments cover the beginning of the adsorption process and the establishment of the equilibrium state. 

In laboratory experiments and field applications the gas is delivered to the rock face either as continuous gas or as a course gas-liquid dispersion. In both cases, for the gas to move into the porous medium, the gas pressure at the rock face must be higher than the capillary entry pressure. For a gas finger or a bubble train to advance through the porous medium, the face pressure must be maintained at a level above the maximum capillary pressure that the gas finger or bubble train will experience along its path through the medium. 

Example 1 Application of FUG Method A large butane-pentane splitter is to be shut down for repairs. Some of its feed will be diverted temporarily to an available smaller column, which has only 11 trays plus a partial reboiler. The feed enters on the middle tray. Past experience with similar feeds indicates that the 11 trays plus the reboiler are roughly equivalent to 10 equilibrium stages and that the column has a maximum top vapor capacity of 1.75 times the feed rate on a mole basis. The column will operate at a condenser pressure of 827.4 kPa (120 psia). The feed will be at its bubble point (q = 1.0) at the feed tray conditions and has the following composition on the basis of 0.0126 kg-mol/s (100 Ib-mol/h) ... 

As a final point in this section, we should mention that as the bubble trains advance through the constricted channels, the capillary resistance will assume its maximum value (the mobilization pressure) only when the lamellae in the train assume their most unfavorable positions with respect to displacement. At other times, the capillary resistance will be below this maximum value with the result that the actual work required to maintain foam flow at a given rate will be below that which would be required if the mobilization pressure was operative at all times. This is easily understood if one pushes a bubble through a single constriction in a tube and notes that the pressure in the train builds up to the mobilization pressure as the drainage surface advances into the constriction and then rapidly falls as the front bubble experiences a Haines jump. To account for such effects in the present model, the Km term in Equation 63 would vary with time as the bubble train moved through the constricted channels. 

If an experiment is performed at an overall composition equal to x in figure 3.2d, the vapor-liquid envelope is first intersected along the dew point curve at low pressures. The vapor-liquid envelope is again intersected at its highest pressure, which corresponds to the mixture critical point at T2 and x. This mixture critical point is identified with the intersection of the dashed curve in figure 3.2b and the vertical isotherm at T2. At the critical mixture point, the dew point and bubble point curves coincide and all the properties of each of the phases become identical. Rowlinson and Swinton (1982) show that P-x loops must have rounded tops at the mixture critical point, i.e., (dPldx)T = 0. This means that if the dew point curve is being experimentally determined, a rapid increase in the solubility of the heavy component will be observed at pressures close to the mixture critical point. The maximum pressure of the P-x loop will depend on the difference in the molecular sizes and interaction energies of the two components. 

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