Expanding drop method

A recent development, termed by the inventors microelectrochemical measurements at expanding droplets (MEMED) [29], is a technique based on forming small droplets of a phase containing a reactant in a second immiscible liquid phase (Fig. 5.24). An ultramicroelectrode (UME, see Section 5.3.2.8 and Chapter 6) measures an electrochemical response as the droplet expands towards it, from which a concentration profile can be derived and, hence, the kinetics of related processes. Because the surface is continuously refreshed, it avoids 

The MEMED technique has been used to study the hydrolysis of aliphatic acid chlorides in a water/l,2-dichloroethane (DCE) solvent system [3]. It was shown unambiguously that the reaction proceeds via an interfacial process and shows saturation kinetics as the concentration of acid chloride in the DCE increases the data were well fitted to a model based on a pre-equilibrium involving Langmuir adsorption at the interface. First-order rate constants for interfacial solvolysis of CH3(CH2) COCl were 300 150(n = 2), 200 100(n = 3) and 120 60 s-1( = 8). 

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In the applications of the capillary pressure tensiometry deseribed, an equivalent to Eq. (4.119) is used in the two particular cases in which either the surface tension (pressure derivative method) or the drop curvature (expanded drop method) are constant. In other applications, like the expanding or growing drop methods developed respectively by Nagarajan and Wasan and McLeod and Radke, respectively [25, 154], the capillary pressure is monitored while the surface area is increasing continuously. In these methods APcap changes due to the variation of the drop radius and of the interfacial tension caused by the dilation of the surface which put the system in a state out of the adsorption equilibrium. The problem is that area change, flow in the bulk phases, and the adsorption kinetics of the present surface active compounds have to be considered in a model simultaneously. 

The adsorption kinetics at liquid/liquid interfaces is a more complicated problem, as the transfer of surfactant from one phase to the other has to be taken into account. In the experiments performed by Liggieri and Ravera [197] using the expanded drop method, no preliminary saturation of the oil phase with CjoEOg was made. For this case, instead of Eq. (4.1), the expression (4.94) should be used, where K is the equilibrium distribution coefficient of surfactant between the oil and water phases, and D2 is the surfactant diffusion coefficient in the oil phase. The reduced distribution coefficient defined by = K(D2/Di) is a parameter that reflects quantitatively the adsorption dynamics at such a liquid/liquid interface. 

All drop and bubble methods are based on the Laplace equation of capillarity. In order to study dynamic aspects of adsorption, the growing drop or bubble and the expanded drop methods are suitable (3). In Figure 12.13, the schematic of a static or growing drop instrument is shown. In applications of capillary pressure tensiometry, an equation which is equivalent... 

All the methods are based on the Laplace equation (4.126). While the eapillary pressure method works with drops or bubbles of constant size, the pressure derivative method [194] has been conceived for measuring the interfacial tension of pure liquids. To study dynamic aspects of adsorption the growing drop or bubble [25, 154] and the expanded drop [195, 196] methods have been developed. 

Interfacial dilatational stress is measured in processes of isotropic expansion (compression) of an interface. Such processes are realized in the maximum bubble pressure method [176-180], the oscillating-bubble method [181-183], the pulsed-drop method [184], and the drop-expanding method [39,83,84,185-187]. Because of the simple spherical sjrmmetry equation (81), together with the projection of Eq. (80) along n, yields... 

The mass spectrometer is a very sensitive and selective instrument. However, the introduction of the eluent into the vacuum chamber and the resulting significant pressure drop reduces the sensitivity. The gas exhaust power of a normal vacuum pump is some 10 ml min-1 so high capacity or turbo vacuum pumps are usually needed. The gas-phase volume corresponding to 1 ml of liquid is 176 ml for -hexane, 384 ml for ethanol, 429 ml for acetonitrile, 554 ml for methanol, and 1245 ml for water under standard conditions (0°C, 1 atmosphere). The elimination of the mobile phase solvent is therefore important, otherwise the expanding eluent will destroy the vacuum in the detector. Several methods to accomplish this have been developed. The commercialized interfaces are thermo-spray, moving-belt, electrospray ionization, ion-spray, and atmospheric pressure ionization. The influence of the eluent is very complex, and the modification of eluent components and the selection of an interface are therefore important. Micro-liquid chromatography is suitable for this detector, due to its very small flow rate (usually only 10 p min - ). 

The adsorption and desorption kinetics of surfactants, such as food emulsifiers, can be measured by the stress relaxation method [4]. In this, a "clean" interface, devoid of surfactants, is first formed by rapidly expanding a new drop to the desired size and, then, this size is maintained and the capillary pressure is monitored. Figure 2 shows experimental relaxation data for a dodecane/ aq. Brij 58 surfactant solution interface, at a concentration below the CMC. An initial rapid relaxation process is followed by a slower relaxation prior to achieving the equilibrium IFT. Initially, the IFT is high, - close to the IFT between the pure solvents. Then, the tension decreases because surfactants diffuse to the interface and adsorb, eventually reaching the equilibrium value. The data provide key information about the diffusion and adsorption kinetics of the surfactants, such as emulsifiers or proteins. 

In the J-resolved projection, the aromatic rings of the SCAL are clearly present where as the polymer resonances have dropped out of the spectrum. In addition, the proton coupling constants arising from alloc group are readily measured as seen in the expanded spectrum (Fig. 13). If a more detailed measure of the couplings is desired, then the full 2D J-resolved spectrum can be evaluated in the normal manner as exemplified in Fig. 14. A similar method to obtain accurate proton-proton coupling constants based on E.COSY spectra has also appeared recently (43). 

Even though there is a great potential in the chemical EOR methods to considerably expand the World oil reserves, they still remain marginal [116, 117] more than 30 years after an unprecedented research effort to understand how petroleum is trapped in an oil reservoir and to develop technologies was carried out. The drop of crude oil price in the early 80s has probably been the main reason for this but a second main limiting issue still to be settled is the incomplete understanding of the interconnection between all occurring processes. 

The surface area expansion process in Figure 3.5 must obey the basic thermodynamic reversibility rules so that the movement from equilibrium to both directions should be so slow that the system can be continually relaxed. For most low-viscosity liquids, their surfaces relax very rapidly, and this reversibility criterion is usually met. However, if the viscosity of the liquid is too high, the equilibrium cannot take place and the thermodynamical equilibrium equations cannot be used in these conditions. For solids, it is impossible to expand a solid surface reversibly under normal experimental conditions because it will break or crack rather than flow under pressure. However, this fact should not confuse us surface tension of solids exists but we cannot apply a reversible area expansion method to solids because it cannot happen. Thus, solid surface tension determination can only be made by indirect methods such as liquid drop contact angle determination, or by applying various assumptions to some mechanical tests (see Chapters 8 and 9). 

Using the classical methods of Celestial Mechanics, we can expand the distance A in the Hamiltonian (19) as a function of the Poincare variables, and we can calculate the so called secular system at order two in the masses (used, for instance, in Laskar 1988 in a model with 8 planets, to study the long term evolution of the solar system). In the secular system the dependency on the angles Ai, A2 (which evolve much faster than the other Poincare variables) is dropped out by simply averaging the Hamiltonian over the angles themselves. Thus, the actions Ai, A2 are first integrals for the secular system, which are replaced with their numerical values corresponding to the data for the real system Sun-Jupiter-Saturn at a fixed initial time. Therefore, we can actually expand the secular Hamiltonian as a power series in the form... 

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