Waves, interfacial

The interfacial width obtained from fitting the dPS-LDPE NR profiles is given in Table II. This measured interfacial width is described by a self-consistent mean-field theory, which is broadened by thermally excited capillary waves [2]. The measured interfacial width is given by Gaussian quadrature addition of the intrinsic (unbroadened by capillary waves) interfacial width, Ao, and the interfacial width associated with the capillary waves, Ac. This gives -... 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

The fluctuations of the local interfacial position increase the effective area. This increase in area is associated with an increase of free energy Wwhich is proportional to the interfacial tension y. The free energy of a specific interface configuration u(r,) can be described by the capillary wave Hamiltonian ... 

Capacitance and interfacial tension measurements were used to study the interface between Hg and mixtures of acetone + nitromethane.330 The potential was measured against an SCEin H20 and corrected for the liquid junction potential by measuring the half-wave potential of the ferrocene-... 

Me et al. (2006) addressed the differences in gas-liquid two-phase flow characteristics that occur in conventional size channels and micro-channels by examining the two-phase flow pattern, interfacial wave, void fraction and friction pressure drop data obtained in circular and rectangular channels with a hydraulic diameter ranging from 50 pm to 6.0 mm. 

A theoretical model for the prediction of the critical heat flux of refrigerants flowing in heated, round micro-channels has been developed by Revellin and Thome (2008). The model is based on the two-phase conservation equations and includes the effect of the height of the interfacial waves of the annular film. Validation has been carried out by comparing the model with experimental results presented by Wojtan et al. (2006), Qu and Mudawar (2004), Bowers and Mudawar (1994), Lazareck and Black (1982). More than 96% of the data for water and R-113, R-134a, R-245fa were predicted within 20%. 

The several industrial applications reported in the hterature prove that the energy of supersonic flow can be successfully used as a tool to enhance the interfacial contacting and intensify mass transfer processes in multiphase reactor systems. However, more interest from academia and more generic research activities are needed in this fleld, in order to gain a deeper understanding of the interface creation under the supersonic wave conditions, to create rehable mathematical models of this phenomenon and to develop scale-up methodology for industrial devices. 

In the past five years, it has been demonstrated that the QELS method is a versatile technique which can provide much information on interfacial molecular dynamics [3 9]. In this review, we intend to show interfacial behavior of molecules elucidated by the QELS method. In Section II, we present the principle and the experimental apparatus of the QELS along with the historical background. The dynamic collective behavior of molecules at liquid-liquid interfaces was first obtained by improving the time resolution of the QELS method. In Section III, we show the molecular collective behavior of surfactant molecules derived from the analysis of the time courses of capillary wave frequencies. Since the... 

The molecular collective behavior of surfactant molecules has been analyzed using the time courses of capillary wave frequency after injection of surfactant aqueous solution onto the liquid-liquid interface [5,8]. Typical power spectra for capillary waves excited at the water-nitrobenzene interface are shown in Fig. 3 (a) without CTAB (cetyltrimethy-lammonium bromide) molecules, and (b) 10 s after the injection of CTAB solution to the water phase [5]. The peak appearing around 10-13 kHz represents the beat frequency, i.e., the capillary wave frequency. The peak of the capillary wave frequency shifts from 12.5 to 10.0kHz on the injection of CTAB solution. This is due to the decrease in interfacial tension caused by the increased number density of surfactant molecules at the interface. Time courses of capillary wave frequency after the injection of different CTAB concentrations into the aqueous phase are reproduced in Fig. 4. An anomalous temporary decrease in capillary wave frequency is observed when the CTAB solution beyond the CMC (critical micelle concentration) was injected. The capillary wave frequency decreases rapidly on injection, and after attaining its minimum value, it increases... 

Where is the applied interfacial voltage and Aq i/2 is the half-wave potential of the IT reaction. 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

In order to clarify the reason for the coupling of the redox reaction between O2 and CQH2 with the ion transfer at the W/DCE interface in system of Eq. (25), current-scan polarograms for ion transfers at the W/DCE interface (cf. curves 3 to 5 in Fig. 5) were compared with that for the interfacial redox reaction (cf. curve 1 in Fig. 8). From the comparison, it is clear that transfers of TPenA" " and TBA+ from W to DCE proceed at potentials in Range A where the polarographic wave due to the redox reaction... 

Dynamic surface tension has also been measured by quasielastic light scattering (QELS) from interfacial capillary waves [30]. It was shown that QELS gives the same result for the surface tension as the traditional Wilhelmy plate method down to the molecular area of 70 A. QELS has recently utilized in the study of adsorption dynamics of phospholipids on water-1,2-DCE, water-nitrobenzene and water-tetrachloromethane interfaces [31]. This technique is still in its infancy in liquid-liquid systems and its true power is to be shown in the near future. 

In both cases, the half-wave potential shifts by RT/ ziF)vaN per pH unit, and a typical example of such a behavior is given in Fig. 9 for the transfer of two acidic fi-diketones at the water-nitrobenzene interface. These results were unexpected, since a current wave is measured at a pH where the compound of interest is by a very large majority neutral, but they in fact represent the typical behavior of ionizable compounds at the ITIES and prove that the interfacial potential and the transfer of protons plays a key role for the distribution in biphasic systems. 

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