Interfacial tension time dependence

For example, the solid can swell in contact with a certain liquid or even interact by chemical interfacial reactions it can also be partially dissolved. In the case of polymer surfaces, the molecular reorientation in the surface region under the influence of the liquid phase is assumed to be a major cause of hysteresis. This reorientation or restructuring is thermodynamically favoured at the polymer-air interface, the polar groups are buried away from the air phase, thus causing a lower solid-vapour interfacial tension. In contact with a sessile water drop, the polar groups turn over to achieve a lower solid-liquid interfacial tension. Time-dependent changes in contact angles can also be observed (33). 

The time required to conduct an interfacial tension experiment depends largely on the properties of the surfactants and less on the chosen measurement method. A notable exception is the drop volume technique, which, due to the measurement principle, requires substantial ly more time than the drop shape analysis method. Regardless of the method used, 1 day or more may be required to accurately determine, e.g., the adsorption isotherm (unit D3.s) of a protein. This is because, at low protein concentrations, it can take several hours to reach full equilibrium between proteins in the bulk phase and those at the surface due to structural rearrangement processes. This is especially important for static interfacial tension measurements (see Basic Protocol 1 and Alternate Protocols 1 and 2). If the interfacial tension is measured before the exchange of molecules... 

Dynamic Methods In dynamic methods, determination of is based on the time evolution of a fluid element shape, from a non-equilibrium to an equilibrium state. The evolution is driven by the interfacial tension and, depending on the initial shape of the element, it can follow different dependencies. 

There are a number of techniques available to measure the surface or interfacial tension of liquid systems, which together cover a wide range of time. In many cases, several methods are required in order to receive the complete surface tension time dependence of a surfactant system. One of the important points in this respect is that the data obtained from different experimental techniques have to be recalculated such that a common time scale results, i.e. one has to calculate the effective surface age from the experimental time, which is typically determined by the condition of the methods. For example, the maximum bubble pressure... 

Fig. 11-13. Apparatus for measuring the time dependence of interfacial tension (from Ref. 34). The air and aspirator connections allow for establishing the desired level of ftesh surface. IV denotes the Wilhelmy slide, suspended from a Cahn electrobalance with a recorder output.

The phase separation process at late times t is usually governed by a law of the type R t) oc f, where R t) is the characteristic domain size at time t, and n an exponent which depends on the universality class of the model and on the conservation laws in the dynamics. At the presence of amphiphiles, however, the situation is somewhat complicated by the fact that the amphiphiles aggregate at the interfaces and reduce the interfacial tension during the coarsening process, i.e., the interfacial tension depends on the time. This leads to a pronounced slowing down at late times. In order to quantify this effect, Laradji et al. [217,222] have proposed the scaling ansatz... 

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

The dependence of the interfacial tension at the W/NB interface on the interfacial potential difference [29,30] was investigated by using an aqueous solution dropping electrode [26,31]. In this investigation, the aqueous solution was forced upward dropwise in NB and the drop time of W was measured as a function of potential difference applied at the W/ NB interface. When W contained 1 MMgS04 and NB contained 4 x 10 " M Cs" TPhB ... 

The retention time tR necessary to give adequate separation of the liquids will depend on their densities and interfacial tension, and on the form of the dispersion, and can only be determined experimentally for that mixture. The retention time is given by ... 

The second complicating factor is interfacial turbulence (1, 12), very similar to the surface turbulence discussed above. It is readily seen when a solution of 4% acetone dissolved in toluene is quietly placed in contact with water talc particles sprinkled on to the plane oil surface fall to the interface, where they undergo rapid, jerky movements. This effect is related to changes in interfacial tension during mass transfer, and depends quantitatively on the distribution coefficient of the solute (here acetone) between the oil and the water, on the concentration of the solute, and on the variation of the interfacial tension with this concentration. Such spontaneous interfacial turbulence can increase the mass-transfer rate by 10 times 38). 

While the quasistatic method is quite accurate, it requires a long time to determine a complete adsorption kinetics curve. This is because a new drop has to be formed at the tip of the capillary to determine one single measurement point. For example, if ten dynamic interfacial tension values are to be determined over a period of 30 min, -180 min will be required to conduct the entire measurement. On the other hand, the constant drop formation method is often limited because a large number of droplets have to be formed without interruption, which may rapidly empty the syringe. Furthermore, the critical volume required to cause a detachment of droplets depends on the density difference between the phases. If the density difference decreases, the critical volume will subsequently increase, which may exacerbate the problem of not having enough sample liquid for a complete run. 

If the interface is chosen to be at a radius r, then the corresponding value for dV13/dA is r /2. The pressure difference T>f) — Pa can in principle be measured. This implies that pp pa 2-y/r and l,f) — Pa = Pf /r are both valid at the same time. This is only possible if, dependent on the radius, one accepts a different interfacial tension. Therefore we used 7 in the second equation. In the case of a curved surface, the interfacial tension depends on the location of the Gibbs dividing plane In the case of flat surfaces this problem does not occur. There, the pressure difference is zero and the surface tension is independent of the location of the ideal interface. 

We start this chapter with electrocapillarity because it provides detailed information of the electric double layer. In a classical electrocapillary experiment the change of interfacial tension at a metal-electrolyte interface is determined upon variation of an applied potential (Fig. 5.1). It was known for a long time that the shape of a mercury drop which is in contact with an electrolyte depends on the electric potential. Lippmann1 examined this electrocapillary effect in 1875 for the first time [68], He succeeded in calculating the interfacial tension as a function of applied potential and he measured it with mercury. 

Viscosity and density of the component phases can be measured with confidence by conventional methods, as can the interfacial tension between a pure liquid and a gas. The interfacial tension of a system involving a solution or micellar dispersion becomes less satisfactory, because the interfacial free energy depends on the concentration of solute at the interface. Dynamic methods and even some of the so-called static methods involve the creation of new surfaces. Since the establishment of equilibrium between this surface and the solute in the body of the solution requires a finite amount of time, the value measured will be in error if the measurement is made more rapidly than the solute can diffuse to the fresh surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d national meeting, Repr. 30, Atlanta, 1960) found that measurements of the surface tension of sodium lauryl sulfate solutions by maximum bubble pressure were higher than those by DuNuoy tensiometer by 40 to 90 percent, the larger factor corresponding to a concentration of about 100 ppm, and the smaller to a concentration of 2500 ppm of sulfate. 

The computational fluid dynamics investigations listed here are all based on the so-called volume-of-fluid method (VOF) used to follow the dynamics of the disperse/ continuous phase interface. The VOF method is a technique that represents the interface between two fluids defining an F function. This function is chosen with a value of unity at any cell occupied by disperse phase and zero elsewhere. A unit value of F corresponds to a cell full of disperse phase, whereas a zero value indicates that the cell contains only continuous phase. Cells with F values between zero and one contain the liquid/liquid interface. In addition to the above continuity and Navier-Stokes equation solved by the finite-volume method, an equation governing the time dependence of the F function therefore has to be solved. A constant value of the interfacial tension is implemented in the summarized algorithm, however, the diffusion of emulsifier from continuous phase toward the droplet interface and its adsorption remains still an important issue and challenge in the computational fluid-dynamic framework. 

Figure 1. Time dependence of interfacial tensions at the air-water interface for WPC at different initial subphase concentrations. The WPC is dispersed in 0.2M NaCl solution in the upper figure and in distilled water in the lower (4).

When the powder particle melts, it wets the substrate (Figure 10-12). The liquid is pulled over the surface by a line tension a. This depends on the interfacial tensions of liquid, solid and gas it is lower than the surface tension. This tension is counteracted by forces due to the viscosity r]. The flattening will also depend on the initial size Rq of the drop. Finally you would expect the drop to become flatter with increasing time t. 

The additional charge and the corresponding additional surface tension are time-dependent quantities in which the equilibrium between the bulk and the interface is not established. The irreversible contribution can be separated from the reversible by considering the time dependence, if the experimental time scale allows for such a test. Time-dependent effects can be observed by impedance measurements at different frequencies. For gold, as an example, impedance measurements showed spectra characteristic for equilibration processes at least over a time scale of 0.1 ms to 100 s. Gold also shows a surface reconstruction depending on the potential [148]. Fortunately, the variation of the interfacial strain with potential is usually so small that the original Lippmann equation (41) for a solid is practically the same as for a liquid electrode 1149]. 

Figure 3.10a shows the time courses of the interfacial tension when the hydrophilic anions were added into the oil phase. The concentrations of these ions were set at 1.0 x 10 M. Here, desorption rate of each case was determined by 1/Ar, where At is the period for the interfacial tension to become the initial value again after the oscillation. The At values of each ion (Cl , Br and I ) were 110, 150 and 1000 seconds, respectively. Figure 3.10b shows the dependence of the desorption rate of the DS ions on AGi w of Cl , Br and 1 from nitrobenzene to water. We can consider that the desorption rate is proportional to the exponential of —AG - /RT R gas constant, T temperature). We plotted the dependence of the log value of the desorption rate (ln(l/Ar)) on the standard free energy of transfer from the interface to the water phase (AGi w). The solid straight line with the slope — /RT R 8.314 J mol , T 298 K) was obtained... 

Flow of the blend at melt temperatures generally stretches the discontinuous phase from its initial shape. Interfacial tension between the immiscible components will oppose this process and attempt to drive the system to a low-energy spherical-morphology state. Studies of these phenomena in a rheometer permit the estimation of the time required for both processes and the interfacial tension [90-93]. Alternatively, one can estimate the time required for the latter process, and the interfacial tension, from the evolving shape of the discontinuous phase using either a fiber break-up [94,95] or fiber-retraction [33,96] experiment. Interfacial tension depends on the molecular weight of each component [96,97] and on temperature, so it is preferable to measure interfacial tension for the materials of interest at their fabrication temperature. 

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