Sinusoidal area changes

Figure 3.41. Response of a viscoelastic monolayer to a sinusoidal area change (a). Peuiels (b), (c) and (d) represent the elastic, viscous lnd total response of the Interfaclal tension. Schematic.

In the drop shape technique sinusoidal area changes can be easily generated via changes of the drop volume in a very accurate way. The Fourier analysis of the surface tension response however shows that besides the main mode with the period T of the generated oscillation there are also modes with periods of 3T/2, T/2, T/4 and T/8. The origin of these modes is not yet fully understood but certainly caused by deviation of the area changes from harmonicity and surface layer compression/expansion beyond the limits of a linear theory. 

Drop and bubble shape tensiometry is a modem and very effective tool for measuring dynamic and static interfacial tensions. An automatic instrument with an accurate computer controlled dosing system is discussed in detail. Due to an active control loop experiments under various conditions can be performed constant drop/bubble volume, surface area, or height, trapezoidal, ramp type, step type and sinusoidal area changes. The theoretical basis of the method, the fitting procedure to the Gauss-Laplace equation and the key procedures for calibration of the instrument are analysed and described. 

The experimental results shown in Figure 12.10 demonstrate the capacity of the drop and bubble shape technique. After the adsorption process has reached an equilibrium state, over a period of time of about 6 h, some square pulses of the drop area are subsequently, produced. Such area perturbations are suitable for determining the surface dilational elasticity of the interfacial layer. Efficient dosing systems even allow a sinusoidal area change, again providing information... 

The techniques used to measure dilational surface properties have been described in detail (4, 6). Surfaces of surfactant solutions are subjected to small amplitude, sinusoidal area variations, and the dilational modulus is given by the ratio between surface tension change measured and fractional area change applied. The modulus generally depends on the frequency at which the experiment is carried out, and this frequency... 

The software driven apparatus allows different types of area changes step and ramp type, square pulse and trapezoidal as well as sinusoidal area deformations. The construction ensures that area changes are almost isotropic. Area changes used in transient and harmonic relaxation experiments are of the order of 1 to 5%. The surface tension response measured via the Wilhelmy balance has an accuracy of better than 0.1 mN/m. 

The change in interfacial tension during a sinusoidal surface area change for a sunflower oil drop in a protein solution at a eomparatively low oscillation frequency is shown in Fig. 18. Due to flie time required for image acquisition in the ADSA experiments faster oscillations are not possible wifliout the use of VCR (with a frame frequency of 25 Hz one can perform oscillation experiments at a maximum frequency of 1 Hz). 

Although no direct comparison with other commercial products are given we can state that the instrument PATl discussed here has the best features in respect to interfacial rheology studies. It provides a comfortable function generator for any type of transient and harmonic relaxation studies and also the theoretical tools to analyse trapezoidal and sinusoidal relaxation experiments. The on-line control of the interfacial area changes is very accurate and the oscillations performed in the range between 0.01 and 0.2 Hz are ideally smooth sinusoidal functions in contrast to experiments performed with other instruments. 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

After the accomplishment of the above mentioned experiment on the nonlinear viscoelasticity of the DPPE thin film, we have tried to construct a new instrument for the measurement of the dynamic surface tension. We have noticed that, the blades used to change the surface area in the commercial instrument, did not show genuine triangle or sinusoidal trajectory but rather mathematically undefined. With our newly designed instrument, the time change of the surface area can be controlled according to a chosen function with the aid of a micro-computer. 

Figure 16 shows the experimental arrangement for the measurement of the surface pressure. The trough (200 mm long, 50 mm wide and 10 mm deep) was coated with Teflon. The subphase temperature was controlled within 0.1 C by means of a jacket connected to a thermostated water circulator, and the environmental air temperature was kept at 18 °C. The surface tension was measured with a Wilhelmy plate of platinum(24.5 x 10.0 x 0.15 mm). The surface pressure monitored by an electronic balance was successively stored in a micro- computer, and then Fourier transformed to a frequency domain. The surface area was changed successively in a sinusoidal manner, between 37.5 A2/molecule and 62.5 A2/molecule. We have chosen an unsaturated phospholipid(l,2-dioleoyl-3-sn-phosphatidyI-choline DOPC) as a curious sample to measure the dynamic surface tension with this novel instrument, as the unsaturated lipids play an important role in biomembranes and, moreover, such a "fluid" lipid was expected to exhibit marked dynamic, nonlinear characteristics. The spreading solution was 0.133 mM chloroform solution of DOPC. The chloroform was purified with three consecutive distillations. 

When a chemical or biochemical reaction takes place in the sensor area, only the light that travels through this arm will experience a change in its effective refractive index. At the sensor output, the intensity (I) of the light coming from both arms will interfere, showing a sinusoidal variation that depends on the difference of the effective refractive indexes of the sensor (Neff,s) and reference arms (Neff,R) and on the interaction length (L) ... 

The traditional way is to measure the impedance curve, Z(co), point-after-point, i.e., by measuring the response to each individual sinusoidal perturbation with a frequency, to. Recently, nonconventional approaches to measure the impedance function, Z(a>), have been developed based on the simultaneous imposition of a set of various sinusoidal harmonics, or noise, or a small-amplitude potential step etc, with subsequent Fourier- and Laplace transform data analysis. The self-consistency of the measured spectra is tested with the use of the Kramers-Kronig transformations [iii, iv] whose violation testifies in favor of a non-steady state character of the studied system (e.g., in corrosion). An alternative development is in the area of impedance spectroscopy for nonstationary systems in which the properties of the system change with time. 

Chronic congestion leads to an enlarged and plump liver with a dark red (purplish) colour. The central veins are dilated. In continued congestion, stasis paths develop between the central veins, resulting in the formation of confluent stasis areas. Various degrees of fatty changes in the liver cells as well as pigment deposits (lipofuscin, ceroid) appear. In the course of time, fibrosis of sinusoidal reticular fibres takes place fibroses can also be observed... 

As a measure of the deformation of the area, i.e. of the strain, the relative change in interfacial area AA/A (= dlnA for very small deformations) is taken. For a sinusoidal variation of the interfacial area, the relative change in the strain d In A may be written as ... 

Three corrugated ducts are schematically shown in the insets of Fig. 5.59. Hu and Chang [265] have analyzed the / Re for fully developed laminar flow in circumferentially corrugated circular ducts with n sinusoidal corrugations over the circumference as shown in Fig. 5.59, inset a, for e = da = 0.06. The perimeter and hydraulic diameter of these ducts must be evaluated numerically. However, their free flow area Ac is given by Ac = m2(l + 0.5e2). 

For very small sinusoidal changes of the interfacial area of hemispherical drops the pressure amplitude can be calculated from the force balance. The measured pressure amplitude can be written as the sum of a geometric (radius) component, a contribution caused by changes in the interfacial tension Ay, and a hydrodynamic contribution. The dynamic pressure can be described by Eq. (4.129). 

FIGURE 28.18 Mouse liver 2 h after p.o. administration of 140 pg/kg gambierol. Prominent congestions of sinusoidal capillaries appeared at the periphery and fatty changes (white) appeared in the central area. P portal veins, C central vein. (Reprinted from Ito et al. Toxicon, 42, 733, 2003. With permission from Elsevier.)... 

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