Bubble growth surface pressure effect

The growth of the bubble induces a micro-convective flow on the electrolyte that pushes each bubble from an ideal center of the surface ( active site ) in various radial directions (Figure 14.5). When each bubble attains a certain size, the buoyancy exceeds its adhesion and the bubble leaves the surface producing a drag flow. However, in the electrochemical cell, the radial and the azimuthal directions produces the opposite drag flow to the platinum surface displaying the so-called surface pressure effect. 

From the adduced dependencies, it can be seen that at small values of AC — the approximate dependencies (22.14) to (22.16) can lead to exaggerated values for the bubble radius. With the increase of AC — digressions from the true value of R shift to the region of smaller values of yo — y. Thus, at AC rp the capillary pressure has a noticeable effect only at the initial stage of bubble growth. At yo > 10", the radius Rh of the bubble that achieves the layer surface (y = 0) is determined to a sufficient accuracy by the formula... 

Some results of the numerical solution of Eqs. (22.60) are shown in Figs. 22.5 to 22.7. Dependences on parameters f and n that characterize the influence of the surfactant, and also on the parameter K that determines the influence of pressure, are of greatest interest. At small values of r, the effect of the surfactant causes a reduction of surface tension, and the bubble grows faster than it would grow in the absence of the surfactant. At n = 0, the surfactant layer on the surface does not impede the transition of dissolved substance into the bubble, and the influence of the surfactant is manifest only in the reduction of surface tension. With an increase of n, the rate of bubble growth slows down considerably. An increase of the parameter K (the fall of pressure poo) results in enhancement of the bubble growth rate. Fig. 22.6 shows the change of surface concentration of surfactant at K = 4.45 n = 0 xioo = 1, and = 1 for various values of fi. An in-... 

The acoustic pressure amplitude determines the growth of a cavitation bubble and consequently the chemical effects upon collapse. The amplitude of the pressure wave can be measured with a hydrophone or can he calculated using a calorimetric method (9,10), in which it is possible to determine the ultrasoimd power (Qus) that is transferred to the liquid. With the ultrasound power and the surface area of the ultrasound source (Aus), the acoustic amplitude can he calculated according to equation (2), for which the ultrasoimd intensity is the power input divided by the surface area of the source (11). 

By combining the Rayleigh-Plesset equation with a mass and energy balance over the bubble, the temperature and pressure in the bubble can be calculated (16,17). The model also describes the dynamic movement of the bubble wall, which results in a calculated radius of the cavitation bubble as a fimction of time (see Fig. 2). The explosive growth phase and the collapse phase of the bubble can clearly be distinguished. Moreover, in case dynamic effects are more important than the surface tension, the cavitation threshold can be calculated with the dynamic model, while the Blake threshold pressure cannot be used at these conditions. 

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