Bubble diffusion region

Once the bubbles leave the electrode surface (when they have a radius equal to the departure radius) they diffuse into the bubble diffusion region. This region has a very high bubble concentration [12] with a typical thickness of a few millimetres. The bubbles can still grow. 

Figure 3.8 Schematic representation of the bubble layer structure (according to Janssen [67] and Boissonneau and Byrne [12], with kind permission from Springer Science+Business Media). Three regions axe identified the adherence region, the bubble diffusion region, and the bulk region.

The bubbles in the inter-electrode gap (bubble diffusion region and bulk region) increase the inter-electrode resistance, as they affect the electrical conductivity of the electrolyte. The parameter describing this increase is the gas void fraction e, defined as the fraction between the volume of gas and the total volume of liquid and gas. Several relations are used in the electrochemical literature to quantify this effect. The most widely used are the relations from Bruggeman [16] ... 

Let us first start with the description of the bubble diffusion region that is directly accessible to visual observations. The important parameters that characterise the bubble diffusion region are the gas void fraction e and the geometrical shape of the bubble layer, both of which are dependent on the cell geometry. We will restrict the discussion to the case that is most representative of micromachining with electrochemical discharges the case of a thin electrode dipped inside an electrolyte. The electrochemical cell is much larger than the electrode. 

The consequence of the existence of the bubble diffusion region is that the potential distribution at a gas evolving electrode contains an additional potential drop compared with Equation (3.22) ... 

The expression for R(9) contains three contributions. The first is the resistance of the bulk electrolyte. The second is due to the bubble diffusion region. As discussed in Section 3.4, this contribution is almost constant. The third comes from the shielding effect of the bubbles growing on the electrode surface. This contribution is a function of 0. A possible ansatz for R(9) is (see also Fig. 3.11 and the corresponding discussion) ... 

Note that, in this description, the shadowing of the surface by the bubbles in the adherence region was not considered. With increasing bubble coverage fraction 6, the resistance in the diffusion region ff will also increase. A possible ansatz is to write (3.44) as ... 

Fig. 3. Thresholds of cavitation. Region A Bubble growth through rectified diffusion only. Region B Bubble growth through transient cavitation. RD, Threshold for rectified diffusion Rlt threshold for predomination of inertial effects RB, Blake threshold for transient cavitation. [After R. E. Apfel (S).]...

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