Inter-electrode resistance

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] ... 

To describe the contribution to the inter-electrode resistance a simplified model will be used. Let us assume that the bubble diffusion layer has a mean thickness d, and that the gas void fraction is constant and equal to e over the whole electrode height h. The efficient conductivity of the electrolyte is... 

Equation (3.68) does not constitute a close description of the mean stationary I—U characteristics unless the expression for the apparent inter-electrode resistance R(9) is known. 

This is the ohmic region. For higher currents, 6s will grow and significantly affect the inter-electrode resistance. The current will saturate at its maximal... 

Increase in the nominal current density With increasing nominal current density I/A, the bubble coverage fraction increases. When it reaches a critical value, as computed by (4.16), a gas film is formed. Such a scenario happens, for example, in current-controlled cells or, as will be seen in Section 4.1.3, in a voltage-controlled cell if for some reason the inter-electrode resistance decreases. 

In order to estimate the gas film formation time, the bubble evolution equation (3.61) is used. For simplicity, it is considered that the inter-electrode resistance R 6) may be estimated using ... 

Figure 4.10 Voltage step input for various voltages in the case of a high inter-electrode resistance. Reprinted from [130] with the permission of the Journal of Micromechanics and Microengineering.

A third way to influence the critical voltage is to play with the inter-electrode resistance. As seen in Equation (3.73), the higher the inter-electrode resistance, the higher will be the critical voltage. If low terminal voltages are desired for electrochemical discharges, attention has to be paid to the electrode geometry and the electrical conductivity of the electrolyte in order to minimise the inter-electrode resistance. 

Depending on the inter-electrode resistance, the gas film formation may be fast (a few milliseconds) if formed electrochemically (Section 4.1.2) and/or by joule heating (Section 4.1.1), or the gas film formation may be slow (a few seconds) in the case of a hybrid process (Section 4.1.3). As the gas film is unstable (i.e., the gas film often collapses and has to be built up again), the gas film formation time is an important parameter for the mean machining speed of SACE. 

Figure 6.5 Example of SACE glass gravity-feed drilling with a 0.4 mm stainless steel tool-cathode at 31 V in the case of high inter-electrode resistance. In situation (a) the gas film needs to be built up more often than in situation (b). This results in an overall slower machining for situation (a) than situation (b). Reprinted from [130] with the permission of the Journal of Micromechanics and Microengineering.

The decrease in the material removal rate with decreasing inter-electrode resistance is not specific to glass drilling. The same effect was also observed in Si3N4 drilling [97]. 

The counter-electrode chosen should be as large as possible and made up of a material that is resistant to the electrolyte used. For sodium hydroxide, a good choice is stainless steel or nickel. As the counter-electrode is generally used with anodic polarisation, one should be aware that some electrochemical dissolution will take place. If the electrode surface is very large, current densities will remain small and therefore limit anodic dissolution of the electrode material. The geometry of the counter-electrode should be such that the inter-electrode resistance will remain constant during machining. This resistance should also... 

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