V.5 No 1

39

On physical processes in showering arcs

To estimate the amplitude of force constricting liquid areas of the contact surface in electric field with the strength 2,510⁸ V/m, consider a simplified model of plane capacitor whose plates are approximately twice larger than the bridge diameter d_m =1,4 m. We have to account that alternating pattern of electric field does not cause an alternating-in-sign constriction, as sign change on the capacitor plates will anyway excite the force directed to lessen the between-plate gap.

To reach this aim, we have to determine the value of charge accumulated on the plate surface. Given we consider a plane capacitor disregarding the edge effects, its capacitance will be [34, p. 161]

where C is the capacitance in F; is the dielectric permeability of material, in our case we can take it equal to 1; S is the active area of plates in cm²; n is the number of plates, in our case two; and h is the between-plates distance in cm.

We can determine the active area of plates, taking them disk-shaped with the diameter, as above, twice larger than the bridge diameter. Then

Taking h = 8010^-4 cm , we yield

The charge on the plates we will yield by a standard formula

Thus, the charge density on the plates is

On the grounds of (19) and knowing the field strength in the capacitor, we can determine the electric field pressure exerted on the plates. With it we have to note, given the said above, that electric field will be pulsing, so we can estimate just the average electric pressure whose expression will be the following:

We see that electric field exerts a great effect on plates, which in our case are liquid surfaces of electrodes in the region of showering arcs. And we intentionally substituted all intermediate computations to (20) in order to show electric pressure dependent on potential difference on the plates and on the between-plates distance. When decreasing distance, electric pressure grows as the square of distance decrease.

Next, it will be natural to compare the yielded value of electric pressure with the surface strain of material of electrodes which prevents the surface layers of electrode from bridge extracting. For it, we have to determine the work which electric pressure supplied by electric pressure when extracts the bridge. We have to account that during the showering arcs development, both electrodes are heated and on them both the liquid holes are produced in the regions of discharge, i.e. in the regions from which the bridge is pulled loose. Hence, though for each electrode the electric pressure delivers the work proportional to about a half of gap, the value of electric pressure grows twice faster on the account of bridge pulled loose from the second electrode. Thus, noting (20), the work of electric pressure can be estimated as

As we see, the work which electric pressure is able to develop unlimitedly grows with decreasing distance between the surfaces producing the bridge. So if electrodes consist liquid holes, or, as in case of fixed capacitors, the plate has been soldered in not so rigid as needed, the bridge producing, when begun, will go on up to full closing of surfaces. In any case, this is typical for the gap values considered in our problem. For larger gaps, when there is not enough material of holes to strap the gap, we will observe plasma jets which will be described below.

An important property of the described process is the condition under which the bridge extraction can begin. This condition is easy to yield, comparing the work delivered by electric pressure with that of surface resistance with surface of liquid metal warped by dh from the initial plane state. Proceeding from (21), the work of electric pressure will be

To determine the work delivered by the surface pressure, let us think the pulled loose surface as a spherical segment with diameter equal to that of bridge d_m and with height dh. Then the value of initial area of surface from which the bridge is pulled loose will be determined by an expression for the circle area,

The area of segment of height dh is known to be

Thus, the work of surface strain delivered when pulling loose the surface of liquid hole will be

From (25) we see that the work of surface strain at the initial instant of bridge formation is a first-order small in comparison with the work of electric pressure determined by (22). This speaks that forces of electric pressure have available all conditions necessary to pull loose the bridge from liquid holes in the contact surfaces formed in the region of showering arcs. The rate of bridge extraction will much depend on the degree of metal heating in the holes and on the material of contacts which in its turn has an effect on the rate of metal pulling. Furthermore, the proportion, of material of which contact the bridge will form preferably - and hence, the erosion of contact pair, - will depend on these parameters. And in case of heterogeneous materials of contacts, the proportion can vary during the showering arcs growth and changed conditions of bridge production with growing contact gap, and as the sign of potential applied to moving contact can affect erosion, too. But with all complicacy of affection of these factors on the bridge formation, the very fact that bridge formation occurs due to electric pressure exceeding the surface strain is obvious.