Duocel® foams are often used as porous electrodes, thus predicting the electrical conductivity is a valuable design tool. It should be no surprise that the low amperage, direct current bulk electrical conductivity of Duocel® foam has the same form of equation as that for the bulk thermal conductivity. In its electrical form, it is:
Csolid ligaments = Csolid × relative density × .33
Csolid ligaments = low amperage direct current electrical conductivity of the 3-D ligament array
Csolid = conductivity of the solid material of the struts
Relative density = % relative density in decimal form, i.e. 10% = .1
.33 = coefficient representing the foam structure geometric or “tortuosity” factor.
It should be noted that the .33 coefficient is derived both from conductivity tests and conceptual analysis wherein the foam can be analogized to a three-dimensional orthogonal pin fin array. In this case is it obvious that one third of the pins or pin mass are oriented in each of the orthogonal x, y, and z directions.
It should also be noted, as with the thermal form of the equation, that this is a somewhat simplified form that does not address electrical transients, alternating current, or large amperages where induced electromagnetic effects may significantly alter the predicted conductivity.