Homogeneous nucleation of new bubbles within an element i of the sample may be explored through use of an Arrhenius expression for the nucleation rate per unit volume,
| Ji = φpiBN exp( − EN /RT) , | (42) |
where the pre-exponential factor BN and activation energy EN are parameters to be set by the user. The number of nucleation sites to be established within element i during any given timestep is determined by the accumulation of fractional values
| Ni = Ni + JiΔt | (43) |
for the element over time. Whenever the value of exceeds one, the appropriate number of bubbles of zero volume are distributed at random locations within Ni the element, and the remainder of Ni is left to accumulate toward the next nucleation event. If any element is devoid of bubbles, a nucleation site is provided. At least one bubble is necessary to receive the gases generated within the element during the next timestep.