In the homogeneous, 0-D reactor models, Ansys Chemkin allows for the deposition and etching of bulk phase of materials in the reactor, although we do not account for changes in reactor volume or surface area with time due to etch or deposition processes. When there is only a single bulk species in a bulk phase, the bulk species mole fraction is trivially defined as one. When more than one bulk species exist in a bulk phase, the composition of the bulk phase may change with time, requiring solution of the bulk-species mole fraction. For bulk phases that are being deposited, the mole fractions of the bulk-phase species are assumed to be initially unknown and are determined through time-dependent species balance equations for each bulk species:

(8–11)

or

(8–12)

Here is the bulk species mole fraction of the kth species in phase of the m th material. is the film thickness for the nth bulk phase of the m th material. is the average molar concentration of the species in the nth bulk phase of the m th material.

The molar growth rate of the bulk phase , can be written as

(8–13)

while the bulk mass density is defined as

(8–14)

where is the mean molecular weight of the bulk phase. Combining Equation 8–13 and Equation 8–14 with Equation 8–12 and rearranging gives the following relation:

(8–15)

which simplifies to:

(8–16)

The linear growth rate (cm/sec) of the bulk phase on the th material, , is defined as the sum of linear growth rates of all bulk species on the phase

(8–17)

When the linear growth rate is positive, we sometimes refer to it as the linear deposition rate of the bulk phase.

We define the film-thickness length scale, , somewhat arbitrarily. For steady-state, we define it as the linear growth rate of the bulk phase multiplied by the reactor residence time, as given in Equation 8–18 . For transient cases, we use Equation 8–18 , but replace the residence time with the time-step value.

(8–18)

For deposition phases, then, Equation 8–16 and Equation 8–18 provide a false transient equation that is employed for the bulk species:

(8–19)

Note that does not appear in Equation 8–19 ; Ansys Chemkin makes no assumption about the total amount of bulk-phase deposits, other than that their total amount is small compared to the total volume of the reactor. Equation 8–19 is only used when the right-hand side is greater than zero; that is, when there is net deposition of the bulk species. Under etching conditions, the bulk species equations must be treated differently.