An effect of dividing the momentum equations with ϕc and
ϕd, respectively is that for example
ud obtains a value even if
ϕd = 0. In many cases
ud will tend to
uc in lack of a dispersed phase. So on inlets where
ϕd = 0, it is appropriate to set
ud = uc.
A fixed value for ϕd should only be prescribed if there is no transport of
ϕd toward the inlet. If, for example, a cloud of dispersed phase with higher
ϕd than the prescribed value somehow reaches the inlet,
ϕd will actually be “consumed”.
