Source term for contunuity
 

In my continuity equation owing to density difference i have to write a source term udf. the source term is,

source term= ∂/∂t[∝(ρl-ρs)fs ]-∇[∝.fs.ρl.ul]

where ∝ = the volume of fraction variable
fs = solid fraction
ul = Velocity vector
ρl and ρs = liquid and solid density respectively
how to go about it?

do i have to differentiate the term?
or can i simply discretize the equation with respect to temperature and space and put it in the udf?
what do i have to put in dS[eqn] term?

Please anybody who has experience reply.