Unusual condition between two fluids

Hello, i`m new here, then sorry if this is a silly question...

I need to set the follow condition in the interface between two fluids:

ro_v*u_v*hfg = ro_l*u_l*hfg = lambda_v*(dTv/dx) - lambda_eff*(dTl/dx)

Where:
ro = density
u = velocity
lambda = condutivity
hfg = latent heat

That is a balance of heat flux.
I must find an boundary condition that lets me set the velocities in the interface, for the two fluids, following that condition.

Someone have any idea, please??