I want to determine the surface tension (interfacial tension) for two fluids with different viscosities by conducting some bubble tests with different diameters. I use multicomponent SC model. I have found several papers in which the results of bubble tests for fluids with same TAU (or viscosity) have been reported, but I could not find any for two fluids with different viscosities. May anyone help me to find such results which I can use for verifying my code?
Another question is that what is the relation between surface tension and viscosity ratio of two fluids?

I think that the surface tension and the viscosity ratio of the two fluids are two independent quantities. Surface tension is the energy density of the surface (a static property), viscosity tells us something about momentum diffusion (dynamic property). Thus I see absolutely no reason why there should be a connection between the surface tension and the viscosity ratio of the two fluids.

I agree with you about the independancy of surface tension and viscosity ratio. But my numerical simulations show that surface tension deponds on viscosity ratio. Additionally, when both fluids have the same viscosity, using higher viscosity results in highjer surface tension (the results of simulation when tau1=tau2=0.9 is different from the result when tau1=tau2=1.1).
I am wondering if there is a bug in my program or a it is a inherent defect in SC formulation.

If you change the numerical viscosity (relaxation time) you also change the conversion factors between lattice and physical quantities. This - of course - also affects the physical value of the surface tension.
Whenever you change the numerical viscosity, make sure that you know the change of the physical time step (I assume the lattice constant is conserved). This modified time step will result in a modified conversion factor for the surface tension. I bet that the surface tension will be correct if you take this into account.