  Second-order dissipative hydrodynamic equations for each component of a
multi-component system are derived using the entropy principle. The shear
viscosity of the whole system, appearing in the equation summed-up over all
components, is related to the partial shear pressures and cannot be considered
as an external parameter. We demonstrate that it is essential to solve
hydrodynamic equations for each component, instead of treating a mixture as an
effective one-component system with a free parameter $\eta/s$. Thus,
extractions of the $\eta/s$ value of the QGP at RHIC and LHC have to be
reexamined.
