  We explore the convergence rate of the Ka\v{c}anov iteration scheme for
different models of shear-thinning fluids, including Carreau and power-law type
explicit quasi-Newtonian constitutive laws. It is shown that the energy
difference contracts along the sequence generated by the iteration. In
addition, an a posteriori computable contraction factor is proposed, which
improves previously derived bounds on the contraction factor in the context of
the power-law model. Significantly, this factor is shown to be independent of
the choice of the cut-off parameters whose use was proposed in the literature
for the Ka\v{c}anov iteration applied to the power-law model. Our analytical
findings are confirmed by a series of numerical experiments.
