The latter is a convention which we will use throughout this paper. Clearly, $F$ grows to infinity as approaching the singularity, without contradicting the constraint (\[F1\]) and assuring well-behaving solutions without superluminal signals. In this regard, it is rather natural to realize that the value of $F$ should significantly grow in extremely relativistic regimes as near the cosmological singularities. As suggested in [@BK_Bianchi], we assume that in the region of low density the viscous coefficients can be expressed as power-laws of the energy density with exponents greater than unity, i.e., $$\begin{aligned}
\eta&=\eta_{1}\rho^{\alpha_{1}}, && \zeta=\zeta_{1}\rho^{\beta_{1}}, &&\rho\rightarrow 0, && \alpha_{1}\geq1, \beta_{1}\geq1. \label{visc1}\end{aligned}$$ It is worth noting that for an incompressible fluid the $\zeta$-terms automatically drop out from the field equations. This is also the case treated in [@BK_Bianchi] because there the bulk viscosity contributions is asymptotically negligible for small energy densities, taking $\beta_{1}>\alpha_{1}$. In our analysis, in order to search for a consistent solution, we assume that the density vanishes faster than the volume $R^{3}$ as the system approaches the singular point $(H,\rho)=(+\infty,0)$ in the $(H,\rho)$ plane[^1]. Moreover, in the right-handed side of equation (\[H\_punto\]) we can retain the quadratic term in $H$ only. Then, the limiting form of the equations (\[H\_punto\]) 