  In this work we present a simple qualitative model to describe shear
rheological behavior of the twist-bend nematic liquid crystals. We find that at
relatively low shear rate the effective viscosity decreases with the shear rate
manifesting so-called shear-thinning phenomenon. At intermediate shear rate the
stress is almost independent of the shear rate (a sort of plateau), and at
large shear rate Newtonian rheology takes place. Within our theory we estimate
the critical values of the shear rate in terms of coarse grained shear
viscosity coefficients of the effective smectics equivalent to the twist-bend
phase at large scales. The results of our work are in the agreement with recent
experimental studies.
