JETP Letters: issues online

In this work we present a simple qualitative model to describe shear rheological behavior of the twist-bend nematic liquid crystals (N_TB). We find that at relatively low shear rate ( ${\dot \gamma } \leq {\dot \gamma}_{c1}$ ) the stress tensor σ created by this shear strain, scales as $\sigma \propto {\dot \gamma }^{1/2}$ . Thus the effective viscosity decreases with the shear rate ( $\eta \propto {\dot \gamma }^{-1/2}$ ) manifesting so-called shear-thinning phenomenon. At intermediate shear rate ${\dot \gamma }_{c1} \leq {\dot \gamma} \leq {\dot \gamma }_{c2}$ , σ is almost independent of ${\dot \gamma }$ (a sort of plateau), and at large shear rate ( ${\dot \gamma } \geq {\dot \gamma}_{c2}$ ), $\sigma \propto {\dot \gamma }$ , and it looks like as Newtonian rheology. Within our theory the critical values of the shear rate scales as ${\dot \gamma }_{c1}\propto ({\tilde {\eta }_2^0}/{\tilde {\eta }_3^0})^2$ , and ${\dot \gamma}_{c2} \propto ({\tilde {\eta }_2^0}/{\tilde {\eta }_3^0})^4$ respectively. Here ${\tilde \eta }_2^0$ and ${\tilde \eta }_3^0$ are bare coarse grained shear viscosity coefficients of the effective smectics equivalent to the N_TB phase at large scales. The results of our work are in the agreement with recent experimental studies.