Non-Newtonian Rheology in Twist–Bend Nematic Liquid Crystals

Abstract

A simple qualitative model has been presented to describe shear rheological behavior of the twist–bend nematic liquid crystals (NTB). It has been found that at relatively low shear rate (dot {gamma } leqslant {{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}}} leqslant dot {gamma } leqslant {{dot {gamma }}_{{c2}}}, σ is almost independent of dot {gamma } (a sort of plateau), and at large shear rate (dot {gamma } geqslant {{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}{text{/}}tilde {eta }_{3}^{0})}^{2}}, and {{dot {gamma }}_{{c2}}} propto {{(tilde {eta }_{2}^{0}{text{/}}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 NTB phase at large scales. The results of our work are in the agreement with recent experimental studies.