Non-Newtonian Rheology in Twist-bend Nematic Liquid Crystals

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 ((gamma) over dot <= (gamma) over dot(c1)) the stress tensor sigma created by this shear strain, scales as a sigma proportional to (gamma) over dot(1/2). Thus the effective viscosity decreases with the shear rate (eta proportional to (gamma) over dot(-1/2)) manifesting so-called shear-thinning phenomenon. At intermediate shear rate (gamma) over dot(c1) <= (gamma) over dot <= (gamma) over dot(c2), sigma is almost independent of (gamma) over dot (a sort of plateau), and at large shear rate ((gamma) over dot >= (gamma) over dot(c2)), sigma proportional to (gamma) over dot and it looks like as Newtonian rheology. Within our theory the critical values of the shear rate scales as (gamma) over dot(c1) proportional to ((eta) over tilde (0)(2)/(eta) over tilde (0)(3))(2), and (gamma) over dot(c2) proportional to ((eta) over tilde (0)(2)/(eta) over tilde (0)(3))(4) respectively. Here (eta) over tilde (0)(2) and (eta) over tilde (0)(3) 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.