PERMEATION FLOWS IN CHOLESTERIC LIQUID CRYSTAL POLYMERS UNDER OSCILLATORY SHEAR

We investigate the permeation flow of cholesteric liquid crystal polymers (CLCPs) subject to a small amplitude oscillatory shear using a tensor theory developed by the authors [8]. We model the material system by the Stokes hydrodynamic equations coupled with the orientational dynamics. At low frequencies, the steady permeation modes are recovered and the director rotates in phase with the applied shear. At high frequencies, the out of phase component dominates the dynamics. The asymptotic formulas for the loss modulus (G '') and storage modulus (G') are obtained at both low and high frequencies. In the low frequency limit, both the loss modulus and the storage modulus are shown to exhibit a classical frequency omega dependence (G '' proportional to omega, G' proportional to omega(2)) with the proportionality of order O(Er) and O(q), respectively, where 2 pi/q defines the pitch of the chiral liquid crystal and Er is the Ericksen number of the liquid crystal polymer system. The magnitudes of dimensionless complex flow rate and complex viscosity are calculated. They are shown to have two Newtonian plateaus at low and high frequencies while a power-law response at intermediate frequencies.