General Equations and Simulation Procedures

The simulations in this and following sections are based on the continuum theory of weak viscoelastic nematodynamics [22, 23]. The closed set of constitutive equations 

Equation (11.1) is coupled with anisotropic equation for the evolution of extra 

In Eqs. (11.1) and (11.2), is a characteristic nematic viscosity, 0o = t)o/Go nd 0 ( 0o) are relaxation times, and k, are the elastic and viscous tumbling parameters, respectively, a, p, and n, r2 are parameters characterizing anisotropy, n n is dyadic with components nitij, e and w are strain rate and vorticity tensors, 

The shearing flows are commonly analyzed using a standard Cartesian coordinate system % = %i, X2,X where Xi is directed along the flow and X2 along the velocity gradient. In this coordinate system, the velocity vector v is v = y t)x2,0,0, and the tensors of strain rate e(f) and vorticity m(t) for homogeneous shearing flows have the matrix forms  

the shear rate -/(t) is a given function of time. We will use below a common simplifying assumption that vector of director is located in shear plane, so the 2D expression for director is n = ni,n2,0. Substituting this expression along 

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