On the Ginzburg–Landau expression for the free energy of solutions under flow

The classical Ginzburg–Landau expression for the free energy has been used as an ingredient in the description of shear-induced effects in polymer solutions. However, terms of the form c• u• c (c being the concentration and u the barycentric velocity of the fluid) have never been considered in the free energy. Since these terms yield corrections to the structure factor which are of a similar form as the effects derived from the dynamical equations, the justification of the existing literature requires to show that the new terms are small in comparison with the previous ones. It is shown here that the contribution of the previously neglected terms is of the order of 4% of the total shear-induced shift of the critical temperature.