Role of shear in the isotropic-to-lamellar transition

In the isotropic-to-lamellar transition, nonlinear fluctuation terms lower the transition temperature ${\tau }_c$ and drive the transition first order. Here we show that steady shear, by suppressing the fluctuations, raises ${\tau }_c$; in a certain temperature range the lamellar phase can be induced by applying shear. A study ofo the effective potential indicates that the transition remains first order, though becoming very weak at high shear rate. We argue heuristically that the lamellar ordering first occurs with wave vector normal to both the velocity and the velocity gradient.