Abstract
The phase equilibrium of two different nematic phases in a solution of rod-like molecules subjected to a flow field is found by the application of an iterative solution to the Onsager integral equation for the orientational distribution function. It is shown that there exists no isotropic phase but an additional critical point in the phase diagram when a flow field is applied. It is demonstrated that the nematic ordering induced by a flow field, at a certain critical value of the flow parameter, is always accompanied by a phase transition to a highly ordered nematic phase.