We study the unwinding of the ferrocholesteric helical structure induced by a combined action of a magnetic field and a shear flow. Both influences are able to induce the ferrocholesteric-ferronematic transition independently; however, the differences between the magnetic field orientation and the flow alignment direction lead to a competition between magnetic and hydrodynamic mechanisms of influence on the ferrocholesteric structure. We analyze various orientations of a magnetic field relative to the direction of a shear flow. The pitch of the ferrocholesteric helix is obtained as function of the strength and the orientation angle of the magnetic field, the shear velocity gradient and a reactive parameter. Phase diagrams of ferrocholesteric-ferronematic transition and the pitch of the ferrocholesteric helix as functions of the material and the governing parameters are calculated. We find out that imposing a shear flow leads to a shift of the magnetic field threshold. The value of the critical magnetic field depends on the magnetic field orientation, the velocity gradient, and the viscous coefficients. We show that the interplay of a magnetic field and a shear flow can induce reentrant orientational transitions that are ferrocholesteric-ferronematic-ferrocholesteric.
Keywords: ferrocholesteric; helix unwinding; liquid crystals; magnetic field; shear flow.