The effect of an axial magnetic field on the Poiseuille flow of nematicp-azoxyanisole (PAA) has been computed using the Ericksen-Leslie continuum theory. The apparent viscosity decreases appreciably in the presence of the magnetic field. Orientation and velocity profiles for different shear rates and magnetic fields are presented.

It is shown that the essential features of Helfrich’s permeation model for flow along the helical axis of a cholesteric liquid crystal can be derived approximately on the basis of the Ericksen-Leslie theory.

The paper discusses the theory of Couette flow of a nematic liquid crystal. The apparent viscosity, orientation and velocity profiles are computed forp-azoxyanisole as functions of shear rate and magnetic field for symmetric and asymmetric molecular alignments at the boundaries and for different relative radii of the cylinders. For symmetric homeotropic boundary condition an azimuthal field exhibits a threshold analogous to a Freedericksz transition. An expression is also derived for the Freedericksz threshold in the hydrostatic case.

The flow of a nematic liquid crystal between plane parallel plates, with one plate moving with uniform velocity relative to the other, is discussed. The apparent viscosity, orientation and velocity profiles are computed forp-azoxyanisole as functions of shear rate and magnetic field for symmetric and asymmetric molecular alignment at the plates. For symmetric homeotropic boundary condition, a magnetic field applied along the flow direction exhibits a threshold reminiscent of a Freedericksz transition in the hydrostatic case. In general the apparent viscosity for the asymmetric boundary condition is less than that for the symmetric case.

The effect of a magnetic field on the instability threshold in shear flow and plane Poiseuille flow of nematics has been worked out for the case of unperturbed director orientation normal to the plane of shear. The critical shear rate for the onset of instability has been studied as a function of destabilising field. The dependence of the time constantν on shear and field for time dependent perturbations in shear flow is found to be explained by two solutions which differ from one another to the extent that wave vectors which are real for one solution are imaginary for the other; these solutions exist for different ranges of shear and field but have one common point where they yield the sameν value making possible a continuous description ofν. In Poiseuille flow even for a destabilising field applied along the primary velocity the occurrence of an instability associated with net secondary flow (flow transverse to the primary velocity) is found to be more favourable than one having no secondary flow. This trend is also observed for low destabilising fields applied along the velocity gradient but for higher fields the occurrence of an instability without net secondary flow becomes more favourable. Simultaneous application of a stabilising electric field does not change the qualitative nature of the results.

Steady cholesteric flow at low shear rate normal to the helical axis is studied analytically for shear flow and plane Poiseuille flow on the basis of Leslie’s continuum theory. For general asymmetric solutions the angle made by the director at the sample centre with the primary flow is found to profoundly affect the oscillations of the apparent viscosity with pitch for pitches of the order of the sample thickness. The velocity and orientation profiles are also found to change drastically. These considerations may be important in flow experiments on long pitch cholesterics.

The effect of destabilizing fields on the roll instability (RI) threshold for shear flow and on the homogeneous instability (HI) threshold for plane Poiseuille flow of nematic HBAB (μ_s>0) is studied on the basis of the continuum theory of nematics for flow cells of infinite lateral width. It turns out that the critical shear rate and wave vector at RI threshold decrease with increasing destabilizing field but do not approach zero at the Freedericksz transition. However calculations show that beyond the Freedericksz threshold HI may be favourable over a range of destabilizing field with shear in the stabilizing role. For plane Poiseuille flow a similar analysis points to the existence of a HI threshold in the presence of destabilizing field beyond the Freedericksz threshold again with shear acting as a stabilizing field. These results are compared with theoretical results obtained previously for MBBA.