  Motivated by experiments on wormlike micelles, we study the early stages of
the shear banding instability using a two-fluid Johnson-Segalman model. We
perform a linear stability analysis for coupled fluctuations in shear rate,
micellar strain and concentration about an initially homogeneous state. First
we calculate the ``spinodal'' onset of instability in sweeps along the
intrinsic constitutive curve. For startup ``quenches'' into the unstable
region, the instability usually occurs before the intrinsic constitutive curve
can be attained so we analyse the fluctuations with respect to the homogeneous
startup flow to find the selected length and time scales at which inhomogeneity
first emerges. In the uncoupled limit, fluctuations in shear rate and micellar
strain are independent of those in concentration, and are unstable when the
intrinsic constitutive curve has negative slope; but no length scale is
selected. When coupled to concentration, this instability is enhanced at short
length scales; a length scale is selected, as seen experimentally. The unstable
region is then broadened. Far from an underlying (zero-shear) demixing
instability, the broadening is slight and the instability is still dominated by
shear rate and micellar strain. Close to demixing, instability sets in at very
low shear rate, where it is demixing triggered by flow.
