We study theoretically the deformation of polyelectrolyte brushes in s
trong flows of good solvent using a scaling theory which calculates th
e deformation of grafted chains and the solvent flow profile within th
e brush in a mutually consistent fashion. We consider the cases of per
meation flows normal to the grafting surface and shear flows parallel
to the grafting surface. For the case of permeation flows, we find tha
t strongly charged brushes are more uniformly extended than weakly cha
rged ones and that the crossover region separating the weak deformatio
n and strong deformation regimes shifts to higher solvent flow rates a
nd becomes somewhat broader with increasing charge fraction. For the c
ase of shear flows, we find that chains are more uniformly stretched a
nd less strongly tilted with increasing charge fraction. Furthermore,
we demonstrate that with increasing charge fraction, there is a revers
al of the dependence of brush thickness on shear rate: weakly charged
brushes expand in strong shear flows, while strongly charged brushes c
ollapse somewhat in the same flows, in qualitative agreement with prev
ious theoretical predictions.