  We theoretically study transient electroosmotic flow of general Maxwell
fluids through polyelectrolyte grafted nanochannel with a layered distribution
of charges.
  By applying the method of Laplace transform, we semi-analytically obtain
transient electroosmotic flow from Cauchy momentum equation and Maxwell
constitutive equation.
  For nanochannels grafted with polyelectrolyte layers having different layered
distribution of charges, we study the influence of dimensionless relaxation
time, dimensionless polyelectrolyte layer thickness and dimensionless drag
coefficient on transient electroosmotic flow.
  We present the results for some particular cases. Firstly, we unravel that
for the case of polyzwitterionic brush that the sum of positive and negative
structural charges is zero, total electroosmotic flow is non-zero. In
particular, depending on charge distribution within end part of polyelectrolyte
layers, the direction of electroosmotic flow can be reversed critically.
Secondly, in order to quantitatively evaluate a reversal of electroosmotic flow
for two polyelectrolyte layers of opposite signs, we introduce a critical
number ks as the ratio between layered charge densities of two polyelectrolyte
layers. Increasing ks allows electroosmotic flow to be reversed easily.
  We verify that adjusting charge distributions of the layer can control
intentionally the direction of the flows as well as strength of electroosmotic
flow.
