  We propose a mechanical-hydrodynamical experimental setup in which the
microfluidic motion manipulates the optical birefringence of levitated graphene
oxide liquid crystal. The birefringence of the sample is changed by flowing
graphene oxide liquid crystal in the micro-channel. By measuring the ordinary
and extraordinary refractive indices at five flow rates, one can determine the
value of the birefringence of the samples, precisely. Our results demonstrate
that, by adjusting the concentration and flow rate of dispersion of the
graphene oxide nano flakes, the induced birefringence can be controlled. It is
also shown that this approach can be used as an optical switch.
