The configuration of a single polymer chain and polymer brush in equilibrium with a solvent that is subject to a shear flow is presented. When a force exerted at the end of a polymer chain

the chain deformation will be vary with the force

firstly has a trumpet regime

and then a stem flower regime occurs with the force increasing. In the monodisperse brushes

the monomer density has a parabolic distribution along the normal direction of the brush surface. During the oscillatory flow

extreme shear thickening occurs when the ratios of the Weissenberg number to the flow frequency

W i

/ω=3

shear-induced diffusion is shown to create this thickening. In the polydisperse brushes

there is a conformation transition

meanwhile

interaction between two particle brushes

neutral and charged polymer brushes are studied in details.