  Self-consistent field approach is used to model a single end-tethered polymer
chain on a substrate subject to various forces in three dimensions. Starting
from a continuous Gaussian chain model, the following perturbations are
considered: (i) hydrodynamic interaction with an externally imposed shear flow
for which a new theoretical framework is formulated; (ii) excluded volume
effect in a good solvent, treated in a mean field approximation; (iii)
monomer-substrate repulsion. While the chain stretches along the flow, the
change of the density profile perpendicular to the substrate is negligible for
any reasonable simulation parameters. This null effect is in agreement with
multiple neutron scattering studies.
