  A theory of nonlinear convective depletion is set up as a nanosphere
translates fast through a semidilute polymer solution. For nanospheres a
self-consistent field theory in the Rouse approximation is often legitimate. A
self-similar solution of the convective depletion equation is argued to be
feasible at high velocities. The nature of the thin boundary layer in front of
the propagating particle is analyzed. One example of convective depletion is
when a charged protein moves through a semidilute polymer under the influence
of a high electric field. The protein velocity is then proportional to the
fifth power of the field. The theory could be useful in interpreting the
separation of protein mixtures by microchip electrophoresis.
