  We study the mechanism of nuclear spin relaxation in quantum dots due to the
electron exchange with 2D gas. We show that the nuclear spin relaxation rate is
dramatically affected by the Coulomb blockade and can be controlled by gate
voltage. In the case of strong spin-orbit coupling the relaxation rate is
maximal in the Coulomb blockade valleys whereas for the weak spin-orbit
coupling the maximum of the nuclear spin relaxation rate is near the Coulomb
blockade peaks.
