The effect depth-dependent viscosity has on convective mixing and sampling (or degassing) of primitive mantle beneath ridges is explored in two-dimensional models. Higher relative viscosities in the deep mantle decrease convection velocities and strain rates and prolong the residence time of material in the deep mantle. If the average viscosity of the lower mantle is at least 100 times the viscosity of the upper mantle, then some mantle material could have survived from very early in the earth's history. If, in addition, the depth of degassing under ridges has been less than 75 km, on average over earth history, then helium isotopic systematics are qualitatively consistent with whole mantle convection.