Abstract
We study a single grafted or tethered polymer chain in the mushroom regime in a spatially varying flow. Unlike the case of constant flows discussed previously, a flow with a weakly spatially increasing velocity can cause a coil-stretch transition. In particular for velocity fields of the form vx = V(x/l)α, where V and l are constants, there is a critical value of the exponent α above which coil-stretch transitions take place. This is αc = (2ν - 1)/(1 - ν), where ν is the Flory exponent for the chain. We also study the case of shear flows, where a similar relation holds. We then study more general flows. In the particular case of a chain in a good solvent, αc = 1/2 and a flow in a covering cone causes a coil-stretch transition for cones above a critical angle and for fluid fluxes above a critical value.