  During accretion, a neutron star (NS) is spun up as angular momentum is
transported through its liquid surface layers. We study the resulting
differentially rotating profile, focusing on the impact this has for type I
X-ray bursts. The viscous heating is found to be negligible, but turbulent
mixing can be activated. Mixing has the greatest impact when the buoyancy at
the compositional discontinuity between accreted matter and ashes is overcome.
This occurs preferentially at high accretion rates or low spin frequencies and
may depend on the ash composition from the previous burst. We then find two new
regimes of burning. The first is ignition in a layer containing a mixture of
heavier elements with recurrence times as short as ~5-30 minutes, similar to
short recurrence time bursts. When mixing is sufficiently strong, a second
regime is found where accreted helium mixes deep enough to burn stably,
quenching X-ray bursts altogether. The carbon-rich material produced by stable
helium burning would be important for triggering and fueling superbursts.
