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Sharp chemical discontinuities can occur in protoplanetary discs,particularly at `snow-lines' where a gas-phase species freezes out to form icegrains. Such sharp discontinuities will diffuse out due to the turbulencesuspected to drive angular momentum transport in accretion discs. Wedemonstrate that the concentration gradient - in the vicinity of the snow-line- of a species present outside a snow-line but destroyed inside is stronglysensitive to the level of turbulent diffusion (provided the chemical andtransport time-scales are decoupled) and provides a direct measurement of theradial `Schmidt number' (the ratio of the angular momentum transport to radialturbulent diffusion). Taking as an example the tracer species N$_2$H$^+$, whichis expected to be destroyed inside the CO snow-line (as recently observed in TWHya) we show that ALMA observations possess significant angular resolution toconstrain the Schmidt number. Since different turbulent driving mechanismspredict different Schmidt numbers, a direct measurement of the Schmidt numberin accretion discs would allow inferences about the nature of the turbulence tobe made.

Snow-lines as probes of turbulent diffusion in protoplanetary discs