Fig. 6: Results from the numerical model.

a Calculated (lines) and experimentally obtained (symbols) relative changes in the v-SFG intensity along the mineral surface for different flow rates. We show only the averaged values from Fig. 3 without the spread of the individual data points for clarity. b Calculated surface charge along the mineral surface for different flow rates, showing enhancements under flow-on conditions by ~50% compared to flow-off conditions. c Calculated fluoride concentration at the surface \({\rho }_{{{{\rm{F}}}}}(x,R)\) relative to the bulk along the mineral surface for several flow rates. d The calculated net dissolution rate \({{{\bf{J}}}}(x)\) along the mineral surface for different flow rates. Note the orders of magnitude increase upon turning on the flow. Under flow-off conditions, the dissolution rate is a small fraction of the maximum dissolution rate \(|{{{\bf{J}}}}|\approx {10}^{-5}{k}_{{{{\rm{dis}}}}}\) while during flow the net dissolution increases by several orders of magnitude, to approximately half the maximal dissolution rate \(|{{{\bf{J}}}}|\approx {k}_{{{{\rm{dis}}}}}\). The position is given as displacement from the center with values increasing in the direction of flow, indicated by the arrow in panel (c).