Hmmm - I wish I'd never mentioned centripetal forces acting on ash particles in the first place!
Suffice it that an ash particle entering a high-bypass engine near the cicumference of the fan will DEFINITELY go down the bypass duct and cause no problem, a particle near the hub will DEFINITELY go into the core and might not emerge at the other end! Other particles at other points between hub and circumference will have varying chances of going 'through' or 'round' the hot section.
The point that even with a high bypass ratio, the core must still eat tons of air to get enough power to turn the fan is well taken.
Bottom line: only engine manufacturers can offer definitive numbers for the max ash particle density per cubic metre of intake air, taking account of everything that might happen to the air and the particles going through their turbine.