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‘Duration of time’ (understood as residence time) is assumed as Tres = k*L/(N*D*S) (L=length, D=internal diameter, S=slope, N=RPM of the mill, k=constant), even though this may be a simplified rough approximation. The formula with k=0.19 is reported in Perry for Rotary Driers (5th ed, p 20-40, Solids-Drying Equipment), and I verified it for a pilot Rotary Kiln too (more complex formulae consider additional factors and material properties). A mill is also a rotating cylinder, but with balls in it, so k is expected to be different. At any case Tres can be assumed more or less independent of feed rate.
Hold up (understood as held mass fraction) in steady state is feed rate * residence time; thus hold up can be assumed proportional to residence time. Apparently longer residence time will result in thinner granulometry at the exit (all other parameters remaining same), but Tres is assumed to remain constant under supposed conditions as said (constant L, N, D, S). Get ball mill,ball mill,beneficiation From http://www.ballmill8.com