Template:Model theory (Text, Mill, Perfect Mixing, Dynamic, Discharge Rate)

The classical Leung definition of discharge rate of solids from a perfectly mixed mill is:

$p_{i}=D_{i}.s_{i}$

where:

$D_{i}=d_{\rm {max}}.C_{i}$

$C_{i}={\begin{cases}1&{\mbox{for }}d_{i}<x_{\rm {m}}\\{\dfrac {\ln {\bar {d}}_{i}-\ln x_{\rm {g}}}{\ln x_{\rm {m}}-\ln x_{\rm {g}}}}&{\mbox{for }}x_{\rm {m}}<{\bar {d}}_{i}<x_{\rm {g}}\\0&{\mbox{for }}d_{i}>x_{\rm {g}}\\\end{cases}}$

and:

• $d_{\rm {max}}$ is the fraction of load presented to the mill discharge
• $C_{i}$ is the classification function, the fraction of particles of size $i$ reporting to the mill product
• ${\bar {d}}_{i}$ is the geometric mean size of particles in size interval $i$ (mm)
• $x_{\rm {m}}$ is the particle size below which all mass in the size interval reports to mill product, i.e. like water
• $x_{\rm {g}}$ is the largest particle size which can report to mill product