  The drift velocity has been proven to have significant relevance to the
filtered Eulerian drag force by numerous correlative analyses of fully resolved
simulations. It is a sub-grid quantity defined as the difference between the
filtered gas velocity seen by the particle phase and the resolved filtered gas
velocity. In literature, it is shown that various algebraic models for the
drift velocity fail to give entirely satisfactory prediction of the filtered
drag force. Unlike previous works, we theoretically derived the transport
equation for the drift velocity from the standard two-fluid model (TFM)
equations without any additional assumptions. The new approach, though requires
additional closures for the new unresolved terms, is believed to have the
potential to improve the precision of the estimation of this sub-grid quantity
and hence give better prediction of the filtered drag force for gas-solid
fluidization problems.
