  Tap density of a granular powder is often linked to the flowability via Carr
Index that measures how tight a powder can be packed, under an assumption that
more easily packed powders usually flow poorly. Understanding how particles are
packed is important for revealing why a powder flows better than others. There
are two types of empirical equations that were proposed to fit the experimental
data of packing fractions vs. numbers of taps in literature: The inverse
logarithmic and the stretched exponential. Using the rate process theory and
the free volume concept, we obtain the tap density equations and they can be
reducible to the two empirical equations currently widely used in literature.
Our equations could potentially fit experimental data better with an additional
adjustable parameter. The tapping amplitude and frequency, the weight of the
granular materials, and the environment temperature are grouped into one
parameter that weighs the pace of packing process. The current results, in
conjunction with our previous findings, may imply that both dry(granular)and
wet(colloidal and polymeric) particle systems are governed by the same physical
mechanisms in term of the role of the free volume and how particles behave (a
rate controlled process).
