  A rigorous homogenization theory is derived to describe the effective
admittivity of cell suspensions. A new formula is reported for dilute cases
that gives the frequency-dependent effective admittivity with respect to the
membrane polarization. Different microstructures are shown to be
distinguishable via spectroscopic measurements of the overall admittivity using
the spectral properties of the membrane polarization. The Debye relaxation
times associated with the membrane polarization tensor are shown to be able to
give the microscopic structure of the medium. A natural measure of the
admittivity anisotropy is introduced and its dependence on the frequency of
applied current is derived. A Maxwell-Wagner-Fricke formula is given for
concentric circular cells, and the results can be extended to the random cases.
A randomly deformed periodic medium is also considered and a new formula is
derived for the overall admittivity of a dilute suspension of randomly deformed
cells.
