Processes implying the flow of rheologically complex fluids simultaneously with a gas phase
through packed beds are multitudinous in biochemical processing. Paradoxically, conceptual
models relating the packed-bed bioreactor hydrodynamics to the rheological characteristics of
the non-Newtonian fluids in play are virtually nonexistent in this particular area. An attempt
has, therefore, been made with this contribution to fill in this gap by providing a series of
hydrodynamic models for the prediction of pressure drop and liquid holdup in cocurrent and
countercurrent two-phase flow through packed beds in the so-called film-flow conditions, i.e.,
trickle-flow, preloading, and near-loading zones. The class of slit models has been generalized
by extending the modeling to yield-stress inelastic non-Newtonian fluids such as Herschel−Bulkley and Bingham plastic fluids and, as particular cases, to the Ostwald−De Waele and
Newtonian fluids. Model asymptotic formulations have also been derived for Herschel−Bulkley
fluids flowing downward with stagnant gas (pure trickle flow) to yield their liquid holdup under
gravity-driven flows, as well as in single-phase-flow conditions to yield the single-phase frictional
pressure drops. The response of these models to changes in yield stress, consistency and power-law index, and gas density, for both cocurrent downflow and countercurrent flow, reveals that
non-Newtonian fluids behave qualitatively as their Newtonian homologues in terms of fluid
throughputs, apparent viscosity, and gas density.