Dynamic shear-stress-enhanced rates of nutrient consumption in gasliquid semi-continuous-flow suspensions

Abstract

The primary objective of this investigation is to establish guidelines for generating significant mammalian cell density in suspension bioreactors when stress-sensitive kinetics enhance the rate of nutrient consumption. Ultra-low-frequency dynamic modulations of the impeller (i.e., 35104 Hz) introduce time-dependent oscillatory shear into this transient analysis of cell proliferation under semi-continuous creeping flow conditions. Greater nutrient consumption is predicted when the amplitude A of modulated impeller rotation increases, and stress-kinetic contributions to nutrient consumption rates increase linearly at higher modulation frequency via an application of fluctuation-dissipation response. Interphase mass transfer is required to replace dissolved oxygen as it is consumed by aerobic nutrient consumption in the liquid phase. The theory and predictions described herein could be important at small length scales in the creeping flow regime where viscous shear is significant at the interface between the nutrient medium and isolated cells in suspension. Two-dimensional flow around spherically shaped mammalian cells, suspended in a Newtonian culture medium, is analyzed to calculate the surface-averaged magnitude of the velocity gradient tensor and modify homogeneous rates of nutrient consumption that are stimulated by viscous shear, via the formalism of stress-kinetic reciprocal relations that obey Curie's theorem in non-equilibrium thermodynamics. Time constants for stress-free free and stress-sensitive stress nutrient consumption are defined and quantified to identify the threshold (i.e., stress,threshold) below which the effect of stress cannot be neglected in accurate predictions of bioreactor performance. Parametric studies reveal that the threshold time constant for stress-sensitive nutrient consumption stress,threshold decreases when the time constant for stress-free nutrient consumption free is shorter. Hence, stress,threshold depends directly on free. In other words, the threshold rate of stress-sensitive nutrient consumption is higher when the stress-free rate of nutrient consumption increases. Modulated rotation of the impeller, superimposed on steady shear, increases stress,threshold when free is constant, and stress,threshold depends directly on the amplitude A of these angular velocity modulations.