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We offer here an extension of our previous work [Apostolidis and Beris, J. Rheol. 58, 607–633 (2014)] of modeling blood flow rheology in simple shear steady state flows to time-dependent conditions. The basis of our model is a scalar, structural, parameter thixotropic model. More specifically, we show that a modified version of the “Delaware model” [A. Mujumdar et al., J. Non-Newtonian Fluid Mech. 102, 157–178 (2002)] is capable of predicting the time-dependent shear flow rheology of blood at low and moderate values of shear rate. At steady state, the model reduces to the Casson constitutive model for low and moderate shear rate values consistent to the findings of our previously mentioned work. At high shear rates it reduces to a Newtonian model, correcting our previous model and consistent to data from the literature [Merrill and Pelletier, J. Appl. Physiol. 23, 178–182 (1967)]. Exploiting the existing parameterization developed before for the steady state Casson model and the Merrill and Pelletier steady state data, the transient thixotropic model introduces only three additional parameters. Each one of these parameters has a specific physical meaning: A zero-shear rate maximum strain, and two kinematic parameters governing the relaxation of the structural parameter and the elastic modulus, respectively. The model is able to naturally account for the additional yield strengthening effect attributable to the red blood cell rouleaux structures developed within blood. The proposed model can fit excellently the experimental data of Bureau et al. [Biorheology 17, 191–203 (1980)], on simple triangular steps in shear flow at low shear rates. The predictions of the present model are then validated comparing them against additional experimental data, collected on the same samples, either on triangular steps in shear flow but at higher shear rates or on rectangular step-up and step-down experiments. The model is further validated by comparing its predictions against recent large amplitude oscillatory shear data [P. C. Sousa et al., Biorheology 50, 269–282 (2013)]. In all these comparisons there is good, at least semiquantitative, agreement, with the observed discrepancies only appearing at the higher shear rates, where the isotropic description resulting from the use of a single scalar internal parameter to describe the blood microstructure naturally breaks down.

Fed-batch and perfusion cell culture processes used to produce therapeutic proteins can use microfilters for product harvest. In this study, new explicit mathematical models of sieving loss due to internal membrane fouling, external membrane fouling, or a combination of the two were generated. The models accounted for membrane and cake structures and hindered solute transport. Internal membrane fouling was assumed to occur due to the accumulation of foulant on either membrane pore walls (pore-retention model) or membrane fibers (fiber-retention model). External cake fouling was assumed to occur either by the growth of a single incompressible cake layer (cake-growth) or by the accumulation of a number of independent cake layers (cake-series). The pore-retention model was combined with either the cake-series or cake-growth models to obtain models that describe internal and external fouling occurring either simultaneously or sequentially. The models were tested using well-documented sieving decline data available in the literature. The sequential pore-retention followed by cake-growth model provided a good fit of sieving decline data during beer microfiltration. The cake-series and cake-growth models provided good fits of sieving decline data during the microfiltration of a perfusion cell culture. The new models provide insights into the mechanisms of fouling that result in the loss of product sieving. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:1323-1333, 2017.

We present a careful evaluation of non-Newtonian blood rheology effects in arterial flow simulations. We achieve that by comparing the converged solutions obtained a) from a Casson viscoplastic modeling of blood rheology using a recently developed parametrization [Apostolidis and Beris, J. Rheol., 58: 607-633 (2014)], and b) from a Newtonian model. We emphasize on the proper implementation of outlet boundary conditions (OBCs) in a way that ensures consistency with the pressure/flow predictions of the downstream network, which is modeled approximately using a 1D model [Johnson et al., Comp. Chem. Eng., 35: 1304-1316 (2011)]. We further improve and validate the iterative scheme proposed by [Johnson et al., Int. J. Num. Meth. Fluids, 66: 1383-1408 (2011)] for the implementation of the OBCs, by employing it in conjunction with a) Casson-derived simulation data, b) a more accurate geometrical model and c) an accelerated convergence iterative scheme through application of Shanks transformation. Finally, we performed a rigorous analysis to ensure appropriately converged solutions. Our investigation shows significant differences (up to 50%) between the simulation output of Newtonian and non-Newtonian models. The differences are attributed to the coupling that exists between low and high shear rate areas in the flow. They show the significance of non-Newtonian blood rheology and motivate further work towards an even more accurate modeling of the thixoropic and three-dimensional characteristics of the blood flow rheology that go beyond the Casson model utilized in the present work.

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