The biochemical conversion of lignocellulosic biomass to liquid transportation fuels involves a multitude of physical and chemical transformations that occur in several distinct processing steps (e.g., pretreatment, enzymatic hydrolysis, and fermentation). In this work we focus on development of a computational fluid dynamics model of a dilute biomass slurry, which is a highly viscous particle-laden fluid that can exhibit yield-stress behavior. Here, we model the biomass slurry as a generalized Newtonian fluid that accommodates biomass transport due to settling and biomass-concentration-dependent viscosity. Within a typical mixing vessel, viscosity can vary over several orders of magnitude. We solve the model with the Nek5000 spectral-finite-element solver in a simple vane mixer, and validate against experimental results. This work is directed towards our goal of a fully coupled computational model of fluid dynamics and reaction kinetics for the enzymatic hydrolysis of lignocellulosic biomass.