Viscoelastic properties of proteoglycan subunits and aggregates in varying solution concentrations

Using a cone-on-plate mechanical spectrometer, we have measured the linear and non-linear rheological properties of cartilage proteoglycan solutions at concentrations similar to those found in situ. Solutions of bovine nasal cartilage proteoglycan subunits (22S) and aggregates (79S) were studied at concentrations ranging from 10 to 50 mg ml-1. We determined: (1) the complex viscoelastic shear modulus G (omega) under small amplitude (0.02 radians) oscillatory excitation at frequencies (omega) ranging from 1.0 to 20.0 Hz, (2) the non-linear shear rate (gamma) dependent apparent viscosity napp (gamma) in continuous shear, and (3) the non-linear shear rate dependent primary normal stress difference sigma 1 (gamma) in continuous shear. Both the apparent viscosity and normal stress difference were measured over four decades of shear rates ranging from 0.25 to 250 s-1. Analysis of the experimental results were performed using a variety of materially objective non-linear viscoelastic constitutive laws. We found that the non-linear, four-coefficient Oldroyd rate-type model was most effective for describing the measured flow characteristics of proteoglycan subunit and aggregate solutions. Values of the relaxation time lambda 1, retardation time lambda 2, zero shear viscosity no, and nonlinear viscosity parameter muo were computed for the aggregate and subunit solutions at all of the solute concentrations used. The four independent material coefficients showed marked dependence on the two different molecular conformations, i.e. aggregate or subunit, of proteoglycans in solution.