Chemical structure of the hyaluronic acid (HA) molecule.
(a) Schematic drawing of a synovial joint highlighting the important anatomic features. (b) Simplified picture of the squeeze flow in a synovial joint undergoing a compressive deformation (such as occurs in the knees during locomotion). The black arrows indicate the flow of the synovial fluid being squeezed outwards orthogonal to the compression axis, resulting in a biaxial extensional flow at the mid-plane between joint surfaces and a stagnation point at the center of symmetry (marked by the red “x”).
Steady shear viscosity of HA/PBS solutions measured using an AR-G2 stress-controlled cone-and-plate rheometer (closed symbols) and an m-VROC microfluidic rheometer (open symbols). The viscosity is well-described by a Carreau-Yasuda model (solid lines), except for the fluid containing BSA and γ-globulin at low shear rates.
(a) 3D view of the OSCER geometry showing the upstream and downstream characteristic channel dimension H and the uniform depth d. (b) Light micrograph of the actual OSCER geometry. The inflow is along the y- and the outflow along the x-direction. At the center of the geometry there is a stagnation point, here marked as the origin of coordinates. The superimposed green line represents the prescribed profile determined from numerical optimization.
(a) Streak imaging showing the nature of the flow field in the OSCER with a Newtonian fluid at U = 0.01 , with superimposed colored hyperbolae for comparison. The superimposed white lines indicate the symmetry axes of the geometry, which coincide at the stagnation point. Flow enters through the top and bottom channels and exits through the left- and right-hand channels. (b) Experimental flow velocity vector field, measured using μ-PIV, for an analogue synovial fluid at U = 0.2 (Re = 2.8, Wi = 3.1). (c) Outflow velocity vx (x) measured along y = 0 for the analogue synovial fluid. At any given flow rate vx varies linearly with x and the slope of the straight line provides the elongation rate along the exit channel centerline. (d) Elongation rate as a function of superficial flow velocity for HA1.6 solutions in the OSCER, compared with the result for a Newtonian fluid.
Flow induced birefringence measured over a range of extension rates in solutions of HA1.6: (a) 0.1 wt. %, (b) 0.3 wt. %, (c) 0.3 wt. % + BSA + γ-globulin. The color scale bar represents retardation in the range R = 0–10 nm.
(a) Measured birefringence ( ) as a function of the strain rate ( ) for HA1.6 solutions in the OSCER. In the 0.1 wt. % solution the experiment is curtailed at lower due to the onset of an inertio-elastic instability that distorts the birefringent strand (as illustrated by the inserted image for U = 0.36 m , Re = 29, Wi = 2.4). (b) Derivatives of the curves shown in part (a) (i.e., , normalized by their maximum values) plotted against . The data are fitted with log-normal distributions, the peak of which can be used as a measure of the fluid relaxation time ( ). (c) Extensional viscosity ( ) as a function of , determined from birefringence measurements using the stress-optical rule. (d) Trouton ratio ( ) as a function of the Weissenberg number ( ).
Parameters used to fit the Carreau-Yasuda model to the steady shear rheology data.
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