Summary
A series of pathological synovial fluids are examined for viscoelastic properties in oscillatory shear flow at frequencies of physiological significance. When tested at varying amplitudes of shear at a frequency of 2 Hertz, the fluids show marked nonlinearity for shear rates above 10 sec−1, the elastic component of the shear stress truncating in the range from 1 to 10 dynes/cm2. At low shear rates, the fluids are linear and viscoelastic and have frequency dispersions matching the character of Gaussian chain theory for polymer solutions. Enzymatic degradation of the hyaluronate destroys the viscoelasticity, leaving a Newtonian fluid of relatively low viscosity. The concentration and molecular weight of the hyaluronate produce substantial intermolecular interaction. The relaxation times, viscosity, and elasticity of the synovial fluids are greatly increased over values expected for noninteracting molecules of hyaluronic acid in solution. While both the viscosity and elasticity vary greatly among the pathological fluids, the elasticity is the more sensitive indicator of viscoelastic properties.
Zusammenfassung
Es wird eine Serie pathologischer Synovialflüssigkeiten bezüglich ihrer viskoelastischen Eigenschaften in einer oszillatorischen Scherströmung mit physiologisch signifikanten Frequenzen untersucht. Bei einer Frequenz von 2 Hz zeigen die Flüssigkeiten eine ausgeprägte Nichtlinearität, wenn ein rms-Wert von 10 s−1 überschritten wird: Die elastische Komponente der Schubspannung flacht im Bereich von 1–10 dyn/cm2 ab. Bei niedrigen Schergeschwindigkeiten verhalten sich die Flüssigkeiten dagegen linear-viskoelastisch, und ihre Frequenzabhängigkeit läßt sich durch die Theorie der Gaußschen Netzwerk-Lösungen beschreiben. Enzymatischer Abbau des Hyaluronats zerstört die Viskoelastizität, so daß eine newtonsche Flüssigkeit mit relativ niedriger Viskosität übrig bleibt. Infolge seiner Konzentration und seines Molekulargewichts unterliegt das Hyaluronat einer erheblichen intermolekularen Wechselwirkung. Relaxationszeiten, Viskosität und Elastizität zeigen erheblich größere Werte, als sie für nicht in Wechselwirkung stehende Hyaluronsäure-Moleküle in Lösung zu erwarten wären. Obgleich bei den verschiedenen pathologischen Flüssigkeiten sowohl die Viskosität als auch die Elastizität stark schwanken, stellt sich doch die Elastizität als der von den viskoelastischen Eigenschaften empfindlichere Indikator heraus.
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Abbreviations
- a :
-
Tube radius (cm)
- b :
-
Gaussian chain segment length (cm)
- c m :
-
Mass concentration (g/cm3)
- f :
-
Frequency (Hz)
- G * :
-
Complex shear rigidity (dynes/cm2)
- h * :
-
Hydrodynamic interaction factor for the Gaussian chain theory
- k :
-
Boltzmann's constant (ergs/deg)
- M :
-
Molecular weight
- N :
-
Number of Gaussian subchain segments
- N a :
-
Avogadro's number
- P * :
-
Pressure gradient, complex form (dynes/cm3)
- P′, P″ :
-
Real and imaginary parts ofP * (dynes/cm3)
- t :
-
Time (sec)
- T :
-
Absolute temperature (K)
- u :
-
Volume rate of flow (cm3/sec)
- \(\tilde \dot \gamma \) :
-
Shear rate, instantaneous value (sec−1)
- \(\dot \gamma _M \) :
-
Shear rate, amplitude (sec−1)
- \(\dot \gamma _{NL} \) :
-
Critical shear rate for onset of nonlinearity (sec−1)
- λ p :
-
Eigenvalue,p-th value
- η * :
-
Complex coefficient of viscosity (P)
- η v :
-
Viscosity, real part ofη * (P)
- η E :
-
Elasticity, imaginary part ofη * (P)
- η 0 :
-
Limiting viscosity at zero frequency (P)
- η s :
-
Viscosity of solvent (P)
- η ∞ :
-
Limiting viscosity at infinite frequency (P)
- [η]0 :
-
Intrinsic viscosity at zero frequency (cm3/g)
- φ :
-
Phase angle between shear rate and shear stress (rad)
- (Φ/f′):
-
Gaussian chain theory parameter
- \(\tilde \tau \) :
-
Shear stress, instantaneous value (dynes/cm2)
- τ M :
-
Shear stress, amplitude (dynes/cm2)
- τ * :
-
Shear stress, complex form (dynes/cm2)
- τ v :
-
Viscous component of the shear stress (dynes/cm2)
- τ E :
-
Elastic component of the shear stress (dynes/cm2)
- τ p :
-
Relaxation time,p-th value (sec)
- τ 1 :
-
Terminal (longest) relaxation time (sec)
- ω :
-
Radian frequency (rad/sec)
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Thurston, G.B., Greiling, H. Viscoelastic properties of pathological synovial fluids for a wide range of oscillatory shear rates and frequencies. Rheol Acta 17, 433–445 (1978). https://doi.org/10.1007/BF01525959
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DOI: https://doi.org/10.1007/BF01525959