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Investigating Stress-relaxation and Failure Responses in the Trachea
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Rounded stretched exponential for time relaxation functions.

J G Powles1, D M Heyes, G Rickayzen

  • 1School of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom. j.powles@swansea.ac.uk

The Journal of Chemical Physics
|December 9, 2009
PubMed
Summary
This summary is machine-generated.

A new rounded stretched exponential function accurately models various relaxation processes. It fits soft-sphere fluid shear stress relaxation and provides correct high-frequency limits for dielectric and mechanical relaxation spectra.

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Area of Science:

  • Soft Matter Physics
  • Rheology
  • Statistical Mechanics

Background:

  • Relaxation processes are fundamental in understanding material dynamics.
  • Existing models like the stretched exponential function have limitations in describing certain physical requirements.
  • Accurate modeling of relaxation functions is crucial for interpreting experimental data in soft matter systems.

Purpose of the Study:

  • Introduce and validate a novel rounded stretched exponential function for relaxation processes.
  • Demonstrate the function's applicability to shear stress relaxation in soft-sphere fluids.
  • Analyze the function's behavior in Cole-Cole plots for dielectric and mechanical relaxation.

Main Methods:

  • Derivation of the rounded stretched exponential function: C(t)=exp{(tau(0)/tau(E))(beta)[1-(1+(t/tau(0))(2))(beta/2)]}.
  • Fitting the function to shear stress relaxation data of model soft-sphere fluids.
  • Analysis of low and high-frequency limits in Cole-Cole plots for modulus and viscosity.

Main Results:

  • The proposed function converges to a stretched exponential at long times and exhibits an even time expansion, satisfying statistical mechanical requirements.
  • Excellent agreement was found between the function and shear stress relaxation data for soft-sphere fluids.
  • The function correctly predicts the high-frequency behavior of dielectric and shear stress relaxation spectra, distinguishing inertial effects in modulus versus viscosity.

Conclusions:

  • The rounded stretched exponential function offers a versatile and accurate description of relaxation dynamics in various systems.
  • The function's even time expansion provides insights into the physical underpinnings of relaxation phenomena.
  • High-frequency inertial effects are more clearly observed in the modulus Cole-Cole plot than in the viscosity plot.