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First-principles constitutive equation for suspension rheology.

J M Brader1, M E Cates, M Fuchs

  • 1Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany.

Physical Review Letters
|October 15, 2008
PubMed
Summary

We developed a new constitutive equation for dense colloidal suspensions, revealing how microstructure and flow interact. This advances understanding of colloidal glasses and their dynamic yield behavior.

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Area of Science:

  • * Soft Matter Physics
  • * Rheology
  • * Colloidal Science

Background:

  • * Understanding the nonlinear rheology of dense colloidal suspensions is crucial for predicting material behavior under flow.
  • * Previous models often simplified flow conditions, limiting their applicability to complex scenarios.

Purpose of the Study:

  • * To derive a comprehensive constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow.
  • * To elucidate the relationship between macroscopic stress and the distorted microstructure.
  • * To identify the full tensorial structure of mode-coupling theory for rheological applications.

Main Methods:

  • * Utilizing mode-coupling theory to formulate the constitutive equation.
  • * Generalizing existing theories for simple shear flow to arbitrary homogeneous flows.
  • * Analyzing the emergence of macroscopic deformation measures like Cauchy-Green tensors.

Main Results:

  • * A constitutive equation was derived, capturing the nonlinear rheology of dense colloidal suspensions.
  • * The interplay between slow structural relaxation and imposed flow was illuminated.
  • * Flow curves for steady planar and uniaxial elongation were presented and compared to simple shear.

Conclusions:

  • * The derived equation provides a tensorially complete description of colloidal suspension rheology.
  • * Nonlinear Trouton ratios suggest a nontrivial dynamic yield condition for colloidal glasses.
  • * The findings offer new insights into the fundamental mechanics of soft glassy materials.