Related Experiment Video
Updated: Jun 29, 2026
08:42
Challenges in Rheological Characterization of Highly Concentrated Suspensions — A Case Study for Screen-printing Silver Pastes
Published on: April 10, 2017
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
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.
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.
Related Concept Videos
01:18Newtonian Fluid: Problem Solving
Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
01:17Colloids and Suspensions
Children at play often make suspensions such as mixtures of mud and water, flour and water, or a suspension of solid pigments in water known as tempera paint. These suspensions are heterogeneous mixtures composed of relatively large particles visible to the naked eye or seen with a magnifying glass. They are cloudy, and the suspended particles settle out after mixing. The suspended particles in a suspension settle out after some time of mixing. The separation of particles from a suspension is...
01:22Generalized Hooke's Law
The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
01:15Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
01:28Euler's Equations of Motion
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
01:26Hooke's Law
Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.