Related Experiment Video
Updated: May 18, 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. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study details a new method for analyzing interacting Brownian particles in time-dependent flow, crucial for understanding colloidal suspensions and their glass transitions.
Area of Science:
- Physics
- Physical Chemistry
- Materials Science
Background:
- Dense colloidal suspensions exhibit slow structural relaxation and can undergo a glass transition.
- Understanding particle dynamics under external flow is essential for characterizing these systems.
- Existing theories may not fully capture the interplay between interactions, relaxation, and time-dependent flow.
Purpose of the Study:
- To derive a first-principles approach for calculating averages in systems of interacting, spherical Brownian particles.
- To apply this method to systems under homogeneous, incompressible, time-dependent flow (shear and extension).
- To provide a theoretical framework for studying colloidal suspensions near the glass transition.
Main Methods:
- Detailed derivation of a first-principles calculation method.
- Utilizing approximations from mode-coupling theory.
- Developing a fully tensorial theoretical framework.
Main Results:
- The derived approach accurately calculates averages for Brownian particles in time-dependent flow.
- Mode-coupling theory approximations are suitable for dense colloidal suspensions.
- The theory captures slow relaxation and the glass transition phenomenon.
Conclusions:
- The developed theory enables the study of colloidal suspensions under arbitrary homogeneous, incompressible, time-dependent flows.
- This framework is particularly suited for dense systems exhibiting slow dynamics and glass transitions.
- It offers a new tool for investigating the complex behavior of colloidal matter.
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.