Effective viscosity of dense colloidal crystals
1Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
Summary
This study presents an exact method to calculate effective viscosity in hard sphere suspensions. The findings offer accurate predictions for various lattice structures and concentrations, improving upon previous models.
Area of Science:
- Fluid dynamics
- Materials science
- Computational physics
Background:
- Understanding the effective viscosity of particle suspensions is crucial for many industrial applications.
- Previous models for hard sphere suspensions often lack accuracy, especially at higher concentrations or for complex lattice structures.
Purpose of the Study:
- To develop an exact numerical scheme for determining the effective viscosity tensor of periodic hard sphere arrays.
- To validate the method against existing literature and investigate its accuracy across various lattice types and volume fractions.
- To analyze the behavior of effective viscosity in simple tetragonal lattices and compare it with experimental data.
Main Methods:
- Numerical calculation of the effective viscosity tensor for cubic and simple tetragonal lattices.
- Comparison with analytical and numerical results from existing literature.
- Analysis of sphere motion and angular velocity in response to shear flow.
- Determination of concentration-dependent shear viscosity for various microstructures.
Main Results:
- The proposed method accurately calculates the effective viscosity tensor for cubic lattices, outperforming previous theoretical results.
- New insights into sphere dynamics in simple tetragonal lattices reveal non-zero angular velocities and finite viscosities in contact scenarios.
- The viscosity diverges only in the case of close packing for any Bravais lattice.
Conclusions:
- The developed exact scheme provides a reliable tool for predicting effective viscosity in hard sphere suspensions.
- The findings offer a more accurate understanding of fluid behavior in ordered particle systems.
- The study highlights the importance of considering specific lattice structures and particle dynamics for accurate viscosity predictions.
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