Macroscopic properties of electrically interacting suspensions

• Main Author: Bonnecaze, Roger Temor
• Format: Others
• Language: en
• Published: 1991
• Online Access: https://thesis.library.caltech.edu/2843/1/Bonnecaze_rt_1991.pdf; Bonnecaze, Roger Temor (1991) Macroscopic properties of electrically interacting suspensions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/bshd-xb74. https://resolver.caltech.edu/CaltechETD:etd-07092007-143213 <https://resolver.caltech.edu/CaltechETD:etd-07092007-143213>

Several bulk or macroscopic properties of electrically interacting suspensions -or at least electrically interacting by mathematical analogy- are studied using simulation methods. These bulk properties include the effective conductivity, percolation transitions, effective reaction rates, and the effective viscosity of an electrorheological fluid. In order to compute these properties, the detailed potential field in the suspension is not required, but rather only the linear relationship between the charge and dipole moments of the particles to their potentials and the applied electric field is needed. A method is developed to compute this relationship accurately and efficiently for arbitrary particle configuration and shape. The method includes both the many-body far-field and near-field particle interactions and properly accounts for the long-ranged interactions common to electrostatic problems. The method is applied as part of a simulation to determine the effective conductivity of spherical particles. The simulation accurately reproduces the known values of the conductivity for cubic lattices of spheres for any volume fraction and particle-matrix conductivity ratio providing confidence in the method. It is then applied to determine the conductivity of mono-disperse, random hard-sphere suspensions for a variety of conductivity ratios of up to sixty volume percent particles. This is the first rigorous theoretical determination of the effective conductivity at such large volume fractions. The method is also used to study the percolation behavior of highly conducting spherical particles in close contact. It is found that such a system does exhibit a percolation transition, but only when the near-field effects are extremely large compared to the far-field interactions. This indicates that such a condition is a necessity for modeling a suspension as a percolating system. The diffusion-limited reaction rate of a highly mobile reactant with spherical traps is also computed using the simulation method. Here the average "charge" on the particle is the effective consumption of the reactant by the spherical particle. The results are quite good up to a volume fraction of 30%, but then unphysically deviate from the expected increasing reaction rate with volume fraction and show a maximum rate at forty volume percent. The deviation is explained and serves as an example of the limitations of the method developed earlier. Using the effective conductivity results, however, a self-consistent Brinkman medium-like theory is developed that predicts the effective reaction rate quite accurately. The method is finally applied to the dynamic simulation of electrorheological (ER) fluids -suspensions of dielectric particles with electric field tunable effective viscosities. Using the method developed in earlier chapters, the electrostatic interparticle forces in the ER suspension can be determined accurately and efficiently for arbitrary particle configurations, especially in capturing the strong near-field interactions. Coupled with Stokesian dynamics to account for the hydrodynamic interactions among the particles, the dynamics of the microstructure and its rheology can be determined. Dynamic simulations of an unbounded monolayer for a variety of electric field strengths and shear rates reproduce qualitatively and quantitatively experimental behavior. From the correlation of the dynamics and rheology, a theory for the dynamic yield stress observed in the suspensions is proposed and then successfully tested with the dynamic simulation. From the theory a simple model of the dynamic yield stress is created to predict its dependence on the volume fraction and the particle to fluid dielectric constant. The power of simulations to provide insight into the physics of multiphase materials and then to allow the testing of theories is particularly well illustrated with the study on ER fluids.