Validated predictive computational methods for surface charge in heterogeneous functional materials: HeteroFoaM™

Abstract: Prosperetti's seminal Physalis method for fluid flows with suspended particles is extended to electric fields to directly resolve finite‐sized particles and to investigate accurately the mutual fluid–particle, particle–particle, and particle–boundary interactions. The present paper shows the straightforward extension of the two dimensions [Liu, Q., 2011, J. Comput. Phys. 230:8256–8274] to three dimensions as one of the important advantages. The method can be used for uncharged/charged dielectrics, uncharged/charged conductors, conductors with specified voltage, and general weak and strong discontinuous interface conditions. These general interface conditions can be in terms of field variable, its gradients, and surface integration, which has not been addressed by other numerical methods. In addition, for the first time, we rigourously derive the force and torque on the finite‐sized particles resulting from the interactions between harmonics. The method, for the first time, directly resolves the particles with accurate local charge distribution, force, and torque on the particles, making many applications in engineering, mechanics, physics, chemistry, and biology possible, such as heterogeneous materials, microfluidics, electrophotography, electric double‐layer capacitors, and microstructures of nanodispersions. In the present paper, the accuracy of the coefficients in the general analytical solutions is extensively investigated. The method is numerically verified to be accurate even for very strong jump in the weak and strong discontinuous interface conditions, which have not yet been investigated in any other numerical methods. The efficiency of the method is demonstrated with up to 100,000 3D particles, which suggests that the method can be used for many important engineering applications of broad interest. Copyright © 2011 John Wiley & Sons, Ltd.

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