Higher order imperfect interface models of conductive spherical interphase

This paper presents a study of the Bövik-Benveniste methodology for high order imperfect interface modeling of steady-state conduction problems involving coated spherical particles. Two types of imperfect interface models, that reduce the original three-phase configuration problem to the two-phase configuration problem, are discussed. In one model, the effect of the layer is accounted for via jumps in the field variables across the traces of its boundaries, while in the other via corresponding jumps across the trace of its mid-surface. Explicit expressions for the jumps are provided for both models up to the third order. The obtained higher order jump conditions are incorporated into the unit cell model of spherical particle composite. The multipole expansion method is used to derive the convergent series solutions to the corresponding boundary value problems. Numerical examples are presented to demonstrate that the use of higher order imperfect interface models allows for accurate evaluation of the local fields and overall conductivity of composites reinforced with coated spherical particles.