Field-Property Bounds for Porous Sintered Ceramics

Three sets of equations provide upper and lower values bound ing the experimentally obtained electrical and thermal conduc tivities as well as the magnetic permeabilities (="field properties") of porous ceramics. These equations are as I-order upper bound: φ _p=φ_M (1 -P ) (φ=effective field property of the porous material, φ_M=field property of the nonporous material, P =porosity), and as I-order lower bound: φ_r=φ_M (1- P )⁷. Closer bounds corresponding to isotropic porous materials are the II-order upper bound: φ_P^II ,= φ _M ,2(1- P)/ (2+P)], and the II-order lower bound: φ_PIII=φ_M(1- P)³ . Even closer bounds, referring to isotropic porous materials containing closed, unconnected pores are the III-order upper bound: φ_P^III = φ _M (1- P)^3/2 , and the III-order lower bound: φ_PIII = φ_M(1- p)3 .