Rigorous bounds on the asymptotic expansions of effective transport coefficients of two-phase media (Archives of Mechanics - Test, 1997)
The fundamental inequalities for two-point Padé approximants corresponding to two asymptotic expansions of the effective transport coefficients λe(x)/λ1 , x =λ2/λ1 - 1 have been derived, where λ1 and λ2 denote the transport moduli of the composite components. The inequalities achieved constitute the new bounds on the values of λe(x)/λ1 - the best with respect to the given number of coefficients of the asymptotic expansions of λe(x)/λ1 at x = 0 and x = ∞. For the particular cases, our two-point Padé bounds reduce to the classical estimations of λe(x)/λ1 available in literature [7, 9, 17, 24].