The first relaxation is derived from the equivalent permittivity (21) which can be written also as Debye relaxation terms: The relaxation time T that is given by the poles of ˜ ϵ$_{k}$ in (21) is a quite good approximation of the first relaxation time T$_{k}$$_{1}$ The main reason is as follows. At frequencies close to 1 /T there is a huge change in ˜ ϵ$_{k}$ of order ε$_{S}$/ ( δ (1 / 2 − χ$_{k}$ )), and consequently a significant change in the total permittivity ϵ sus given by (23). Therefore T provides an approximate value for the relaxation time T$_{k}$$_{1}$ of the suspension effective permittivity ϵ sus . For a non-conductive shell σ$_{S}$ ≈ 0, or more precisely when σ$_{S}$ ≪ δ (1 / 2 − χ$_{k}$ ) σ$_{1}$ , the relaxation time (26) is: showing a strong dependence on the thickness of the shell and on the shape of the particle, through the eigenvalue χ$_{k}$ . Due to the small parameter δ in (27) the first relaxation (i. e., membrane relaxation) tends to have a lower frequency than the second relaxation, which is present even for particles with no shell (see the discussion below). In addition, cumbersome but straightforward calculations provide the dielectric decrement Δ ε$_{k}$$_{1}$ in (24) that is very large due to the same strong dependence on the thickness of the shell. The effect is even more dramatic when the second largest eigenvalue is very close to the largest eigenvalue, (1 / 2 − χ$_{2}$ ) → 0, like in the case of two cells connected by tight junctions. For a suspension of shelled spheres η = 1 + Δ R/R and δ = η 3 − 1 ≈ 3Δ R/R , where Δ R is the thickness of the membrane, R is inner radius, and R + Δ R is the total radius. Thus both T$_{k}$$_{1}$ and Δ ε$_{k}$$_{1}$ are proportional to R and ε$_{S}$ and inverse proportional to Δ R like in the Pauly-Schwan theory [1, 8]. Moreover, the dielectric decrement Δ ε$_{k}$$_{1}$ in (28) is a generalization of equation (54a) in Ref. [8]. In the same time, the relaxation time (27) differs with respect to equation (56a) in Ref. [8] only by the conductivity term. We will 10 Δ ε$_{k}$$_{1}$ ≈ 4 f p$_{k}$ε$_{S}$ ( δ (1 / 2 + χ$_{k}$ ) $^{2}$(1 / 2 − χ$_{k}$ )) − 1 (28) T$_{k}$$_{1}$ ≈ ε$_{vac}$ ε$_{S}$/ ( δ · σ$_{1}$ (1 / 2 − χ$_{k}$ )) (27) T = ε$_{vac}$ (1 + δ/ 2 + δχ$_{k}$ ) ε$_{S}$ + δ (1 / 2 − χ$_{k}$ ) ε$_{1}$ (1 + δ/ 2 + δχ$_{k}$ ) σ$_{S}$ + δ (1 / 2 χ$_{k}$ ) σ$_{1}$ ≈ T$_{k}$$_{1}$. (26) ˜ ϵ$_{k}$ = ε + Δ ε/ (1 + iωT ) . (25)