Universal Dielectric Enhancement from Externally Induced Double Layer Without $\zeta$-Potential

Motivated by recent experiments showing over $10^4$-fold increase in induced polarization from electrochemically inert, conducting materials in dilute saline solutions, we theoretically demonstrate a new mechanism for dielectric enhancement, in the absence of $\zeta-$potentials at interfaces between non-insulating particles and an electrolyte solution. We further show that the magnitude of such enhancement obeys universal scaling laws, independent of the particle's electrical properties and valid across particle shapes: for a dilute suspension of identical, but arbitrarily shaped particles of a linear dimension $a$ and volume fraction $f$, as $\omega\to0$ the effective real dielectric constant of the mixture is enhanced from that of water by a factor $1+f~(P_r+(a/\lambda)P_i)$, and the frequency-dependent phase shift of its impedance has a scale-invariant maximum $f\,\mathsf{\Theta}$ if particles are much more conductive than the solution. Here $\lambda$ is the solution's Debye length and $P_r$, $P_i$, $\mathsf{\Theta}$ are dimensionless numbers determined solely by the particles' shape. Even for a very dilute electrolyte solution (e.g. $10^{-3}$ molar), sub-mm sized particles, at volume fraction $f=0.1$, can give a $10^4$-fold dielectric enhancement, producing an easily observable phase shift maximum in a simple impedance measurement.We also derive frequency cutoffs as conditions for observing these enhancements, showing that insulating particles produce no enhancement without $\zeta$-potential.To prove these results for particles of arbitrary shapes, we develop a physical picture where an externally induced double layer (EIDL), in contrast to the Guoy-Chapman double layer on interfaces with significant $\zeta$-potentials, dominates the low-frequency dynamics and produces dielectric enhancement.
Comment: 32 pages, no figures, added correction of a typo in the second half of Eq. 10